Semantic algebra

V. E. Lipatov
SEMANTIC ALGEBRA
Moscow
2026

ANNOTATION
Semantic algebra is a fundamental analytical discipline for studying order in reality, understanding the meanings of words, concepts, and relations between them. Semantic algebra provides a methodology to identify the main things from any subject areas and perform operations with them according to the rules of semantic linear algebra to build your own picture of the world.
The monograph is recommended mainly for system analysts, designers and architects of applications, software and hardware complexes – robots and AI systems. The tensor structure of semantics suggests a way to build neuroprocessors and a perspective for programming quantum computers.
However, the book will be useful for a wide range of readers, starting from school age, because semantic algebra is an analytical discipline that forms a culture of thinking, communication and creativity.


KEYWORDS
Semantics, semantic algebra, concepts, semantic unit, semantic object, semantic relations, types of semantic relations, semantic features, intensional, extensional, combinations of semantic features, hyponym, hyperonym, meronym and holonym, semantic multiplication, semantic addition, semantic vector, semantic matrix, semantic tensor, semantic series, semantic axis, keywords: semantic plane, semantic space, semantic gradient, semantic model, unified philosophical table of concepts, static and dynamic semantics, transgression, semantic physics.


PERSONALITIES
Vladimir Ivanovich Dahl; Sergey Ivanovich Ozhegov; Natalia Yulyevna Shvedova; Raimund Lully; Hegel, Georg Wilhelm Friedrich; George Ivanovich Chelpanov; Charles Edgerton Osgood; Stanislav Taktaev; Dmitry Anisimov; Igor Nikolaevich Ostretsov; Dmitry Alexandrovich Bryanchaninov; Archimandrite Platon (Igumnov); St. Luke Voino-Yasenetsky; Ivan Alexandrovich Ilyin; Ausra Augustinaviciute; Grigory Romanovich Reinin; Gradi Butch.

Introduction
A number of mathematical regularities are found in the semantics of the Russian language. The scientific direction is proposed: Semantic algebra is a fundamental analytical discipline for studying the semantic laws of language, the meanings of words, concepts and relations between them. Semantic algebra allows you to identify semantic tensors from a certain domain and perform operations with them according to the rules of linear algebra to build semantic models. Semantic models are needed for object-oriented software design, system design, artificial intelligence systems, building knowledge bases or expert systems, generating game scenarios, and many other purposes.
The monograph contains the following concepts: semantic unit, object, features, axes, planes, space, static and dynamic semantics, semantic tensor. Semantic multiplication and addition operations for concepts and semantic tensors are introduced. A method for constructing semantic models based on object models and binary search of feature combinations is shown. A system of 12 semantic relations is given. 64 global semantic groups are derived.
Semantic algebra is an axiomatic science with a number of axioms, theorems, laws, and hypotheses. Terminology for semantic tensors and semantic relations is proposed. A number of examples of semantic tensors and models for mathematics and geometry, physics and engineering, psychology and theology, linguistics and literature, organization and management, as well as a number of other scientific areas are given. A short training course has been developed.
The monograph is recommended mainly for system analysts, designers and architects of applications, software and hardware complexes – robots and AI systems. The tensor structure of semantics suggests a way to build neuro-processors and a perspective for programming quantum computers. However, the book will be useful for a wide range of readers, starting from school age. Semantic algebra is an analytical discipline that forms a culture of thinking, communication, and creativity.


Remarks
THIS IS HOW KEY CONCEPTS ARE WRITTEN.
This Is How Semantic Units Are Written.
Rule for numbering semantic tensors of rank 3 (cubology):
In the initial sections - (0. XX), where XX is the tensor number,
In the APPLICATION PART section (NN.XX), where NN is the chapter number.

First introduction
Those who don't have much time, but want to try something practical to get an impression of semantic algebra, can consider the following examples.
Antonyms can be antisymmetric, consisting of opposites: "Top - Bottom", "Hot-Cold".
Antonyms can be directed, consisting of the absence and presence of something: "Peace - Movement", "Darkness - Light".
A total of 12 types of such relationships were identified: quality, variation, contrast, comparison, arrangement, complement, transgression, inheritance, multiplicity, neighborhood, belonging, and purpose. 12 corresponds to the edges of the cube, but more on that later.
Words act as signs when forming other words. It is better to indicate this with the multiplication icon:
Woman * Home = Mistress.
Male * Job = Worker.
Worker * Experience = Master.
Inventory * Building = Warehouse.
Shelf * Shelf = Shelf.

Such signs are paired phenomena, and derived words form groups. Several multiplied features form groups of 2, 4, 8, etc. words (in progression), depending on the number of features. Thus, words, in their meaning, form strict structures similar to an architectural ensemble.
Here's a simple example:
girl, girl, woman, old woman,
boy, boy, man, old man,
granddaughter, daughter, mother, grandmother,
grandson, son, father, grandfather.
Here I multiplied the age vector by the gender vector and the kinship vector.
 


1. Part One, Introductory
THE LANGUAGE IS CREATED TO RESOLVE CONFLICTS AND CONTRADICTIONS BETWEEN:
0. The Individual and Society,
1. Male and Female,
2. Fathers and Children,
3. Rich and Poor,
4. Healthy and Sick,
5. Strong and Weak,
6. Smart and Stupid,
7. Bold and Cowardly,
8. Happy and Sad,
9. Friends and Strangers (Foreigners), ...............................

With the development of civilization - there are axes of confrontation-misunderstanding. This is what drives the development of languages and thinking.

1.1. What is semantic algebra and why is it called so?
Semantics is the science of the meaning of words.
Today it is divided into:
1. Linguistic semantics, which studies the influence of parts of a word on meaning.
2. Computer semantics that allows you to interpret and translate expressions, as well as respond to queries in expert systems and machine translation systems.
3. Neural network semantics - for solving routine non-trivial tasks.
4. Analytical semantics-which studies the relations between concepts, provides methods for constructing semantic tensors and semantic models. This is Semantic Algebra.

Explanatory dictionary of V. I. Dahl:
"ALGEBRA g. the science of counting letters and other conventional signs, instead of numbers that are inserted only in the final output; letter counting, general arithmetic. Algebraic, algebraic, related to this method. Algebraist, algebraist M. versed in the science of this"

Semantic algebra has several similarities with mathematical algebra. The fact is that words store several simple concepts at once, just as numbers store their prime factors. For example: The word "girl" stores the signs (intensional) of a person, female gender, and youth. Similarly, the number 6 stores the multipliers 2 and 3 as prime numbers.

Based on features, you can combine words into semantic vectors and matrices, similar to how it is done in linear algebra. In addition, there are semantic scalars, vectors, matrices, and tensors. Semantic tensor is the most general concept. You can also perform semantic operations on all sorts of semantic objects - tensors, matrices, and vectors-similar to linear algebra.
1.2. About the complexity of the material and a number of riddles
The topic is complex. Therefore, I will try to present it simply and concisely, without misuse of terms. However, the complexity of the material has four reasons. This is an independent study, not a compilation of someone else's well-honed quotes.
This study makes extensive use of mathematics in the field of linguistics. Here you can find more than a hundred examples of systematization of terms from different fields of knowledge. Such as: literature, psychology, management, etc. Therefore, you need to have an explanatory dictionary, relevant experience and knowledge at hand.
The language evolves towards the cultivation of its semantic properties. However, in many areas of knowledge, he did not achieve perfection. Therefore, there may be an impression of substitution of concepts. Logic plays an important role in understanding semantics, thanks to dialectical principles and mathematical binary combinatorics. However, associative understanding plays an equally important role. There is often a phenomenon when we feel the connection of concepts, but we can not designate it, because there are simply no words for this yet.
Finally, you need to have the skill to identify and understand the semantic structures that are presented here. The difficulty is that such structures do not create the usual artistic image. To understand this, try to solve a number of riddles.

Insert the missing word in a row:
Flame,..., Solid, Liquid.
Home, Work,..., Organization.
Love, Addiction,..., Craving.
Necessary, Sufficient, Need,....
Usually, Often,..., Rarely.
Street, Road,..., Corridor.
Street, House, Apartment, ....
Law, Conscience, Responsibility, ....
Chief, Beginning, Director, ....
Private, General,..., Basic.

See the final part of the book for answers.

1.3. Background of the issue
Since ancient times, people have tried to understand the structure of the universe. There have been attempts to explain this through mythical creatures, through the elements. However, the most interesting thesis was about the Logos. About the fact that the universe is arranged by means of the WORD. This thesis gave rise to the theological direction (theology) and philosophy.
Then Aristotle made a great contribution, as the founder of formal logic. A significant contribution was made by the 13th-century theologian Raymond Lully with his combinatorial machine, which he manufactured to generate new semantic concepts. The construction of this concept of the art of combinations won the famous martyr of science-Giordano Bruno.
The next stage was Friedrich Hegel's work "The Science of Logic". Concepts of dichotomies were introduced, dialectics began to develop (I recommend the work of Georgy Chelpanov "Textbook of Logic").
Explanatory dictionaries were developed. The concept of word semantics has appeared. Charles Osgood introduced the concept of semantic space and semantic differential.
Then computer programming languages, binary logic, object-oriented programming, and other technologies began to develop. They gave a lot of new concepts and operations.

In 2005. A scientist from Khabarovsk Stanislav Taktaev introduces the concept of Semantic Algebra. He calls a number of operations in the semantic space using the apparatus of vector algebra.
Independently of him, mathematician Grigory Reinin, who is engaged in socionics, performs a number of interesting operations with features and concepts that form the basis of modern semantic algebra.

The monograph Semantic Algebra – has been actively developed since 2010. Over 20 years, it has undergone more than 100 revisions and additions. Axioms and theorems were formulated, a system of semantic relations, operations of semantic addition and multiplication, the concept of a semantic tensor, and many examples of constructing semantic tensors and models were introduced.

1.4. Grigory Reinin's priority
In 2006, I was interested in studying socionics. On one site I came across an excerpt from the work of Grigory Reinin with the following note:
"St. Petersburg mathematician Grigory Reinin using mathematical methods proved that in addition to the well-known division by 4 features, 16 socionic types can be divided in 11 other ways.
The mathematical justification of this division can be found in his work "The group of bipolar features in the typology of C. Jung"."
Further in Grigory's work there were tables with individual, dyad and quadric features and comments. I was then struck by how boldly and accurately the terms were chosen: "Questimity-Declatimity, Constructivism-Emotivism" and others.
I liked the method of multiplying features to get new concepts. This made it possible to extend the compact orthogonal basis to improve diagnostic accuracy. Then I made a note of it and ... just forgot about it, because I was passionate about building schemas to record knowledge. I've never seen anything else like Rainin's signs. And Grigory Reinin and his followers, who are passionate about socionics and psychology, apparently simply did not appreciate the importance and novelty of the method used.
Later, I managed to simplify the construction of schemas to the level of tables. By writing down a lot of tables and comparing similarities, I got close to identifying characteristic factors – signs. Then he began to record the effect of the feature group using the multiplication icon.
This is roughly how semantic algebra was developed. We can say that I simply generalized and extended the Reinin method to the entire Russian language.
Thus, Grigory Reinin and his works are the forerunner of semantic algebra. Grigory Reinin made a significant contribution to the development of socionics and indirectly to the formation of semantic algebra. He has a number of articles and followers. You can find a lot of information about this on socionics websites.

1.5. Stanislav Taktaev's contribution
There is information on the Internet about the works of Stanislav Taktaev, a scientist from Khabarovsk. Apparently, he was the first to introduce the term "Semantic Algebra".
In his works, he mainly followed the traditional approach to the study of semantic space and semantic networks. He hypothesized that the semantic space has some structure and there are a number of semantic operations that include analogues from the object-oriented approach, mathematics and logic. Here's what he wrote in 2005:

"Semantic algebra (algebra of concepts) - Vector algebra, object model, and predicate algebra are used as the basic mathematical apparatus in the theory of the concept space, and their combination for use in the theory of semantic space is proposed to be called semantic algebra. Semantic algebra of concepts introduces a number of specific definitions, mostly without changing the essence of these mathematical systems.
The algebra of concepts introduces a number of specific definitions, mostly without changing the essence of the vector algebra apparatus.
Semantic Algebra supports the following actions:
Map items:
Inheritance, Multiple inheritance, Encapsulation, Aggregation, and Deaggregation.
Vector images:
Superposition, Addition of vectors, Difference of vectors, Scalar product, Vector product;
Propositional logic:
Inversion, conjunction, disjunction, implication, Equivalence of formulas, Correct reasoning."
No comments.

1.6. Comparison of mathematical and semantic tensors
Mathematical tensors are, first of all, a generalization of vectors and matrices to large dimensions. Even a scalar can be considered as a rank 0 tensor.
Secondly, for tensors, as for vectors and matrices in mathematics, a number of operations are defined. The main one is multiplication.
If the reader wants to learn more about this topic, I recommend starting with affine transformations in vector graphics. Everything is very clear there.
The applied value of mathematical tensors is to describe a vector field of a certain space or a transformation of space. For example, to describe the basic geometric transformations: displacement, shift, rotation, scaling - there is an affine matrix. The transformation equations for it look like this:
X1 = t00 * X + t01 * Y + t02;
Y1 = t10 * X + t11 * Y + t12;
Here tXX are the components of the matrix (rank 2 tensor). The equations show the transformation of X,Y coordinates to X1,Y1 coordinates.

Now let's look at multiplication for semantic tensors:
female, male,*
small, young, adult, old,
=
girl, girl, female, old woman,
boy, youth, man, old man,

Here, the gender vector is multiplied by the age vector (matrix). As a result, we get a rank 3 semantic tensor, whose components describe both gender and age at once.

Example of a triangle rule based on inheritance and assignment chains:
Live-Sensation-Warmth,
Live-Plant-Tree-Birch,
Birch-Wood-Fire-Burning-Heat,
Here we have 2 inheritance chains and a destination chain (based on a system of dynamic semantics equations). The length of these chains is 3, 4, and 5, respectively. This example shows that the sum of the lengths of any pair is greater than the length of the third chain. In this example, the triangle rule is saved.
It is likely that this rule is useful for checking whether semantic chains are compiled correctly.

1.7. Why do I need semantic algebra?
The world is now full of complex systems. You need to be able to understand them, highlight the main thing. Semantic algebra defeats complexity. For example, in literature there are many genres that have emerged and are emerging spontaneously. Basically, these are shortcuts and templates. Works should be classified. There is a temptation to select the main genres and make a classification of genres. But this is wrong, because each genre consists of many features. It is necessary to select simple signs. For example: "Reality - Fiction", "About the past – About the future", "News-Analytics", etc. Then it is easier for the reader to navigate by these attributes, without spending money on studying genres. Using a set of simple attributes, like a template, you can create a key for any genre. This approach is relevant for information portals and search engines.

Semantic algebra helps in solving complex issues, resolves disputes and gossip. For example, on one forum there was a question from "kitchen policy". See how the use of semantic matrices helped solve it.
"Avarice, extravagance" - these are the vices.
"Want, Riches" - this is beyond the jurisdiction.
"Poverty, Luxury" is an indicator,
"Beggars, Robbers" is a reason to initiate cases and take action.
With that, the issue was closed.

Semantic algebra in public life is a classification in commodity science, law, economics, science, etc. For example. Vodokanal summed up its results. An economist came to make an estimate of the debt. Debts were incurred on benefits and on compensation. The economist divided all payers into 3 categories (which he bitterly regretted at the end of the day): regular, privileged, and compensated employees. But he did not take into account the fact that the benefit and compensation are a pair of independent factors. This means that there is a group of payers who are covered by both the benefit and compensation. So there are 4 categories in total. You see, what a gross mistake. Such errors often occur when calculating utility bills, pensions, and similar payments and debts. Commercial structures have learned to use such errors to their advantage, so that users and subscribers bring in additional revenue.
It is necessary to explain why much attention is paid to the system of semantic relations here.
The fact is that if you have disparate knowledge and facts in any field, sooner or later they will destroy your ideas, they will float away.
Imagine 4 points that are on the vertices of a square. Just don't connect them with lines yet. What happens if you get some questionable facts? These dots begin to move around as symbols of knowledge in your mind. Definitions of terms start to warp and multiply. This is a disaster.
Now connect the vertices of the square with lines – and you will get a stable, rigid system of knowledge. These lines are semantic relations.
As you can see, Semantic algebra is a subtle and powerful tool. If you want to understand a certain issue,
then constructing a semantic tensor will help you understand the essence.

1.8. On dialectics and axiomatics
I wanted to write an article about the development of dialectics and multidimensional logic in Semantic algebra.
I opened the encyclopedia of Dialectics. There are about a dozen interpretations of this concept. Therefore, I will limit myself to a couple of comments.
"The law of struggle and unity of opposites".
There is no definition of "opposites"in dialectics.
In semantic algebra - there are 8 types of opposites with definitions and examples.
"The law of the transition from quantity to quality".
In semantic algebra, there is a quality relation of the type:
silence - sound, darkness-light, peace-movement.
There is no quantity here. Quality is given axiomatically.

The axiomatic method of cognition based on the construction of semantic models requires compliance with several rules.
The semantic model of the domain must meet a number of conditions:
1. Opposite and symmetry,
2. Orthogonality and parallelism,
3. Multi-dimensionality and compactness,
4.Similarity and projection.
Such principles can be used to construct a semantic tensor.

2. Part Two, Tutorial
2.1. Introductory lesson, about antonyms
In the modern world, we are surrounded by large flows of information.
To find your way around them, you need text analysis methods.
Semantic algebra is a fundamental approach to working with the meanings and concepts of a language. It is based on binary combinatorics, linear algebra, semantic association matching, and object-oriented modeling. Semantic algebra is not only the basis for new information technologies, it is also a certain culture of thinking.

It is known that the language has synonyms and antonyms. We'll leave synonyms alone for now. Let's talk about the role of antonyms.
We know that in the language there are just words, and there are words in pairs, such as" top - bottom"," man - woman","black - white".
They are called antonyms, because they are opposite to each other in meaning. Antonyms play a crucial role in the formation of new words. If there is a basic pair of opposites, then they can act as signs in other words.
For example, the concept of gender: "male - female" defines the ending of a large group of words: "schoolboy - schoolgirl", "teacher - teacher", "employee - employee". You can see how one word indicates two attributes at once: profession and gender.
Another example. Concepts such as "top-bottom" have the prefixes " over - and under -". In the words "surface-underwater", immediately indicate the sign of the environment and the sign of vertical location.
It is very comfortable.
Or so: "tombstone", "stand". A paired attribute does not always generate paired concepts.

Question: Can one concept generate a new concept on its own? And if so, please provide an example.

2.2. Lesson on feature multiplication
Many people know the concept of association. This is when one concept causes a lot of related images. For example, the word "house" evokes images such as: "kitchen", "bed", "building", "family", etc. Please note that the words "structure" and "family" are the defining features here.
You can write the following expression:
"House = Building * Family". Here, using the multiplication icon, we have written the operation of combining features. In the same way, you can write:
"Warehouse = Building * Inventory".

Remember the role of word parts in the last lesson? Let's recall the examples and write them down using multiplication:
"Surface = Top * Water",
"Stand = Bottom * Stand".

Thus, some words play the role of features in the formation of other words. And the operation of combining features is called semantic multiplication.
Now let's look at the question from the previous lesson: "Can one concept generate a new concept on its own?"
Answer: Yes, it can, if you use the semantic multiplication operation. For example:
"Point * Point = Line Segment",
"Shelf * Shelf = Cabinet".

Here's another interesting example. Some words can be multiplied by numbers! For example: "3 * angle = triangle".

Task: If words can be semantically multiplied, is it possible and how to divide them semantically?

2.3. Lesson on antonyms types
Let's analyze the task of the previous lesson: "If words can be semantically multiplied, then is it possible and how to divide them semantically?"
You can divide words, but not all of them, only if the semantic equation is correct. To do this, you need to have a good explanatory dictionary at hand. We read the definition of a word, or rather a concept, and select its defining features. This will be a decomposition of the word into semantic factors. The divisor must be among these attributes. Here we use a complete analogy with integer arithmetic. Just as in a composite number, prime factors are preserved as information units, so in a derived concept, its features(intensional) are preserved.

Let's go back to antonyms. Can all antonyms be divided into groups?
Yes. Antonyms can be divided into several groups. To begin with, we will consider the following three groups: qualitative, opposite, and comparative.

1. Qualitative antonyms. This is similar to the ratio of 0 and 1 in arithmetic. 0 is emptiness, 1 is presence. For example: "rest - movement", "silence - sound". It is important that one concept does not carry any qualities, and the concept of a pair has a whole range of characteristics and properties. For example, the concept of "movement" has the properties direction and speed. The concept of "sound" has the properties volume and key.

2. Opposite antonyms. Unlike qualitative antonyms, these antonyms are equal, but completely opposite. This is similar to pairs of positive and negative numbers. For example: "left - right", "top-bottom", "black - white" , etc.
Please note that in such pairs, one concept has a positive emotional connotation, while the other has a negative emotional connotation. For example: "right, top and white" has a positive color.

3. Comparative antonyms. Such antonyms clearly mean different degrees, strengths, and intensities of something. For example: "much > little", "strong > weak", "bright > dim". The comparison icon is used here to show the character and direction of these pairs.

Note that we have an almost complete semantic analog of the arithmetic apparatus. We have 0 and 1, we have positive and negative values, and we have means of comparison. Previously, semantic multiplication and division operations were defined.
Now that we know that antonyms can be of different types, we need to ask the question: "Is it possible to create not only pairs of words, but also squares or even cubes?". If so, please provide some examples. This is an assignment for the next lesson.
2.4. Lesson on semantic tensors
In the last lesson, we asked the question: "Is it possible to create not only pairs of words, but also squares or even cubes?"
Yes, you can. Here are some interesting examples:
"Digit - Number",
"Letter-Word";

"True - False",
"The Truth Is Fiction."

And here is an example of a cube:
Brave - Cowardly,
Rich - Poor,
Strong - Weak,
Smart - Stupid,

As you can see from these examples, we used more diverse relationships than we mentioned earlier. The fact is that there are 12 types of semantic relations. This will be discussed in the next lesson.
Let's pay attention to the fact that we have received new objects to study. Geometrically, they are similar to squares and cubes. It is convenient to record them in the form of tables. However, they are invariant. This means that rolling such squares and cubes from side to side will not change their essence.
In mathematics, there is a section called linear algebra. It is dedicated to the study of such objects. Pairs are called vectors. Squares are called matrices. And the general name is tensors. Tensors are multidimensional objects. Their dimension is called rank.
If rank=0, then it is a scalar, like a single word.
If rank=1, then it is a vector, like a pair of words (bislovo). 
If rank=2, then it is a matrix, like a square of words (quadword).
If rank=3 or more, then it is a tensor.
A common name for such objects in semantic algebra is semantic tensor.

Semantic tensors can be multiplied. This corresponds to multiplication of feature groups. Here are examples for matrices:
"True-False "
"Good-Evil"
We multiply and get 4 variants of concepts:
1. Truth and Good-Motivator, Incentive,
2. Truth and Evil-Guardian, Law,
3. Lies and Good-Comforter, Fun,
4. Lies and Evil-Monster, Horror Story.

Another example. There are a couple of antonyms:
"Consent – Doubt",
"Understanding Is A Contradiction"

We multiply them and get 4 options:
Consent and Understanding - A rhetorical question,
Agreement and Contradiction - A cognitive question,
Doubt and Understanding - An educational question,
Doubt and Contradiction is a provocative question.

Recommendation: Practice composing semantic matrices.
2.5. Lesson on 12 types of semantic relationships

Now it's time to think about the types of relationships. Relations or connections of words in semantic tensors are based on various kinds of symmetry. Let's look at these types of relationships (the notation is given in parentheses):

QUALITY (+). This means the appearance of quality, the formation of a semantic axis. Examples: "Peace + Movement", "Silence + Sound", " Darkness + Light", "Point + Straight Line + Plane + Space". Where there is "No", there is no quality or it is not enough. Where "Availability" - quality is manifested in a larger spectrum and variety. For "movement", this is the direction and speed. For "sound", this is the volume, duration, and key.

VARIATION (&). This is a variation. A pair of homogeneous and equal-rank words. For example: "Lake & Pond", "Foliage & Needles", " Table & Chair", "Dog & Cat", "Spoon & Fork", "Product & Service".

POLARITY ( -). This is mirror antisymmetry, opposite, compensation. The emotional assessment implicitly appears here. For example: "Black – White", "Top-Bottom", "Left - Right", "Hot – Cold", "Positive - Negative", "Positive - Negative", "Ability - Need".

COMPARISON (> or <). This is a gradation. A pair of words denotes intensity, strength, degree, or excellence. Here, too, there is an emotional assessment. For example: "Much > Little", "Strong > Weak", "Bright > Dim", " Chair > Chair > Stool", "Huge > Big > Small", "Very > Little".

EXTENSION (#). This is orthogonality. Pairs of words complement each other until the semantic plane appears. One is meant for the other. For example: "Form # Content", " Reason # Consequence", "Man # Woman", "Question # Answer", "Task # Solution", " Goal # Means", "Process # Result", " Property # Status".

DEVICE (%). These are aggregation, meronym, and holonym. A pair of words like "Part % Whole". For example: "Apartment % House", "Letter % Word", "Detail % Device", "Branch % Tree".

TRANSGRESSION (\ or /). A pair means an asymmetric opposite that has the character of either decline and damage, or recovery and compensation. For example: "Birth \ Death", "Signal \ Interference", "Building \ Ruins". Or, for example: "Damage / Compensation", "Breakdown / Repair", "Illness / Treatment", "Error / Correction".

INHERITANCE (^). This is a "View" type of relationship. ^ Subspecies" or " Abstract ^ Specific". These are hyponyms and hyperonyms. For example: "Road ^ Street", "Building ^ Building", "Reservoir ^ Lake".

MULTIPLICITY (...). This is a "Quantity" type of relationship. … Quality". For example: "Drop-Rain", "Snowflake-Snow", "Shelf-Cabinet", "Book-Library".

NEIGHBORHOOD ( _ ). Indicates the location or location. The neighborhood is specified by prepositions and verbs. For example: "Headscarf", "Carpet is on the Floor", "Bedspread is laid on the Bed", "Towel is hanging on the Hanger", "The page is located on the Site".

AFFILIATION ( @ ). Affiliation or authorship is specified by verbs. For example: "The book was written by the Author", "The Dance was performed by the Dancer", "The music was written by the Composer", "The poems were composed by the Poet".

ASSIGNMENT ( $ ): Binds nouns with verbs. For Example: "Screw-Screwdriver-Twist", "Nails-Hammer-Hammer", "Part-Machine – Process", "Plate-Food-Eat".

Basis of semantic relations:
1. Abstract – Concrete,
2. Absolute – Relative Values,
3.Homogeneous - Structural.

Based on the basis of three axes, a cube is constructed, the edges of which form 12 types of semantic relations.
Relationships:
1. Качество Absolute, structural quality,
2. Variation specific, uniform,
3. Polarity absolute, uniform,
4. The comparison is relative, homogeneous,
5. Дополнение An abstract, homogeneous addition.
6. Device specific, relative,
7. Transgression relative, structural,
8. Наследование Abstract, structural inheritance,
9. Multiplicity abstract, absolute,
10. The neighborhood is specific, structural,
11. Membership specific, absolute,
12. Назначение An abstract or relative assignment.

Unambiguous relationships form pairs, and multi-valued relationships form many variants. Common relationships have a common defining word. For example: "Silence + Sound" - acoustics, "Top-Bottom" - vertical, "Lake & Pond" - reservoir. Private relations do not have such a general word describing them.

Task: Determine the type of relationship between words.
1. A miser ? Spender
2. Blow ? Block
3. Love ? War
4. Peace of mind ? Excitement
5. City ? Village
6. Home ? Entrance
7. A spoon ? Fork
8. Fencing ? Wall
9. Bank ? Water
10. A chair ? Stool

2.6. Lesson two, about types of semantic relationships

Answers to the task of the 5th lesson:

1. Miser < Spender, this Is A Comparison,
(Spends * Little) < (Spends * A Lot),

2. Shock-Block, this is the Polarity,
(Type * Of Action) – (Type * Of Reaction),

3. Love \ War is a Transgression
(Reason * Date of Birth) \ (Reason * Deaths),

4. Peace of mind + Excitement is a Quality,
(View * Of Rest) + (View * Of Movement),

5. City > Village, this is a Comparison,
(Residents * Many) > (Residents * Few),

6. House % Entrance, this Device,
Entrance = (Part * Of the House), House % Entrance,

7. Spoon & Fork, this is a Variation,
(Spoon & Fork) = Flatware,

8. Fencing ^ Wall, this is Inheritance,
Fence ^ (Wall = Type * Of Fencing),

9. Bank # Water is an Add-On,
(Form View*) # (View * Content),

10. Chair > Stool, this is a Comparison,
(Comfort * More) > (Comfort * Less)


Relationships can be viewed as operations on words. This means that by specifying a word and the type of operation, you can get a different word. Is it so?
Operations on a word may give different results, may not give results, and in some cases they are invalid. So, a pair, a word, and an operation can be:
Unambiguous, Multi-Valued,
General, Private,
Structural, Homogeneous,
Undefined, Invalid Ones.

There may be doubts about the paired nature of concepts. After all, there are words that denote a central or intermediate meaning. Then it turns out that it is necessary to consider not pairs, but triplets of concepts? However, this is not the case. The fact is that the central or intermediate concepts themselves form pairs. For example: "Center-Periphery", "Norm-Exception", "Gray - Color", "Middle-Edge", "Neutral ¬- Significant", and so on.

Task: Give examples for each case of word-operation pairs.

2.7. Lesson on semantic models
Semantic tensors are an interesting tool for modeling subject areas and knowledge. In the last lesson, we looked at 12 types of semantic relationships. Their role is very important for the correct construction of semantic models.

Remember the rule: In the semantic model, parallel links must be of the same type and have the same orientation.

Now see how the semantic model (rank 4 tensor, hyperword) reflects the similarity of mathematics and semantics:
Number, Letter,
Number, Word,
Sign, Value,
Expression, Sentence,
Calculating, Thinking,
Result, Idea,
Task, Product,
Solution, Meaning.

Recommendation: Try to build a semantic model from any area of knowledge. This can be a tensor classification. Don't forget about the parallel connection rule.

2.8. Lesson on reasoning patterns
When constructing semantic tensors, you need to have a correct question for the original concept or a series of concepts. 12 semantic relations, operations of semantic multiplication and addition, as well as working with a series of concepts, allow you to create templates for asking questions:
What inherent qualities, attributes, or properties does this concept have?
What is the closest analog of this concept?
What is the opposite of this concept?
What concepts manifest themselves to a greater or lesser extent than this concept?
What concept complements this concept?
What concept is a part or whole of this concept?
What concept compensates or balances this concept?
Which concept is a special case or more general from this concept?
What is the name of something that has these properties at the same time?
What is the result of combining these concepts?
What is the difference between these two concepts?
What attribute unites these concepts (extensional)?
What concepts that are similar to this concept form a series of concepts?
What concepts come out of this series of concepts?
What features distinguish the concepts of this series from each other?
What features combine some of the concepts in this series?

When constructing a semantic matrix, you should get a structure with the following (binary) distribution of features:
A 0 0,
B 0 1,
In 1 0,
D 1 1.
 


3. Part Three, Theoretical
3.1. Concept

Language concepts form a semantic set. This set is similar to numbers. There are simple concepts (like prime numbers) that can be used as attributes to get complex concepts. To do this, we introduce the operation of multiplying concepts.

Semantic multiplication is a procedure for detecting such a concept, the definition of which consists of words corresponding to the concepts being multiplied. Such multipliers play the role of features.

For example:
House * Woman = Mistress.
Work * Male = Master.

Complex concepts can be decomposed into multipliers. For example:
House = Building * Family.
Warehouse = Building * Inventory.

Semantic division is a complex operation due to the multidimensional and discrete nature of the semantic space. However, sometimes it can be done. For example:
"Granary / Grain = Storage".
In principle, to determine the features (multipliers) of a word, just look at its interpretation. In a good definition, all the features of the concept must be present.

Semantic algebra is similar to: boolean algebra (because it works with paired objects), and linear algebra (because multiplying semantic objects increases their dimensionality as the rank of tensors increases).

It does not follow from semantic multiplication that a dictionary definition of a concept always consists of multiplier concepts. The definition of simple concepts often consists of listing works by association.

Simple paired concepts with antonyms correspond to a vector (semantic vector). They allow you to get semantic matrices and tensors.

Semantic algebra is a metalanguage, because the components of tensors can be written in almost any developed language. This is confirmed by more than a hundred examples of language structures in which meaning and concepts form multidimensional cubes (semantic tensors).
Concepts within the subject area are structured according to orthogonal features-factors and form a strict mathematical form in the form of a cube or hypercube. The dimension of a hypercube is determined by the number of features-factors (intensity). In this paper, there are examples of 3,4,5 and 6 dimensional semantic objects. And semantic structures are formed on the basis of binary combinatorics of attributes-factors.
There are many attempts to classify words, build hierarchies, create thesauri (dictionaries of synonyms) and ideographic dictionaries. This is a very important and difficult job. Important because this dictionary can be translated into any other language. At the same time, the work is difficult, since the dictionary is a semantic network. If I pulled such a network for one word, I built a hierarchy, and if I pulled it for another word, I got a different hierarchy. Such work is ambiguous and can have many interpretations.
I was able to discover the dual nature of the language. Dual – this is at least. It turns out that in the language there are words-concepts that reflect the GIVEN, and then there are words-factors that reflect the POSSIBILITY. Dualism, at a minimum.
Concepts form a multidimensional cube and factors also form a multidimensional cube. These cubes are nested in such a way that concepts rely on the structure of factors, and factors rely on the structures of concepts. This can be represented as the vertex of one cube at the center of another cube. Here is an example of the dualism of the Russian language:
Length – Lives,
Latitude-Souls,
Depth – Thoughts,
Height – Spirit,

As you can see, words form stable pairs that we often use in writing and speech since ancient times. However, there is no objective, no direct logical connection in such correspondences. This is an example of how two independent word systems fit together. There is an indirect connection between such systems. This connection reflects the hidden laws of nature. It is thanks to this dualism that language is able to accumulate and store knowledge.

I want to give you another example of an axiomatic (deductive) approach. the method of building structures. We have two pairs of concepts:
There is Truth and Falsehood = Reproducibility and Performance.
There is Good and Evil = Utility and Agreeableness.

We multiply and get 4 variants of concepts:
1. Truth and Good-Motivator, Incentive,
2. Truth and Evil-Guardian, Law,
3. Lies and Good-Comforter, Compensation,
4. Lies and Evil-Monster, Horror Story.

The classification of questions is constructed in the same way. There are a couple of antonyms:
Consent, Doubt, - correspond to Emotions,
Understanding, Contradiction, - correspond to Information.

We multiply them and get 4 options:
Consent and Understanding - A rhetorical question,
Agreement and Contradiction - A cognitive question,
Doubt and Understanding - An educational question,
Doubt and Contradiction is a provocative question.

Where does this classification come from? How many elements does it contain? - The dictionary will not answer such questions.
Here I gave a couple of examples of strict construction of matrices from pairs of vectors. However, in practice, when researching a topic, you have to use inductive selection to create a tensor. And only then can you identify common properties and combinations of features.


3.2. Fundamental semantic concepts
A semantic object is a universal concept of anything, it is any object and subject, it is what was, is and will be, everything that is real and fictional, everything that is material and spiritual – this is all a semantic object.
A semantic space is the entire set of semantic objects. It is discrete, multidimensional, binary, and fractal.
The unit of measurement for Semantic space is the distinguishing feature of a pair of semantic objects.
The attribute can generate many parallel segments that connect semantic objects in pairs.
A pair of feature segments is orthogonal if they are connected in a single semantic object. In this case, there is a 4 semantic object that allows you to complete the corner to the square-the semantic matrix. And 2 pairs of attributes form the basis of the semantic matrix.
For example:
"Sofa Bed and Armchair".
They form a semantic corner. Then the "Chair" complements this to the matrix. A pair of signs "Lie - Sit" and a pair of "Comfort-Discomfort" form the basis.

A special role is played by means of expressing semantic objects – effectors. This is a special class of semantic objects that are divided into signs and images. The images are similar to the original, and the signs are unique in their series, like letters or numbers.
Names are also signs.
Animals can't use signs; they can only use images.
Effectors can be visual, auditory, gestural, and tactile (I've included the sense of smell and taste here), natural or artificial, simple or composite, static or dynamic.

A sentence is a path that connects semantic objects using the question field.
The meaning of a sentence or idea is a directed graph in semantic space.
For example:
"There is a spoon in the plate" or "The spoon is in the plate".
The meaning is the same, but there are many questions:
What lies there? Where is it located? What does it do?
Who put it in? Who did it?
When did you put it in? For how long?
This is the question field. As in electromagnetism and gravity.

3.3. Semantic tensor expansion
The following concepts: Truth, Truth, Falsehood, and Fiction form a matrix of the nature of information, in which Truth is opposed to Lies, and Truth and Fiction can be True or False. The truth is a subjective result of communication or mystical experience. People can argue about the Truth as a way of expressing objective Truth, projection, interpretation. The truth corresponds to an Opinion, but an Opinion is an emotional assessment. Therefore, if we have a matrix of the nature of information, then there must be a matrix of the nature of emotions:
1. Truth, Consent,
2. Pravda, Opinion,
3. Lie, Doubt,
4. Fiction Or Judgment.

Now it should be noted that Fiction is opposed by a Guess, as a result of working with information. Therefore, there should be a pair of corresponding matrices, for information and for emotion (0.1, 0.2):
1. Truth, Consent, Observation, Feeling,
2. Truth, Opinion, Opinion, Sympathy,
3. Lie, Doubt, Mistake, Illusion,
4. Fiction, Judgment, Guess, Perception;

Here we got an object with 16 components. It is written as a table and looks like a 4*4 matrix, but it is not a matrix. By analogy with linear algebra from mathematics, this is a rank 4 tensor. This is a 4-dimensional object, because it consists of 4 attributes:
1. True, False,
2. Information, Emotion,
3. Objective, Subjective,
4. Process, Result.
The fifth sign can be a pair: Intent and Randomness. Then it would be possible to get a 5-dimensional object from 32 components. However, in this context, the pair "Intention and Randomness" will overlap with the pair "Objective and Subjective".
Similarly, each pair of features will give another pair of antonyms (0.3, 0.4):
1. True, False, Problem, Solution,
2. Information, Emotion, Word, Deed,
3. Objective, Subjective, Intent, Randomness,
4. Process, Result, Cause, Or Effect.

In this case, the "Past and Future" attribute worked. As a result, we obtained from the features of one rank 4 tensor, the second rank 4 tensor, and the feature tensor.
By the way. Men and women process information flows and emotions differently. Therefore, the "Cause and Process" pair is important for women, and the "Result and Effect" pair is important for men. This can be seen in the example of the work that women and men do better. From this, we can assume that one form of writing semantic tensors is preferable for women, and the other form of writing is more understandable for men.

3.4. Semantic gradients, tensors, and series
Emotions are conveyed in words that can be arranged in a row on a scale of some quality (a gradient is formed). For example:
"shack, house, mansions "(comfort or prestige factor),
"Care, Patience, Warning, Attack" - personal policy,
"Softness, Flexibility, Elasticity, Firmness" - the mood of the Soul,
"Thoughtfulness, Taciturnity, Sociability, Talkativeness."

Information is transmitted by words that can be grouped into a vector (antonyms), matrix, or tensor of higher rank (2, 4, 8, etc.words). For example: "house, street, tenant, pedestrian". This is possible because the meaning of words changes due to the binary combinatorics of its features. This is why the semantic tensor is the most compact form of conveying meaning about a fact or phenomenon.
Some pairs of antonyms can be converted to a gradient by using additional words for extreme and intermediate states.
One more point. It concerns the appearance of duplicates in the presentation of structures. The fact is that squares, cubes, and hypercubes share common vertices, edges, and faces. Therefore, the choice of reference frame will affect the inevitable appearance of duplicates. Subsequently, this will help to reveal the topology of higher-dimensional systems.

The VARIATION relation allows you to build semantic series. For example: fir, fir, rowan, birch, aspen, etc. These concepts are united by a common concept-a Tree. However, sometimes there may not be such a word.
For example: stool, chair, chair... saddle?
Semantic series play a crucial role in our lives. For example: Numbers, Letters, Colors, Notes - these are all examples of rows.
However, a semantic series may or may not have an order.

3.5. Metalanguage and semantic invariance
Such properties as antagonism, symmetry, compactness, orthogonality, multi-dimensionality, gradient, and similarity are inherent in semantic tensors in any language (they are inherent in thinking). They are language-independent and closer to the Truth. Therefore, I use the term "metalanguage"for them.
Geometrically, this is similar to squares, cubes, and hypercubes of large dimensions. Just as a cube can be placed on any face-it will remain a cube, so the tensor can be written as a list or table in different ways. This shows its invariance.

If you have a good knowledge of the subject and proficiency in semantic analysis, then you can try to combine tensors of a lower rank into a tensor of a larger one.
The similarity of tensors plays an important role in understanding the Truth. So, for example, it is not necessary to try all the fruits to learn how to distinguish between edible ones. It is enough to study the signs: color, shape, smell, taste, etc. When a researcher finds a similarity, he can make a discovery. For example: cook puffer fish.

Semantic algebra is a good tool for analyzing language as a linguistic apparatus that projects Truth and assesses the quality of knowledge. Just as a cube consists of faces, edges, and vertices, so a tensor consists of tensors of lower rank, up to matrices and vectors. These components at each level should have names for each subject area. In practice, it happens that even a frequently used concept is transmitted by a group of words. For example: "aggregate state of matter", "feedback loop", etc. This indicates the level of knowledge and maturity of the language in a particular area. It also happens the other way around, when a lot of synonyms are formed around a dubious and sometimes fictional concept.

3.6. Classification in semantics and synonyms
There is a certain error in the formation of semantic structures. This is due to the abundance of synonyms that came from other languages in Russian. (From Greek, French, German, English) Therefore, preference should be given to words that are native, but not out of use. It is also very important to identify the semantic coloring of a synonym, because this factor helps to correctly distribute words across structures and within structures.
In addition, the error in the structures may be due to the paucity of knowledge. When the idea of the subject area contradicts the principles proclaimed here. In such cases, I preferred a controversial but coherent theoretical hypothesis. I consider the phenomenon of synonymy to be an unavoidable evil of the language, because it is impossible to combine gradient and structurally similar concepts in one pile. For example: "building, house, building, room" , etc.

Semantic algebra has a huge potential in classification problems. All classifications appeared spontaneously, forming lists. Then such lists were expanded and supplemented. Sometimes a tree hierarchy was obtained. This didn't help much, because the elements of such lists are labels and templates. Sooner or later, experts realize that you need to use combinatorics for classification. Therefore, we need a feature system that can be used to construct a semantic class tensor. However, most analysts use the same labels and templates instead of the feature system. No matter what areas you touch on-music, literature, design, physics ... - everything is a mess and a variety of vinaigrettes from interpretations and definitions. Here are some examples of how this situation can be improved.

3.7. Typology of semantic objects
We introduce the concept ¬of a semantic vector. This is a pair of words that are semantically related. For simplification, I propose to denote the semantic vector by the term "bislovo". That is, a binary (binary) word.
The following. Almost all words of the language form semantic pairs – biwords. (Even all conjunctions and punctuation marks form pairs!) Exceptions are names and titles. Their meaning is often lost and not used, so they are scalar values for semantic algebra.

And here we smoothly approach the understanding of the dimension of semantic objects. Since words form pairs, the base of the degree is always the number "2". But words don't just form pairs. Semantic structures are multidimensional objects. The number of words in such structures is determined by the equation: N = 2^rang. (i.e. 1, 2, 4, 8, 16, etc.) Here rang is the number of dimensions.  We have already got acquainted with scalars (these are names, rang = 0) and vectors (bislovo, rang = 1). If rang = 2, then the structure (semantic matrix, for simplification we will introduce the term "quadword") must have 4 words. Consider the following examples:
"Digit - Number",
"Letter-Word";

"True - False",
"The Truth Is Fiction."

Analogs of linear algebra are used here. The words "vector", "matrix", and for objects of higher dimension – "tensor". Only linear algebra uses numbers, while semantic algebra uses words. When multiplying vectors, matrices, and tensors, the dimension of objects is added up in a similar way.
The semantic tensor of rank 3 is conveniently called "kuboslo", because just as a cube has 8 vertices, so a kuboslo consists of 8 words. There will be 16 words in the rank 4 tensor. It can be called a "hyperword". A hyperword consists of a pair of cuboswords. Here's an example:
1. Digit, Number,
2. Letter, Word,
3. Sign, Expression,
4. Value, Suggestion,
5. Calculation, Result,
6. Reflection, Idea,
7. Problem, Solution,
8. Work, Meaning.

See how the content of this tensor reflects the similarity and independence of the world of numbers and the world of words.
Please note that all such structures are multidimensional objects, despite the fact that they are written in the form of a table. This means that words are connected by orthogonal relationships of various kinds. For a bisword there is one relation, for a quadword there are two kinds of relations, and for a cubist there are three kinds of relations. That is, the number of genera of a semantic tensor is equal to its rank.
There are semantic tensors of rank 5 (32 words). You can call them - "superword". They are quite useful for revealing some deep questions. There is only one tensor of a larger, 6th rank so far. It is difficult to perceive it, and it is quite difficult to create such an object.
So. Let us recall the terms used to denote semantic objects: "Scalar, Vector, Matrix, Tensor of the 3rd rank "(hereinafter-also a tensor).

3.8. Axioms and theorems of semantic algebra

AXIOM ABOUT NECESSARY TRUTH CRITERIA:
Truth is compact, orthogonal, multidimensional, and fractal. This is a necessary criterion for the truth of knowledge.

AXIOM ABOUT ATTRIBUTES:
The meaning of a word is determined by the mutual combination of its semantic features (intensity). This combination of features is called semantic multiplication.

AXIOM ABOUT THE PAIR OF ATTRIBUTES:
All features of concepts in the semantics of a language are connected in pairs based on semantic relations. Such pairs of features define the semantic axis and are called a semantic vector.

AXIOM ABOUT SEMANTIC MULTIPLICATION:
Semantic multiplication is an operation that allows you to select a concept based on a combination of its features.

FEATURE CONSERVATION THEOREM:
In semantic multiplication, the features of multiplier concepts are stored in the product concept, just as primes can be extracted from the product number.

THE SEMANTIC TENSOR THEOREM:
Since a concept can have several attributes, each of which can have several relations, it is possible to construct multidimensional semantic objects from the attributes: vectors, matrices, and tensors. They are invariant. They can be multiplied in the same way as it is done in linear algebra.

SEMANTIC TENSOR TRUTH CONDITION:
In a proper semantic tensor, all parallel relationships must belong to the same semantic type and have the same orientation.

THE SEMANTIC STABILITY THEOREM:
Since the meaning of concepts is based on features, and the meaning of features is based on concepts, any attempt to change the meaning of a word leads to opposition from its features.


3.9. Static and Dynamic semantics
Semantic algebra is divided into static semantics and dynamic semantics. Static semantics studies the relations between concepts (the operation of semantic multiplication was introduced). Dynamic semantics studies concepts about processes (here the operation of semantic addition is introduced).
Pay attention to these statements. Their difference reflects the fact that we can only study processes indirectly, through concepts. If static semantics studies pairwise relations, then the easiest way to study processes is to use the three-term formula: "Concept 1 + Concept 2 = Concept 3". In such a formula, " + "means presence and merging, and" –¬" means absence and need.

For example:
"Man-Woman = Love", a man looking for a woman creates love.
"Male + Female = Child", the fusion of male and female should produce offspring.
"Man-Love = behaves like a Woman",
"Love Woman = behaves like a Child",
If you rewrite the system of these equations, you can understand who has what needs (this is indicated by a negative value), and how it will behave.

Here is a rich material for interpretation. For example:
"Woman + Love = capable of Masculinity",
"Child + Love = shows Femininity",
"Man + Love = Man + (Man – Woman) = Friendship".

In dynamic semantics, when a word is transferred from one part of an equation to another, the meaning of the equation changes, because the word appears in a different context.
Thus, you can work with semantic processes as with mathematical expressions, but you need to specify the interpretation at each step.

Now, the examples are more complicated:
Feeling + Opinion = Intent,
Intent + Consent = Thought,
Thought + Need = Desire,
Desire + Method = Solution,
Solution + Resource = Action,
Action + Request = Evaluation,
Rating + True = Retribution,
Retribution + Attitude = Feeling.

This example is a ring (feedback loop). At each step, we add a new value to the previous result. In 12 steps, the ring closed.

Here we have to assume that a pair of concepts provides the necessary and sufficient conditions for an unambiguous definition of the third concept. For example:
"Seller + Buyer = Deal";
"Sound + Barrier = Echo";
"Dummy + Machine = Part";
Sometimes you can make the process into an independent concept:
"Machine + Worker = Processing",
"Blank + Processing = Part".

Semantic addition is a simple way to record production and technological operations:
"Fabric + Tailoring = Linen".

Parables, myths, anecdotes and, probably, any narrative is a system of equations of dynamic semantics.

The similarity of semantic addition and the quality relation can be considered not accidental. Because as a result of semantic addition, the concept of a new quality is formed. This is noticeable when the material and ideal planes interact.
For example:
"Matter + Method = Substance",
"Substance + Form = Item",
"Item + Schema = Mechanism",
"Mechanism + Engine = Machine",
"The car + Control = The machine",
"Machine Tool + Self-Control = Robot".

Or you can build a classification of sciences like this:

Semantics + Numbers = Math,
Mathematics + Space = Geometry,
Geometry + Time = Kinematics,
Kinematics + Mass = Dynamics,
Dynamics + Energy = Mechanics,
Mechanics + Particles = Quantum physics,
Quantum Physics + Molecules = Chemistry,
Chemistry + Cells = Biology,
Biology + Creatures = Zoology,
Zoology + Reason = Psychology.
 


3.10. Global semantic groups

This chapter was created thanks to the experience, intuition and perseverance of Dmitry V. Anisimov(Moscow).

To begin with, let's write out the semantic correspondence between the main parts of speech and their features:
Noun, Subject, Main, Static,
Verb, Action, Basic, Dynamics,
Adjective, Property, Additional, Static,
Adverb, State, Additional, Dynamics.

Now let's write down the general types of concepts with attributes:
Material, Reality, Concrete,
Ideal, Reality, Abstract,
Objective, Personality, Concrete,
Subjective, Personality, Abstract;

Now, by multiplying a pair of matrices, we get the hyperword of global semantic groups:
Material, Ideal, Objective, Subjective:
Objects, Words, Beings, Entities,
Actions, Signals, Phenomena, Miracles,
Properties, Attributes, Behavior, Character,
States, Positions, Abilities, And Abilities.

We arrange them according to the characteristics of the next level.
Items (material):
Natural - Artificial, Simple-Composite,
Words (perfect):
Basic-Official Names, Proper - Common Names,
Creatures (objective):
Living - Animate, Primitive-Intelligent,
Entities (subjective):
Carnal - Disembodied, Individual-Group,

Actions (material):
Forced - Own, Simple-Complex,
Signals (ideal):
Attenuation - Gain, Stabilization-Switching,
Phenomena (objective):
Natural - Anthropogenic, Regular - Spontaneous,
Miracles (subjective):
Warning - Edification, Caused-Induced,

Properties (material):
Permanent - Temporary, Qualitative-Quantitative,
Attributes (ideal):
Characteristic - Exclusive, Similar - Distinctive,
Behavior (objective):
Stable - Unstable, Proper -Imitative,
Character (subjective):
Direct - Evasive, Positive - Negative,

States (material):
Static - Dynamic, Individual - Group,
Positions (ideal):
Stable - Changeable, Absolute     - Relative values,
Abilities (objective):
Transmissions - Conversions, Normal - Unusual,
Skills (subjective):
Innate - Acquired, Real - Fictional;

Total: 4*4*4 = 64 attributes.

Each global group is not only categorized by features, but can also generate classifications for knowledge domains. Here, the matrix of groups has undergone transposition and projection onto the matrix of knowledge levels.

Knowledge and experience levels:
Stochastic, Concrete, Intuitive,
Empirical, Concrete, Logical,
Axiomatic, Abstract, Logical,
Mystical, Abstract, Intuitive;

Stochastic, Body:
Bodies-Mechanisms,
Letters – Words,
Particles - Substances,
Notes-Melodies,

Empirical, Soul:
Movement-Tension,
Signals – Messages,
Feelings – Sensations,
Reflexes – Imagination,

Axiomatic, Reason:
Digits – Numbers,
Coordinates – Forms,
Operations – Operators,
Equations – Functions,

Mystical, Spirit:
Work – Achievements,
Communication – Collaboration,
Experience-Imitation,
Forecasting – Creativity,

Each global group (out of 16) gave a pair of concepts related to the device (aggregation) or complement (orthogonality) relations. A detailed analysis of these pairs and their semantic multiplication should provide a tensor classification of disciplines. Specifically, the disciplines: sciences, arts, culture, and sports.
Because only an all-encompassing approach will allow you to create semantic tensor classification. Otherwise, problems in definitions and distinctions are inevitable.

Here you need to make an important note! The construction of global semantic groups is based on parts of speech of a particular language. Consequently, the tensor classification of disciplines will also be not absolute, but dependent on a specific language. This suggests that a language determines the abilities and specializations of its native speakers.
Here is an example of convolution of global semantic groups:
The body has the properties of hardness and warmth, and on the other hand, hardness and warmth are a kind of sensation.

Further, examples of the distribution of concepts into groups:
year - changeable position
man is a rational being
time is a regular occurrence
business - your own action
life is a natural phenomenon
day - dynamic state (time of day)
the hand is a natural object
times-quantitative property
work      - forced action
location - absolute position
the face is a natural object
a friend is a spiritualized being
the eye is a natural object
question-acquired action
a house is an artificial object
side     - stable position
country - anthropogenic phenomenon
the world is an anthropogenic phenomenon
chance - a random occurrence
type - a similar feature
system-a composite item
problem - static state
opportunity is a regular occurrence
result-dynamic state
number - a quantitative property
group - composite item
condition - changeable position
form is a qualitative property.
 


3.11. Relationships and groups in a single framework
Semantic relations and global groups in a single framework
A single basis for semantic relations:
1. Abstract – Concrete,
2. Absolute – Relative Values,
3.Homogeneous - Structural.

Based on the basis of three axes, a cube is constructed, the edges of which form 12 types of semantic relations.
Semantic relations:
1. Качество Absolute, structural quality,
2. Variation specific, uniform,
3. Polarity absolute, uniform,
4. The comparison is relative, homogeneous,
5. Дополнение An abstract, homogeneous addition.
6. Device specific, relative,
7. Transgression relative, structural,
8. Наследование Abstract, structural inheritance,
9. Multiplicity abstract, absolute,
10. The neighborhood is specific, structural,
11. Membership specific, absolute,
12. The assignment is abstract and relative.

Global groups are constructed on the vertices of the semantic cube:
1. Phenomena. Abstract, absolute, or structural. For example: motion, light, or sound.
2. States. Specific, relative, or homogeneous. For example: coordinate, speed, brightness, volume.
3. Items. Concrete, absolute, and structural. For example: tree, stone, word, number.
4. Properties. Concrete, absolute, homogeneous. For example: hardness, color, capacity.
5. Signals. Specific, relative, and structural. For example: sign, note, symbol.
6. Signs. Abstract, absolute, homogeneous. For example: a person, a plant, or a car.
7. Regulations. Abstract, relative, or structural. For example: near, on the left, it looks like.
8. Actions. Abstract, relative, or homogeneous. For example: run, shine, talk.

 


3.12. About the Semantic Dictionary
One of the main tasks of semantic algebra is to build a semantic dictionary. Conversations with Igor Konstantinovich Garshin helped me realize the importance of this task and concentrate on it.
There are a number of considerations here regarding this topic.

The dictionary generally has 4 levels:
Spelling, is a spelling correction,
Stylistic shades are emotional diversity,
Speech forms are a logical variety,
Dictionary signs — this is a record of the essence.

Stylistic emotional nuances are usually produced by suffixes and endings. A logical manifold is usually formed by prefixes, such as: not -, bes -. However, from the point of view of semantics, they are all derived. Therefore, it is important for a semantic dictionary to form a system-forming core of dictionary signs and morphemes. Speech forms and stylistic shades can be generated.

Next question. You need to define a form for recording semantic relationships and operations. This is ambiguous. Let's look at some examples.
Here the key role is played by the pair of concepts.

(Top – Bottom) * Direction = Up and Down;
(Top – Bottom) * Comparison = Above > Below;
(Top – Bottom) * Position = Top & Bottom;
(Top – Bottom) * Attribute = Upper # Lower;

The transgression relation appears where there is an energy exchange.
(Top – Bottom) * Move = Ascent / Descent;
(Top – Bottom) * Flight(gas) = Rise / Fall.
(Top – Bottom) * Float(liquid)= Pop Up \ Dive in.
(Top – Bottom) * Earth (firmament) = Fill in \ Dig;

You can play with the form of writing relationships, as in arithmetic:
(Top & Height) – (Bottom & Depth) =
(Top - Bottom) & (Height - Depth);

However, there is ambiguity in fixing semantic links. Here is an example of a dynamic semantics equation:
Mechanism + Engine = Machine.
And on the other hand, we have a relationship of inheritance, instantiation and device aggregation:
Mechanism ^ Machine;
Car % Engine.

What can be a semantic dictionary? Example:
Lampshade (
 % of the lamp, A. part of the lamp,
 ^ (Light * Diffuser), A. type of light diffuser,
 & Plafond, A. variation of plafond,
 (Fabric & Paper) + Frame %, A. consists of fabric or paper with a frame,
 + Decoration), A. can be decorated.

The following notations are used here: prefix and postfix notation of semantic relations, as well as semantic multiplication and addition.
Thus, for a semantic dictionary, the following minimum task is formed: building a dictionary in the form of a table based on prefix and postfix relations, as well as operations of semantic multiplication and addition.

And the maximum task:
Generating a complete hypertext dictionary,
Word distribution by linguistic level,
Distribution of words by parts of speech and morphological features,
Reflection of the relationship between semantic topology and geometry,

PRACTICE of creating a semantic dictionary.
The simplest and most convenient form of a c-dictionary is a spreadsheet. The first column contains a list of words. In subsequent columns – the post and prefix of the relation, terms or multipliers. 
In practice, it turns out to be too much fine work in finding differences over a large amount of data. Therefore, such work needs a simplified approach. What can be combined and what relationships will remain? Let's break it down into columns:
Attributes-factors, semantic factors and terms ( * + ), as well as relations of the super-type (^).
The device ratio of a certain part ( % ).
The ratio of specific device details ( %).
Relations of quality ( + ), opposites ( - ) and transgressions ( / \ ), additions ( # ) and variations (&).

This results in a semantic plane: "Similarity - Difference", "Device-Detail".
The Device-Part relationship is relatively straightforward.
There are 4 columns of differences in relationships, it all depends on the perseverance of the dictionary compiler, who must put down the relationship icons.
However, there are a lot of issues with regards to 1 column. These are semantic loops and holes. Loops lead to ontonymy, and holes force you to use abbreviations or borrow words. All of this leads to bad confusion. And here, probably, it is necessary to start from the literal meaning of words. For example, if we say "Value", then there is a dimension. And if we say "Value", then we are talking about comparison.

So, the complexity of working with the dictionary has decreased by about half. 1+4 = 5 columns are conveniently located on the screen. Where necessary, you can put icons of the relationship type. More order of magnitude than with an arbitrary distribution of relations.
The work is simplified by the fact that you can omit some inverse relationships. Computational processing of the dictionary can make up for this. In semi-automatic mode, you can eliminate collisions in other columns.
Next question: identifying tensor relationships between words. Here you need to focus on the similarity of all relationships. Only one difference is allowed. Only then will it be an orthogonal relationship. Based on these relationships, we can identify c-tensors and unload them for further processing.
Look for a similar project: "Explanatory and combinatorial dictionary", "Semantic tables", "Tables of concepts".

3.13. Developing triads
Often, triads of words appear in different areas of knowledge. Trying to convert them to a square can confuse even an experienced researcher. What is the reason?
The fact is that triads are often an orthogonal basis of the 3rd rank. They are called factors or aspects. They should be carefully considered and supplemented to the semantic cube. This should result in 12 components.
The most obvious example is a color cube.
Black + RGB + CMY + White.
And a quadra like CMYK is a very big semantic ambush. Therefore, the researcher needs to know both semantics and the subject area well.
Here's another example: in the field of information security, there are three aspects: data integrity, availability, and confidentiality. How do I update it? I assume that this will be an information hack with the following methods: attack, interception, and substitution. I'll leave the development and disassembly of this cube to the experts.

I must say that I spent several years tinkering with different triads, complementing them to the star of David. For example:
Sensor – Conductor-Effector and
Analyzer-Filter-Controller.
There were several dozens of such sixes. Finally, I realized that the star of David is a projection of a cube placed on a vertex onto a plane. Now most of those sixes are converted to cubes.
Therefore, we should try to understand the nature of semantic objects, i.e. their dimension.
Thus, we have 3 cases of a triad sweep:
Gradients with an average value,
Incomplete matrices,
Cube slices, - orthogonal basis.

Examples of triads and their extension to a matrix:
Past, Future, Present - Fiction,
Male, Female, Middle, - Plural,
Vertical, Horizontal, Range, - Scale.

Here I must say that triads are a simplified model of knowledge. It is worth going a little deeper into the topic, as the semantic tensor is immediately revealed.
 


3.14. Scanning parts of speech
The role of parts of speech is to reduce the dimension of semantic objects. This is the primary morphology. Here we come very close to semantic geometry.

First, let's look at the independent parts of speech and identify the corresponding concepts:
Noun, Subject,
Verb, Action,
Adjective, Property,
Adverb, State,
Pronoun, Link,
Numeral, Number.

They represent 6 faces of a cube. Using language, we project the concept onto one of these facets. Each face has a three-dimensional coordinate grid of secondary morphology:
Noun : gender, number, case,
Verb : infinitive, participle,gerund,
Adjective : quality, attitude, possessiveness,
Adverb : quality, action, subject,
Pronoun : person, attribute, subject,
Numeral : number, order, collective.

Now let's define an orthogonal coordinate system:
Subject, Action,
Property, State,
Link, Number.

Now you can identify 8 vertices of this cube and draw a table of these vertices for each face. After that, you can make a list of 12 edges of the cube.

The situation is similar for official parts of speech. Here we have a square:
Preposition, Specific information,
Union, Abstract information,
Particle, Specific emotion,
Interjection, an abstract emotion.

It is interesting to compare this chapter with the chapter on semantic global groups. They complement each other.
 


3.15. Fundamental axes of c-space
The experience of identifying tensors in semantic space shows that there are axes formed by the Quality ratio (+):
Rest + Movement,
Silence + Sound,
Darkness + Light,

A c-tensor is formed around each such pair. For example:
Rest, Movement,
Deceleration, Acceleration,
Speed, Direction,
Offset, Rotation.

Pay attention to the indirect connection of each pair with a part of speech.
Rest, Move, - verb,
Slowed down, Accelerated, - an adverb,
Speed, Direction, - noun,
Constant, Rotational, is an adjective.

3.16. Fundamental planes of c-space
The experience of identifying features of semantic tensors shows that semantic axes tend to pair orthogonal groupings due to the Complement relation (#):

Spirit, Soul,
Body, Mind,

Space, Time,
Matter, Energy,

Smell, Light,
Taste, Sound,

Input, Output,
Path, Barrier,

Emotion, Information,
Feelings, Sensations,

Intuition, Logic,
Ethics, Sensorics,

Etc.
This shows that such semantic matrices (planes) play a key role in the semantic space. This is unusual for mathematics, where all axes are independent and equal.
There are c-matrices that look like a pair of parallel axes. For example:

Absolute, Relative,
Abstract, Concrete,

Private, General,
Personal, Mass,

The f-c plane is characterized by traversing elements along the Z contour. For example (on the Z contour):

Solid, Liquid,
Gas, Flame,

Past, Present,
The Future, Fiction,

Childhood, Youth,
Maturity, Old Age,

Point, Line,
Plane, Volume,

This is an important property of the f-c plane.

The fundamental axes and planes form the c-tensor. For example:
Solid, Liquid, Gas, Flame,
Body, Soul, Spirit, Mind,
Past, Present, Future, Fiction,
Matter, Time, Space, Energy.

Time-Truth tensor and physical quantities:
Past, Future, relative time,
Memory, Forecast, relative distance,
Perception, Fiction, absolute impulse,
Reality, Illusion, absolute energy,

This c-tensor provides a key to understanding the field of psychophysics. It shows how we perceive physical quantities. So time and distance are relative values – they need to be compared with something to understand. And momentum and energy are perceived as absolute values, through peace and relaxation.
Momentum is perceived or imagined as the speed of a massive object. Energy is felt as sensations or a hypnotic illusion, autosuggestion.
However, this is not the case in modern physics. For calculations, you have to enter the axes of space and time, counting the distance and time relative to these axes. The absolute nature of momentum and energy is expressed in the corresponding conservation laws. Accordingly, it is necessary to speak not about the constancy of the speed of light, but about the constancy of the light pulse and its energy.

3.17. Decomposition of words into attributes
I must say that semantic algebra does not provide any classifications, unlike logic, ontology, linguistics or theology. The relationship between semantic signs and words, their spelling and pronunciation, is formal. Semantic algebra provides a method for constructing tensor relations when working with features.
A good example of implementing attributes is the construction of words. In Russian, this can be shown by the example of verb formation. For an example, let's analyze the word "Ran":
Singular number in contrast to "Ran",
Masculine in contrast to "Ran",
Past tense as opposed to "Running" or "Running",
The goal is implied, as opposed to "Running".
It implies incompleteness, as opposed to "Reached".

See how many semantic features a simple verb can contain! However, the semantics of the word "Running" contains 3 more features: "Fast ""Movement" with the help of"Legs". So, the simple word " Ran " contains at least 12 semantic features!
In this way, you can create words based on a combination of features. Verbs are the simplest example: "Red - Blushed", "Goods-Bought", "Glass-Settled".
However, it should be remembered that linguistic forms often plug semantic holes: "Sunset", "Sunrise", "Zenith", "Eclipse". On the other hand, in semantics, you can't focus on the root of a word, because there are homonymic loops.

As for verbal signs, we must say that they also form a semantic tensor:
"He-She-It-They" are 4 signs of gender and plurality.
Signs of time, purpose (completeness) and attitude to yourself give 8 options: "Ran, Ran, Runs, Runs, Runs, Runs, Runs, Ran, Ran, Ran." However, many verb forms do not end there. Thanks to prepositions, suffixes, and endings, you can construct even more forms: "Run out, Run in, Run in".

3.18. Classification of homonyms
Dmitry Anisimov writes:
For example, there are also vile homonyms.
Homonyms are words that have the same sound and spelling, but different meanings.
Homonyms appear exactly from the same thing that causes a combinatorial explosion.
Because it is necessary to describe the infinite world by finite means.
Therefore, a person uses the same words to name approximately similar objects.

I must say that when faced with homonyms, one is tempted to find some basis, a fulcrum. This is a matter of etymology, not semantics.

We need to put the question like this: who is to blame for the formation of homonyms? My answer is people with a narrow specialization, who were profitable to give tempting explanations. Historically, these are: doctors, teachers, merchants, translators, and scientists from various fields. In short, homonyms are the result of professional linguistic speculation.

When a homonym occurs, there is a context defined by a certain activity or field of activity. For its designation, in my opinion, verbs are best suited. Thus, we can identify one of the defining semantic features. You just need to construct a semantic tensor for features, and homonyms can be considered as a special case of single-root words.

3.19. Semantic topology
Let's look at a rank 4 semantic tensor:
girl, girl, woman, old woman,
boy, boy, man, old man,
granddaughter, daughter, mother, grandmother,
grandson, son, father, grandfather.

Here we see 3 factors: gender, kinship, and age.
The age factor can be considered a 1*4 vector, but it is a matrix. To understand this – you need to delve into psychology.
We are talking about multiplying the vectors: "Personal - Public" and "Growth - Reproduction".

For clarification, let's expand this by the "Age - Goal" vector:
Childhood, Pleasure, Personal Growth,
Youth, Achievements, Personal Reproduction,
Maturity, Self-Esteem, Overall Growth,
Old Age, Dedication, General Reproduction (Upbringing).

An obvious addition to the first tensor is:
Mother-in-law, Father-in-Law,
Mother -in-law,
Aunt, Uncle,
Niece, Nephew.

The obvious exception here is the "Brother - Sister"vector. However, it is included in the equal-rank relationship tensor:
Brother, Sister,
Employee, Female Employee,
Neighbor, Neighbor,
A Friend, A Friend.

We should talk not only about tensor structures, but also about semantic topology. Semantic topology is based on dynamic semantics. For example:
Relatives + Son = Nephew.
Relatives + Father = Uncle.

The semantic space is very compact. In most cases, 4 steps are sufficient. For example:
Body-Alive-Feels-The-Hardness-Of-The-Body.

Let's estimate the size of the semantic space. Let's assume that the multidimensional dimension depends on 12 semantic relations.
Then:
4^8 = approximately 65k variants.
8^8 = approximately 16 million variants.
On the other hand, there are many semantic chains that contain more links. For example, from biology: body ^ live ^ plant ^ tree ^ coniferous ^ Christmas tree.

3.20. Dialectics, Logic and theology
The logical subspace is already well described. It is based on dichotomies:
1. Abstract - Concrete,
2. Absolute-Relative,
3. Homogeneous-Structural,
which give 12 semantic relations.

The theological subspace is still poorly understood.
There are dichotomies:
1. True-False,
2. Good-Evil,

They are related to the logical subspace by the following relations:
1. Objective - Subjective,
2. Information-Emotion.

I tried to identify the 3rd dichotomy, but so far the best candidate is the Male-Female vector.
At the same time, it immediately divides the theological space. An alternative matrix appears:
1. Frankness - Secrecy,
2. Good - Bad.
 


3.21. Fundamental bases of the real and ideal
The semantic relation of Quality provides an interesting model of the structure of reality and abstract, most general relations that form the fundamental basis.

So, the basis of reality:
1. Rest – Movement,
2. Inertia – Interaction,
3. Darkness – Light,
4. Silence – Sound,
5. Void – Matter,
6. A Moment is an Eternity,
7. Place – Space,
8. Personality is a Living Thing.

It is noteworthy that the relationships "One - Many" and "Safe - Dangerous"are typical here. This is the food of the sages!

Now the basis of ideal, most general and abstract relations, combinations of which characterize the concepts of subsequent levels. This basis is represented by pairwise relations that illustrate the main area of applicability.

So, the ideal basis is:
1. Absolute – Relative, Meaning-Concept.
2. Abstract – Concrete, Similarity-Difference.
3. Homogeneous – Structural, Analysis-Synthesis.
4. Unambiguous – Polysemous, Relation-Choice.
5. Direct – Reverse, Influence-Follow.
6. Reversible – Irrevocable, Decision-Action.
7. Complement – Transgression, Donor-Acceptor.
8. Combination – Aggregation, Male – Female.

The dimension of this semantic tensor is - 8*2*2 = 32 concepts, rank 5.


3.22. Fundamental types of transgression
There is a broad and important type of semantic relationship that I call Transgression. If we try to generalize this phenomenon, it turns out that the creative function is one, like Birth, and Death can occur for many different reasons. Based on the Invertible - Irrevocable and Absolute - Relative relations, a tensor of fundamental types of transgression is constructed according to the combinatorial principle. Each subspecies corresponds to the "Spirit, Soul, Body, Mind" basis.
Spirit:
Order – Chaos,
Signal-To-Noise Ratio,
True – False,
Serviceability – Breakdown,

Soul:
Good – Evil,
Cleanliness – Dirt,
Holy and Bad,
Blessing Is A Curse,

Body:
Path – An Obstacle,
Health – Disease,
Life and Death,
A Fork In The Road Is A Dead End.

Mind:
Right-Violation,
Mindfulness – Absent-Mindedness,
Hit – Miss,
Luck Is A Mistake.

It should be noted that this basis is chosen intuitively. You may find more accurate words in foreign languages. The dimension of this semantic tensor is 16 * 2 = 32 concepts, rank 5.
 


3.23. Fundamental types of semantic augmentation
Types of semantic additions refer to the basis built on intuitive understanding. However, this is a fairly accurate model.

Spirit, Time, Direct-Reverse:
1. Past – Future,
2. Cause And Effect,
3. Motive – Action,
4. Q & A,
5. Process-Result,
6. Goal – Funds,
7. Possibility – Inevitability,
8. Known – What You Were Looking For.

Soul, Space, Abstract – Concrete:
1. Original – Similar,
2. Main – Secondary,
3. Primary – Secondary,
4. Identity – Equality,
5. Difference – Similarity,
6. Kinship-Reflection,
7. Yav – Dream,
8. Reality Is Fiction.

Body, Matter, Homogeneous-Structural:
1. Form-Content,
2. Body-Substance,
3. Properties – Abilities,
4. Quantity – Quality,
5. Destination Device,
6. Item-Phenomenon,
7. Environment-Inhabitants,
8. A Person is A Collective.

Mind, Energy, Absolute-Relative:
1. Faith – Experience,
2. Right – Obligation,
3. Law – Conscience,
4. Tradition – Innovation,
5. Rule-Exception,
6. Growth – Reproduction,
7. Male – Female,
8. General – Private.
The dimension of this semantic tensor is - 4*8*2 = 64 concepts, rank 6.


3.24. Some semantic opposites and additions
Semantic opposites, additions, and comparisons are often found in many sciences: mathematics, geometry, physics, biology, economics, linguistics, and even psychology.
Separating one type from another is quite difficult. Therefore, I will give them according to the degree of kinship with respect to science or the intersection of sciences.

Math:
More – Less,
Positive – Negative,
Integers – Fractions,
Irrational – Transcendent,
Addition And Subtraction,
Multiplication-Division,
Degree – Logarithm,
Derivative-Integral.

Trigonometry:
Radius-Angle,
Hypotenuse Catheter,
Sine – Cosine,
Tangent-Cotangent.

Geometry:
Point-Line,
Plane-Space,
Straight Line – Curve,
Area – Volume.

Space:
Mid – Edge,
Center-Side,
Near Or Far,
Here-There-Everywhere-Nowhere,
Left – Right,
Top – Bottom,
Ahead – Behind,
Inside – Outside.

Time:
A Moment is an Eternity,
Past – Future,
Earlier – Later,
Now-Then-Always-Never.

A combination of geometry and physics:
Point -To-Vertex, Prick,
Line -Edge, Cut,
Plane – Surface, Beat,
Volume – Body, Explode.



Physics:
Cold – Hot,
Weak – Strong,
Temperature – Pressure,
Period-Amplitude,
Often – Rarely,
Slow – Fast,
Braking – Acceleration,
Speed – Acceleration.

Classification of materials:
Crystals, solid, structural, homogeneous,
Alloys, solid, amorphous, inhomogeneous,
Composites, solid, structural, heterogeneous,
Plastics, solid, amorphous, homogeneous,
Ligature, plane, structural, homogeneous,
Fabric, plane, amorphous, inhomogeneous,
Fur, plane, structural, non-uniform,
Skin, flat, amorphous, homogeneous,

Materials Sciences:
Geology,
Chemistry,
Nanotechnology,
Biology.

Material geometry:
Point, Sand,
Line, Thread,
Surface, Fabric,
Volume, Body.

Here are some more relationships:
Quiet – Loud,
Blunt – Sharp,
Suspension Support,
Attraction – Repulsion.

Smooth – Crooked,
Smooth - Rough,
Glossy-Matt,
Black – White,
Dark – Light,
Dim – Bright,
Monochrome – Color.


4. Part Four, Tensor Grammar
This part was inspired by conversations with Dmitry Anisimov, who is the author of the universal translation system "PRAVDA", the book" The TRUTH about Machine Translation", as well as a number of lectures. Regardless of my work and earlier, Dmitry implemented the operation of multiplying words using tables. Moreover, he constructed a semantic tensor of the 5th rank of verb tense. I believe that this is a serious contribution to Semantic Algebra, along with the contribution of Grigory Reinin and Stanislav Taktaev.

What is a keyword? A phrase is a trajectory in semantic space. If we decompose each word into semantic features, then each such feature will correspond to a certain coordinate in the semantic space. This is a static representation of the phrase.

However, a static trajectory is not enough to reveal the meaning. Because there are homonyms. Then there is not enough information to plot the trajectory correctly. What should I do?
Dynamic members of phrases and predicates come to the rescue. They can be compared to the velocity vector of a point in semantic space. Thus, the phrase is decomposed into a list of coordinate-velocity pairs, which gives a dynamic trajectory. For example:
"I will run" = "I will + Do + Running".
Perhaps this is the most abstract and universal grammatical form of phrases. This is justified by the sign system of deaf-mute people. It contains both static and dynamic gestures. However, in practice, it is also more convenient to have a national grammatical form.
4.1. Reflections on the grammatical tensor
When parsing phrases in the Russian language, it is better to focus on global semantic groups. That is, immediately divide the semantic space into subspaces.

On the other hand, if we recall the Kholmsky grammars, their matrix is formed by multiplying the vectors "Static - Dynamic" by "Basic - Additional". This has a basis.
However, Dmitry Anisimov showed in his work" The TRUTH about Machine Translation " the effectiveness of a different, 6-link grammar. But I have not found a systematic justification for this approach. This is the question of whether the grammar of a phrase should consist of tensor elements. Is there a grammatical tensor?

Here is the raw material for developing the grammatical tensor of the Russian language:

Noun : Static * Basic,
Verb : Dynamic * Basic,
Adjective : Static * Additional,
Adverb : Dynamics * Additional,

Pronoun : person, attribute, subject,
Numeral : number, order,collective,

Preposition, Specific information,
Union, Abstract information,
Particle, Specific emotion,
Interjection, an abstract emotion,

( , ) – ( - ),
( : ) – ( ; ),
( ! ) – ( ? ),
( . ) – ( … ),

( () ) – ( «» ),
( paragraph ) – (chapter) ...

There is a suspicion that it is necessary to construct separately universal and national grammatical tensors.
At the same time, it is important to synchronize national semantic spaces.

4.2. Intonation, comprehension mechanism, and reverse tense

This chapter is inspired by Anna Verzhbitskaya's "Metatext in Text", Raimon Lullia's combinatorial machine, and Sergey Pshenichnikov's "Algebra of Meaning" article. This topic relates to research in the field of psychology of text perception in particular and the mechanism of understanding in general.
Understanding the text is impossible without intonation, which is achieved by metatext, punctuation, pronouns, repetitions, rhyme, and similar means.
There is a contour of external events – the process of reading and the internal contour of contemplation. Internal commentary occurs even without reading the text, and can be expressed in the form of internal contemplation. Before our eyes, we see the text, and in our inner eyes-pictures of what is happening in what we read.
Presumably, there is a third-internal circuit of strategic thinking. It is he who corrects the work of the tactical action circuit, controlling the processes of excitation or inhibition of the cerebral cortex.
Thus, perception in the second circuit can be accelerated or slowed down. We perceive time subjectively-sometimes running ahead, sometimes floundering in memories.

Imagine 3 spinning wheels or 3 endless belts. It's a bit like a Turing machine. However, the founder of this model was Raymond Lully – a theologian and philosopher of the 13th century. He designed a combinatorial machine consisting of 3 rotating wheels. This made it possible to generate new concepts based on attributes.

Some flag events can affect the position and speed of rotation of these wheels and their mutual coupling.
Naturally, the language is full of flag words that affect attention – the wheel of tactical actions.
Further, these flag words form a semantic tensor. For example:
Sooner, Later, Now,
Now, Then, While,
Here, There, Here,
Pay Attention, Remember, Imagine.

However, I have a hypothesis that the third internal circuit of strategic thinking is not a circuit at all, but a reverse flow of signals from the future to the present moment. I devoted my article "Complex Physics"to this topic. It is based on the curious conclusion of scientists who developed a physical string theory that allows information to spread from an arbitrary future to the present moment. They say that physicists called these signals Spirits, began to study theology and believed in the existence of God.
Understanding, creative activity, and creativity are based on the reverse flow of time. All ethics and morals, intuition and prophetic gift-are based on signals from the future. Angel in translation means Messenger.
The reverse flow of time dialectically complements the causal mechanism. The universe needs this to stabilize the historical development of civilization, so that heat death, global catastrophe, chaos or apocalypse do not occur. The Book of the Apocalypse has the essence of a Catechon, meaning a ban on certain events that should not happen.

I assume that the reverse flow of time is perceived only by living organisms. This allows them to understand, have a personal and collective consciousness, and most importantly-to evolve. Darwin was right in his theory of evolution about the origin of species. Only evolution is not a random process of stupidly sorting through all possible options, but a purposeful search for optimal options. After all, the opponents of Darwinism did not find intermediate forms of organisms. They just weren't there. A dinosaur egg hatched a chicken, a bird egg hatched a penguin, and a dog gave birth to a whale.
An explanation of the mechanism of perception of signals from the future can be found in the theory of parallel reality, the existence of which is confirmed by practical experiments of biophysicist Simon Schnoll. He made many measurements in processes of different nature, in electricity, chemistry, and atomic reactions. And everywhere he found a characteristic distribution of results, depending on the place and time of the experiments. All this indirectly confirms and justifies the need for a reverse flow of time.

 


5. Part Five, Applied
In this part, I begin to give examples of classifications based on semantic tensors and gradients. Each semantic cube is preceded by the chapter sequence number and the conditional cube sequence number in parentheses. This is done for simplicity and for references to columns in the corresponding tables.

Each chapter relates to a specific science or area of expertise. Further, these chapters should correspond to the classification of sciences based on global semantic groups.

Stochastic data: Empirical data:
Bodies – Mechanisms, Movements-Stresses,
Letters – Words, Signals-Messages,
Substances – Organisms, Feelings-Sensations,
Notes – Melodies, Reflexes-Imagination.

Axiomatic ones: Mystical:
Numbers – Numbers, Work-Achievements,
Coordinates-Forms, Communication-Collaboration,
Operations – Operators, Memorization-Imitation,
Equations – Functions, Forecasting-Creativity.

Knowledge and experience levels:
Stochastic, Concrete, Intuitive,
Empirical, Concrete, Logical,
Axiomatic, Abstract, Logical,
Mystical, Abstract, Intuitive;

Stochastic disciplines require multiple repetitions of experience to get good results. They are almost impossible to generalize, interpolate and extrapolate. There are many exceptions to the rules of such sciences.
Empirical disciplines allow us to identify approximate patterns and use them repeatedly in limited conditions.
Axiomatic disciplines. This is math. Pure absolute abstraction. It is very convenient for repeated use.
Mystical or spiritual disciplines. They depend on personal experience and many factors that do not lend themselves to logical comprehension.

Now let's select the closest disciplines:
Stochastic data: Sports, Linguistics, Chemistry.
Empirical data: Physics, Psychology, Biology.
Axiomatic ones: Mathematics, Computer Science, And Semantics.
Mystical (duh.): Politics, Art, and Theology.

4 types of disciplines come from dichotomies:
1. Concrete - Abstract,
2. Emotional - Informational.

1. Stochastic - Concrete and Emotional,
2. Empirical - Concrete and Informational,
3. Axiomatic - Abstract and Informational,
4. Mystical - Abstract and Emotional.

Other sciences can be obtained by semantic multiplication of basic disciplines.
For example:
Physics * Geometry = Construction,
Physics * Trigonometry = Theory of vibrations,
Linguistics * Logic = Semantics,
Art * Trigonometry = Music,
Music * Physical Education = Dance.

It was a classification of disciplines in terms of level of knowledge and experience. A separate classification of disciplines will be obtained when they are divided into groups: Body, Soul, Mind, Spirit.

Most semantic tensors are identified at stochastic and mystical levels of knowledge. This can be seen from the material of the application part. This is a strange result, because at these levels a person works thanks to intuition.
5.0. Semantic Algebra in Life
Some new semantic tensors come to mind.
There is such a semantic gradient of Character and Attitude to personality:
1. Tenderness,
2. Softness,
3. Pliability,
4. Flexibility,
5. Elasticity,
6. Hardness,
7. Stiffness,
8. Cruelty.

And often Tenderness turns into Cruelty and back again!

Switching speeds in life:
1. Sleep,
2. Daydreams,
3. Awakening,
4. Charging,
5. Cheerfulness,
6. Trip,
7. Work,
8. Avral.

This is not a Balance or a Golden Mean at all.
Here = Compliance with the situation = Adequacy:
To do this, you need to be Here and Now.
And the balance and the golden mean – I wrote about the Sins and Virtues.

Valuable ST (semantic tensor):
Each person has Their own:
0. Holy things and abominations,
1. Virtues and sins,
2. Exploits and vices,
3. Achievements and omissions,
4. Strengths and weaknesses,
5. Joys and sorrows,
6. Friends and enemies,
7. Followers and persecutors...

Valuable SV (semantic vector):
I try to restore Order and Cleanliness, Peace and Tranquility:
0. in your head,
1. in their belongings,
2. in your home,
3. where you are a welcome guest...

I have a friend - Sasha Grinevich.
We rubbed shoulders on the physics forum.
The forum was banned, and Sasha went into esotericism.
But we correspond with him.


Now I consulted him a little - and immediately 2 semantic tensors were born:

0. fields and particles,
1. nuclei and atoms,
2. compounds and molecules,
3. organics and polymers,
4. bacteria and viruses,
5. plants and insects,
6. animals and fish,
7. man and birds (spirits).

More precisely, it will look like this:
0. fields,
1. particles,
2. cores,
3. elements,
4. connections,
5. molecules,
6. polymers,
7. organic products,
8. viruses,
9. bacteria,
10. plants,
11. insects,
12. pisces,
13. birds,
14. animals,
15. people,
16. planets,
17. stars,
18. galaxies,
19. the universe,
20. God.

Well, I missed that one:
quarks,
bosons-mesons,
seaweed mushrooms,
the plant and animal kingdoms are also strongly divided into species-subspecies,
satellites,
comets,
cepheids...
5.1. Classification of literary works and speech styles
1. "Conversation or Email" (2 options).
2. Author's age: "Childhood, Youth, Maturity, Old Age" (4 variants);
3. Awareness of the author (must correspond to the age):
"Beginner, Amateur, Pro, Expert" (4 options);

4. Socionic model of presentation (8 variants):
1. Humanitarian,
2. Historical,
3. Scientific,
4. Educational,
5. Religious,
6. Social,
7. Management,
8. Propaganda.

If we ignore the gender of the source, we get:
multiplying variants of semantic vectors!
2 * 4 * 4 * 8 = 256 STYLE options!

Go further -: What does the author write about (4 options) ?:
0. About the future,
1. About the past,
2. About the present,
3. Fiction.

What is the author's gender (2 options)?: Male - Female.

What is the author's attitude (4 options)?:
0. Friendly,
1. Humorous,
2. Sarcastic,
3. Satirical.

What is the author's goal (8 options)?:
0. Informing,
1. Entertainment,
2. Speculation,
3. Advertising,
4. Instruction,
5. Teaching,
6. Refutation,
7. Justification.

Multiplying semantic options := 4 * 2 * 4 * 8 = 256 additional style options!

TOTAL:
256 Basic styles * 256 Additional styles =:
=: 65536 styles!!!

Any worthy literary work should be considered as a matryoshka doll (also a semantic tensor). This can easily be shown in the literature.
Matryoshka works (1.1):
Design, Vehicle, Body,
Atmosphere, Style, Soul,
Plot, Genre, Reason,
Morals, Morals, And Spirit.

On the right side, I added a semantic matrix:
Human device matrix:
Body, - Growth Carrier,
Soul, - the carrier of Reproduction,
Mind , - the Rider of Growth,
Spirit, - Breeding Rider.
This matrix plays a big role in classifications. It is borrowed from the work of Luka Voino-Yasenetsky "Spirit, Soul and Body", and is supplemented with a component of the Mind.
The shown matryoshka doll (1.1) of works elegantly reveals the philosophical question of form and content. This is very interesting because for each level of the matryoshka doll there is a corresponding semantic tensor of rank 3 (Cube), which I give below.

Cube Design and Tool (1.2):
Painting, Dance,
Music, Poetry,
Literature, Game,
Science, Design;

Kuboslovo Atmosphere and Style (1.3):
1. Persistent, Intermittent,
2. Bright Muted,
3. Spicy, Mixed,
4. Strong, Weak;

Kuboslovo Plot and Genre (1.4):
Item, Mechanism,
A Creature, An Organism,
Word, Program,
Action, Team;

Kuboslovo Morale and Morality (1.5):
Mining, Danger,
Your Own, Someone Else's,
Important, Outsider
Near Or Far;

The four cubes form a rank 5 tensor (32 components). Memorizing such a tensor is not easy. We need to learn how to display them. It is easier to do this inductively, using associations. But you can only choose the name for the tensor deductively.
You can estimate-how many variants of works does this classification cover? If the product solves one problem in one way, then each cube will give 12 options. And eight to the fourth power, that's 4096 options. Complex pieces will give you more options.
I also want to point out that some tensors are similar to a chain of pairs or a closed sequence. There's nothing strange about it. This is how the selected projection (notation form) of the tensor is displayed.

Kuboslovo of literary mastery (1.6):
Conciseness, Versatility,
Accuracy, Imagery,
Rhythmic, Melodic,
Clarity, Euphony.
5.2. Classification in music
Here is an example of how to create
a feature system for music from 4 pairs of antagonists (2.1):
Static, Dynamic,
Cyclicity, Uniqueness,
Structure, Randomness,
Melodic, Rhythmic;

Now you can combine these attributes into 16 main musical styles.
Here is an example of 8 styles (cube 2.2):
Song, Dance,
Birdsong, Nature sounds,
Meditative, Spiritual,
Classical, Marching.

They are conditionally derived from 3 attributes: Origin, Purpose, and Action.
These signs can be divided into pairs of antonyms:
Origin: Natural, Artificial,
Purpose: For the soul, For the body,
Action: Soothing, Stimulating,
Role: Independent, Accompanying Information.

Here is the feature system for sounds (2.3):
1. Timbre: Stable, Vibrating,
2. Height: Low, High,
3. Attack:     Smooth, Sharp,
4. Volume: Quiet, Loud,

Thus, the field of music can be studied through semantic analysis. This is a work for a musicologist, to whom I want to ask the question: Why did the octa, and not the septima, indicate 7 notes?


5.3. Classification in literature and structure of myth
At one time I wrote reviews of the work of some of the site's authors proza.ru. I noticed that I intuitively divide the text into 4-5 paragraphs. Then I was faced with the task of giving a simple classification of a work or creation, so that the reader could easily find what interests him.
To begin with, I wrote out all the genres in a column. Then I selected the size from them. Then, he began to reason: historical and fantastic... past and future. So it turned out the first four. Then, acting in a similar way, I deduced a number of characteristics.
Here's what happened (3.1, 3.2):
Time: Past, Future, Reality, Fiction,
Mood: Serious, Funny, Complex, Simple,
Image: Beautiful, Scary, Right, Ugly,
Goal: Explanation, Mystery, Love, Villainy;

Now we count the number of options. If the product solves one problem in one way, then we get:
4 to the 4th power = 256 options.

Next, I propose to consider the Myth model:
The mathematical model of a plot is a graph with edges – plot lines, and vertices – plot situations. A narrative is a route for traversing this graph. The main route is taken by the main character, and individual branches of the route may correspond to the behavior of secondary characters. So the route is a tree.

When the hero moves from one situation to another,
the following vector occurs:
Motivating reason (goal),
Selected action,
Achievement, (Attitude),
Retribution, (Response);

It should be noted that achieving (3) is not equivalent to eliminating the cause of (1). Now we expand each component of this vector.

The vectors of Cause, Action, Relationship, and Response
form the following matrix (3.3, 3.4):
Challenge, Battle, Demand, Gift,
Need, Bribe, Request, Favor,
Call, Service, Promise, Service,
Boredom, Elimination, Sharing, Attention,

Here you should pay attention to the fact that through the line of the matrix (Boredom - Attention), the reader himself is involved in the action of the plot.
The second point is that (despite the line-by-line correspondence in this matrix) each column forms an independent vector of plot variants. So, for example, a hero can go from a Summon to a Battle, then go to a Request, and get a Favor in return.

What should I do? Who does it? Level:
Fight-Eliminate, Strong-Stupid, Attack,
Demand - Ask, Brave-Poor, Appeal,
Bribe - Promise, Rich-Cowardly, Patience,
Bypass-Cheat, Smart - Weak, Care,

The resulting matrix considers the layer of Direct development of events. In addition, there are other development options. This determines the development vector of events:
"Direct, Positive, Negative, Collateral".

Now, if we multiply the matrix by the event vector, we get the semantic Myth tensor (rank 6 tensor = 3 dimensions * 2 binary power of 4 variants).
It should be noted that the behavior of a mythical hero consists of 4 variants, while the behavior of a real person is based on 8 variants. The answer is that a real person has an inner eye, hearing, etc. – that is, all the feelings that occur inside a person. The mythological hero does not possess them. Well, if the author reveals the inner feelings of the hero, then this is no longer a myth.

Matrices for positive and negative developments are formed from antagonistic pairs.
It is more convenient to write them in the form of a tensor 4*8 (3.5, 3.6, 3.7, 3.8):
Brave, Victory, Valiant, Admiration,
Cowardly, Defeated, Shameful, Outraged,
Rich, Honest, Righteous, Understanding,
Poor, Mean, Spoiled, Bewildered,
Strong, Labor, Glorious, Gaining,
Weak, Cunning, Despicable, Loss,
Smart, True, Knowledge, Interest,
Stupid, Deception, Delusion, Surprise;

Expand the side event development tensor
(context matrix 3.9, 3.10):
Childhood, Craving, Polite, Impression,
Youth, Friendship, Respect, Prosperity,
Maturity, Experience, Dignity, Love,
Old Age, Wisdom, Generosity, Glory;

Pay attention to the fact that the reader leaves the myth through the last column.

When interacting with an inanimate force, the following situations may occur:"Warning, Obstacle, Danger, Attack".
In such cases, the following reactions are possible:
"Escape, Use of force, Use of ingenuity, Help of a friend (Mutual assistance)".
The use of these agents is possible in combination.

All. The semantic Myth tensor is ready. This is a necessary (but not sufficient) basis. You can use it to build scenario generators in adventure games.

Let's consider another option for using semantic tensors: analysis of literary works. To do this, we construct an orthogonal semantic space based on gradients such as:
"Care, Patience, Conversation, Attack",
"Thoughtfulness, Taciturnity, Talkativeness, Talkativeness."

Now you can decompose the behavior of the characters of the work according to this basis and build graphs (trajectories): status from time to time. The combination of such graphs will give a cast of the work, which will reflect the tempo: introduction, beginning, climax, denouement. Then, on the basis of such casts, you can study the genre and stylistic affiliation of works.
When choosing a semantic basis, you should know that some concepts are decomposed into several factors, for example:
 Aggression = Activity + Right.
 Courtesy = Rules + Hierarchy.

I would also like to add how myth determines the evolution of the epochs of civilization.
Look at the following classification (3.11):
A Perfect Mechanism, A Magical Thing,
A Perfect Organism, A Magical Creature,
A Perfect Plan, A Magic Word,
A Perfect Team, A Magical Act.

The goals of the epochs are specified here. Epochs of Perfection are interesting to men, but they are replaced by epochs of Magic that are interesting to women. A number of epochs are called Magical, because people are not able to know and understand all the phenomena of what is happening.
We now live in an era of Perfect Mechanisms, which will be replaced (most likely) by the era of Magical Things, when the complexity of gadgets will be beyond human understanding.
Each epoch has its own set of MYTHS. Whatever we call them - fairy tales, legends, or fantasy.
5.4. Semantic algebra in Engineering

Permanent or Managed (4.1):
"Resistor, Diode or transistor, Capacitance, Inductance".

Control type:
1. Mechanical or Electrical equipment,
2. Manual or Automatic,

Cubology of the element's role (4.2):
1. Connection, Switch,
2. Source, Load,
3. Sensor, Effector,
4. Controller, Indicator;

Oscillation characteristics (4.3):
"Frequency, Amplitude, Phase, Duty Cycle".


Cubology of signal propagation (4.4):
Transmission, Reflection,
Gain, Absorption,
Broadcast, Registration,
Modulation And Demodulation.


Static semantics and peripherals (4.5):
Device type =
 (I / O)
* (Serial - Parallel)
* (Private - Shared):
Remote, Input, Serial, Private,
Scanner, Input, Parallel, Private,
Earphone, Output, Serial, Private,
Screen, Output, Parallel, Private,

Microphone, Input, Serial, Shared,
Camera, Input, Parallel, Shared,
Columns, Output, Sequential, Shared,
Printer, Output, Parallel, Shared,

Dynamic semantics in the evolution of technology:
Matter + Form = Object,
Item + Composition = Device,
Device + Mobility = Mechanism,
Mechanism + Drive = Machine,

The leap from mechanical machines to electronic ones (revolutionary change revolutionary change) can be written as follows, using the example of an adding machine:
Adding machine = A computer.
Computer = Adding Machine * Electronics / Mechanics.

Further, the evolution of machines branched out. While about the computer:

Digital direction:
Machine + Algorithm (Memory) = Controller,
Controller + Arithmetic = Calculator,
Calculator + Logic = Processor,
Processor + Peripherals (Interfaces) = Computer,

Analog direction that returns to digital technologies:
Machine + Setup = Automatic,
Vending machine + Communication = Phone,
Phone + Radio = Radio Station,
Radio Station + Battery = Radiotelephone,
Radiotelephone + Modem = Digital (radiotelephone),
Digital + Radio Network = Cell phone number,
Cellular + Compact = Mobile Phone,
Mobile phone number + Computer = Smartphone,

The concept of "Robot" has changed throughout the evolution of technology. Modern " Robot = Machine + Smartphone".

In general, the machine can operate on various physical phenomena and their combinations, for example (4.6):
Acoustics, Optics,
Mechanics, Thermodynamics,
Electricity, Magnetism,
Chemistry, Organics.

The machine can be either analog or discrete at different levels. For example, RNA and DNA chains are discrete chemical mechanisms.

And here is an example that I called a semantic derivative:
From Growth comes Regeneration and Self-healing.
Reproduction causes Mutation and Adaptation.
All these properties are inherent only in living organisms. I think that the modern civilization of perfect mechanisms is developing towards the maximum approximation of machines to the living in their capabilities. However, I doubt the necessity and correctness of creating new organisms. Most likely, it will be a civilization of magical things.

5.5. Semantic algebra in Psychology
Let's consider semantic tensors of psychology. It includes information on psychology, theology, and socionics, because they fit well with the rest of the matrices. Here, word order matters for all tables. To track this, just match the strings with the same number.
The main tensor is derived based on multiplication of vectors:
"I am the Environment", "Growth-Reproduction".
Growth means territory, resources, knowledge, and technology.
Reproduction means partners, offspring, comfort, and safety.
Growth * Reproduction = Health.

Let's write down the matrix from socionics:
Intuition is about changing the environment in order to grow.
Sensorics are changes in the environment for the purpose of reproduction.
Logic is about changing yourself for growth.
Ethics is about changing yourself for the purpose of reproduction,

Note that this feature structure can be used for classification in biology.
For example:
Crystals - changing the environment for growth, (Intuition),
Viruses - changing the environment in order to reproduce, (Sensory),
Plants - changing themselves for growth purposes, (Logic),
Animals - changing themselves for the purpose of reproduction, (Ethics),

Bacteria = Crystals + Viruses.


Accordingly, the matrix of the human device:
1. Body, - Growth Carrier, (Organs), Sensorics,
2. Soul, - carrier of Reproduction, (Hormones), Ethics,
3. Reason — - rider of Growth, (Nerves), Logic,
4. Spirit, - rider of Reproduction, (Society), Intuition,

Now we multiply this matrix by the vector "Quotient - General",
here you need to go down to specific areas of activity:
1. Work, Production,
2. Craft, Art,
3. Discovery, Knowledge,
4. Love, Communication,

We write out paired values.
Hyperword activity-dignity:
1. Work, Prosperity,
2. Production, Reputation,
3. Creativity, Independence,
4. Art, Prestige,
5. Discovery, Authority,
6. Knowledge, Erudition,
7. Love, Charm,
8. Communication, Friendliness.

Let's change the order to preserve the correspondence with other tensors (which was formed during the research):
Charm,
Friendliness,
Reputation,
Independence,
Affluence,
Prestige,
Authority,
Erudition.

Human device matrix:
1. Body, - carrier of Growth, Work, Functionality,
2. Mind — - Growth Rider, Neighbors, Ability,
3. Soul, - carrier of Reproduction, Family, Well-being,
4. Spirit, - Breeding Rider, Hobby, Behavior,

Growth + Time = Size + Update,
Reproduction + Time = Quantity + Education,

Now we multiply this matrix by the vector "Private — General".
Hyperword value and mood (5.0):
Value: Mood:
1. Impression, Interest, Soul, Private,
2. Communication, Gratitude, Reason, Privacy,
3. Freedom, Calm, Spirit, Private,
4. Love, Happiness, Body, Private,
5. Affluence, Generosity, Body, Public,
6. Influence, Generosity, Spirit, Public,
7. Wisdom, Confidence, Reason, Public,
8. Glory, Dignity, Soul, Public;

 Value: Status: Achievement: Goal:
1. Impression, Private, General, Growth,
2. Communication, Private, General, Reproduction,
3. Freedom, Private, Personal, Growth,
4. Love, Private, Private, Reproduction,
5. Wealth, Public, Personal, Growth,
6. Influence, Public, Personal, Reproduction,
7. Wisdom, Public, General, Growth,
8. Fame, Public, General, Reproduction;

Here, the order corresponds to the projection of the cube into the stages of life:
Childhood, the desire for Impressions and Communication,
Youth, striving for Freedom and Love,
Maturity, desire for Wealth and Power,
Old age, the pursuit of Fame and Wisdom.

How do I choose a configuration for a certain stage of my life?
Creativity - Wealth,
Culture -Communication,
Society - Religion,
Family - Friendship.

The table has 4 rows. You can select either the left or right element in each row, but only 2 elements are selected on the left and right sides. And your loved one (parent, descendant, or spouse) will make the opposite choice. Only then will the system be balanced.  However, it is easier to adapt to the partner's configuration.

Now, we write out the projections of the tensor (5.0) on the matrix
"Body-Soul-Mind-Spirit":
Value tensor(5.1, 5.2, 5.3, 5.4):
0. Body, Soul, Mind, Spirit,
1. Spectacles, Adventures, Insights, Impressions,
2. Dating, Creation, Thinking, Communication,
3. Affection, Desire, Interest, Love,
4. Rest, Dream, Fiction, Freedom,
5. Wealth, Acquisition, Satiation, Affluence,
6. Power, Taming, Subjugation, Influence,
7. Knowledge, Experience, Teaching, Wisdom,
8. Fame, Understanding, Observation, Attention,

The order is changed so that the vertices of the cubes correspond to the stages of development by age: "Childhood, Youth, Maturity, Old Age".

Psychological types (16 types) are shown by 8, as active and 8 – as passive. Males and females have a diametrically opposite distribution.

Hyperwords of psychological types (5.5, 5.6):
Men's active, Women's active:
1. Manic, Depressive,
2. Extraversion, Introversion,
3. Masculinity, Femininity,
4. Complacency, Unbridled behavior,
5. Avarice, Extravagance,
6. Hypochondria, Hysteria,
7. Impulsivity, Psychasthenia Gravis,
8. Rigidity, Schizoidness,


The same goes for mental disorders.
Hyperword of mental disorders (5.7, 5.8):
Selfishness: Altruism:
1. Boredom, Apathy,
2. Vexation, Shame,
3. Envy, Resentment,
4. Arrogance, Humiliation,
5. Avarice, Extravagance,
6. Jealousy, Sadness,
7. Anger, Anxiety,
8. Despair, Guilt.




Hyperword of the main sins and virtues from the works of Ignatius Bryanchaninov (5.9, 5.10):
1. Despondency, Sobriety,
2. Gluttony, Abstinence,
3. Fornication, Chastity,
4. Pride, Love,
5. Avarice, Non-Covetousness,
6. Sorrow, Blissful lament (catharsis),
7. Anger, Meekness,
8. Vanity, Humility,

The cube of sins is laid out on the following bases (6 faces of the cube):
Greed – Extravagance,
Carelessness – Pickiness,
Don't Give a damn – Scaremongering,
(Superficiality - Obsession).

This is where depression, schizoidism, epilepsy, paranoia, and panic attacks are rooted.

From here we also deduce 3 fundamental qualities:
1. Moderation, in Fun and Consolation,
2. Mindfulness, in Motivation and Stimuli,
3. Endurance, in Prohibitions and Laws.

Now read more:
1. Discouragement, Extravagance, Carelessness, Alarmism,
2. Fornication, Extravagance, Carelessness, Indifference,
3. Vanity, Extravagance, Pickiness, Alarmism.
4. Sadness, Extravagance, Pickiness, Whatever,
5. Gluttony, Greed, Carelessness, Alarmism,
6. Anger, Greed, Carelessness, Not Caring,
7. Pride, Greed, Pickiness, Alarmism,
8. Avarice, Greed, Pickiness, Whatever;

Now, when we put the fundamental qualities in the cube of virtues, we find that they lack some qualities other than the virtue of Chastity.

1. Humility, Moderation,
2. Sobriety, Moderation, Attention,
3. Non-Possessiveness, Moderation, Self-Control,
4. Chastity, Moderation, Attention, Self-Control,
5. Abstinence, Endurance,
6. Love, Attention, Endurance,
7. Catharsis,
8. Meekness And Attention.

These semantic tensors clearly show how tensor algebra can be used to test scientific and theological postulates.
In psychology, there are many classifications for personality types and disorders. However, theology describes and classifies this topic much more precisely. Thus, the sin of avarice corresponds to avarice and extravagance. However, psychology considers these phenomena of the psyche separately and then, in popular literature. It was necessary to expand the classification from psychologists in order to draw clear parallels. And this is very important! After all, in Hindu teachings about the chakras, this issue is also silent. But money acts on a person like a hormone that is firmly embedded in his nervous system. The relationship with money affects your well-being, affects your metabolism. It's not a secret.

It should be noted that the so-called sins are not mistakes, unless it is a simulation and pretense. Sins are often symptoms of mental illnesses resulting from the systematic violation of spiritual laws (commandments).
For example (hypothesis):
Violation, Disease: Symptom:
1. Daydreaming, Manic-Depressive, Despondent,
2. Envy, Humiliation-Arrogance, Parasitism,
3. Irresponsibility, Perversion, Fornication,
4. Judgment, Rigidity, Pride,
5. Dishonesty, Schizophrenia, Hoarding,
6. Betrayal, Psychasthenia Gravis, Anxiety,
7. Lies, Vanity, Talkativeness,
8. Slander, Epilepsy, Anger;

* A number of explanations to the table:
Humility and Arrogance are a couple: empathy and emotivism. It gives rise to Parasitism, as a more general form of Gluttony.
Irresponsibility creates Perversion, like a shift on the Masculinity - Femininity scale.
Dishonesty or Dishonesty breeds Schizophrenia, avarice-the desire to accumulate anything. Whether it's money, books, icons.
Vanity is a shift on the Extroversion-Introversion scale. Either pathological Talkativeness (lies accumulate like a snowball), or pathological silence.
Psychasthenia gravis causes Sadness or Anxiety.

* * The second series of explanations about the variants of manifestation of painful reactions, using the example of Slander-Anger:
Anger is a defender of rights and interests.
It happens that a person imitates anger in order to get something.
Anger is a natural reaction to slander.
If a person foolishly amused himself with slander in his thoughts, then he will later be seized with fits of anger, it will seem to him that he is being slandered.
As a result of their real slander, a person can be severely damaged and get epilepsy. This is intense and gratuitous anger.
The disease can also be transmitted from the parents.
After spiritual study, remorse - it will be an epileptoid, a person will be intuitively drawn to the establishment of truth and the resolution of injustice. Then he can make a good lawyer, a lawyer.
Something like this. This applies to all 8 cases of diseases.

Now about the parallels with socionics. Socionics has a lot of semantic structures, because it actively uses mathematics. Socionics provided a good example for the development of semantic algebra.
Cubology of functions from socionics and goals (Model A, 5.11):
1. Basic, Impression,
2. Creative, Communication,
3. Role-playing, Love,
4. Bolevaya, Svoboda,
5. Suggestible, Affluent,
6. Activation, Impact,
7. Observant, Glory,
8. Demonstrative, Knowledge,

A brain model based on the theory of automated control:
There are 2 neural networks that work as feedback loops.
The first, external circuit works as a parallel processor and is responsible for the perception of reality and control of organs.
The second, internal circuit corrects the excitation-inhibition processes of the first circuit and works as a serial processor for generating algorithms, making predictions, and organizing memories.

The ratio of the operation speeds of these circuits gives a subjective idea of the passage of time.
During sleep, the operation of contours changes to balance the internal contour. If the internal circuit works in reverse time flow during sleep - that is, it looks for a new solution in the present for a specific goal in the future, then this can be taken as a good justification for reasonableness and self-organization.

On the other hand, intelligence and self - organization can be seen as a way to resolve the conflict between growth and reproduction - the fundamental goals of all living things.
Only:
the female sex in the outer loop senses growth signals and outputs reproduction signals.
the male sex in the outer contour receives reproduction signals and outputs growth signals.
And also:
Women build breeding algorithms based on the realization of growth. That is, they use the achievements of civilization to increase their attractiveness and status.
Men build growth algorithms based on the implementation of reproduction.

So we have come to construct a semantic tensor based on semantic vectors:
1. Males - Females,
2. Internal - External, also known as Parallel-Sequential,
3. Growth - Reproduction,
4.Wakefulness - Sleep,
The excessive dimension of the semantic tensor allows you to determine 4 male and 4 female genders in accordance with the timbre of the voice, perversion and the level of the hormones testosterone and prolactin.

Semantic model of personality based on socionics and TAU (automatic control theory):
1. Basic-reception of emotions in the internal circuit,
2. Creative-output of information from the internal circuit,
3. Role-playing-output of emotions from the internal circuit,
4. Painful-reception of information in the internal circuit,
5. Inspired-reception of emotions in the external circuit,
6. Activation - output of emotions from the external circuit,
7. Observational - receiving information to the external loop,
8. Demonstrative - issuing information from the external loop,

Relevant mental states:
1. Rigidity,
2. Schizoidness,
3. Hysteria,
4. Hypochondria,
5. Depressiveness,
6. Manic behavior,
7. Psychasthenic condition,
8. Impulsivity;

Hyperword of the main sins and virtues from the works of Ignatius Bryanchaninov, in order of socionics functions (see 5.9, 5.10):
1. Pride, Love,
2. Vanity, Humility,
3. Fornication, Chastity,
4. Despondency, Sobriety,
5. Avarice, Non-Covetousness,
6. Gluttony, Abstinence,
7. Sorrow, Blissful lament (catharsis),
8. Anger, Meekness;

Here, the order corresponds to the above semantic model of personality. As you can see, what psychologists began to understand only a few decades ago, theologians knew it back in the 18th century!

Please note that a single tensor can be derived in two ways:
Growth – Reproduction, Carrier-Rider, Private – Public, (This is about Spirit-Soul-Mind-Body);
Information – Emotion,
Issue – Receive,
Internal – External,
 (This is about TAU contours-The Theory of Automatic Control).



Kuboslovo of spiritual moods (5.12):
1. Interest,
2. Generosity,
3. Gratitude,
4. Dignity,
5. Generosity,
6. Happiness,
7. Calmness,
8. Confidence;
Here it is interesting how moods correspond to disorders. Disorders are a couple of extremes. And the mood is the golden mean (the balance between them). The mood and doing something useful play a key role in getting out of the disorder.

Hyperword of strengths and achievements (5.13, 5.14):
1. Charm, Peace,
2. Sociability, Friend,
3. Caring, Family,
4. Independence, Home,
5. Prestige, Dobro,
6. Authority, Power,
7. Reputation, Work,
8. Erudition, Really.

Cubology of Mind Functions (5.15):
1. Remembering,
2. Attention,
3. Concentration,
4. Assiduity,
5. Reaction,
6. Forecasting,
7. Planning,
8. Remembering;

Hyperword of Body and Character Qualities (5.16, 5.17):
1. Sharpness, Shutter Speed,
2. Strength, Speed,
3. Smoothness, Romance,
4. Flexibility, Pragmatism,
5. Dexterity, Narration,
6. Plastic, Intrigue,
7. Grace, Aesthetics,
8. Accuracy And Accuracy.

Hyperword of Soul and Character Qualities (5.18, 5.19):
1. Forgiveness, Short Temper,
2. Transformation, Restraint,
3. Repentance, Courage,
4. Awe, Caution,
5. Respect, Justice,
6. Condescension, Generosity,
7. Empathy, Control,
8. Wisdom, Trust;

Hyperword of Qualities of Mind and Character (5.20, 5.21):
1. Observation Skills, Taciturnity,
2. Brevity, Talkativeness,
3. Resourcefulness, Prudence,
4. Determination, Spontaneity,
5. Imagination, Firmness,
6. Talent, Flexibility,
7. Smartness, Compliance,
8. Methodical, Persistent Approach.

This tensor is interesting because it is transformed into a gradient, which is a ring:
1. Taciturnity,
2. Talkativeness,
3. Talkativeness,
4. Prudence,
5. Spontaneity,
6. Improvisation,
7. Hardness,
8. Flexibility,
9. Softness,
10. Compliance,
11. Persistence,
12. Stubbornness;
It is suspected that the topology of this structure corresponds to the edges of the cube. So it has 12 elements.

Hyperword of qualities of Spirit and character (5.22, 5.23):
1. Consistency, Compromise,
2. Reporting, Uncertainty,
3. Mandatory, Guaranteed,
4. Reliability, Simplicity,
5. Modesty, Complexity,
6. Honesty, Rigor,
7. Cleanliness, Friendliness,
8. Loyalty And Integrity.


Passion intensity gradients for emotions and information (5.24, 5.25):
1. Love, Interest,
2. Adoration, Desire,
3. Sympathy, Desire,
4. Need, Lust,
5. Dependency, Saturation,
6. Necessity, Satiety,
7. Slavery, Satiety,
8. Hatred, Disgust;

Aggression-terror gradient (5.26):
1. Aggression,
2. Hate,
3. Anger,
4. Outrage,
5. Dislike,
6. Fear,
7. Fear,
8. Horror;

Semantic gradient Boldness-Caution:
Short temper,
Courage,
Caution,
Restraint;

Semantic gradient Justice-Rigor:
Generosity,
Justice,
Strictness,
Stiffness.

Semantic gradient Taciturnity-Sociability:
Closed-Mindedness, Thoughtfulness,
Taciturnity,
Sociability,
Talkativeness, Talkativeness;


Semantic gradient Persistence-Compliance:
Persistence,
Hardness,
Flexibility,
Compliance.

Semantic gradient of assertiveness:
Care,
Patience,
Conversation,
Attack;

Hyperword of emotional ratings (5.27, 5.28):
1. Pleasant, Painful,
2. Attractive, Disgusting,
3. Useful, Harmful,
4. Curative, Pernicious,
5. Funny, Scary,
6. Reliable, Dangerous,
7. Creative, Destructive,
8. Good, Evil;

Hyperword relations of mental states and military tactics (5.29, 5.30):
1. Alarm, Danger,
2. Worry, Hindrance,
3. Irritation, Counteraction,
4. Jealousy, Infidelity,
5. Arousal, Mobilization,
6. Calmness, Readiness,
7. Satisfaction, Reinforcement,
8. Consent, Surrender;

So. Here I have given more than 30 semantic cubes on psychology. Brought almost no comments or links. The material is voluminous. Theoretically, it can be expanded to 32x cubes. Then the general tensor in psychology will be rank 8 and will have 256 components. But that's not the main thing. The main thing is reader reviews.
Now there is a groundwork for implementing an explanatory dictionary in the textbook.
You can also create an application for working with semantic structures. You can write a dissertation generator. There's a lot that can be done.
In the meantime, I specifically did not describe the logic of combining words in most tensors, so as not to scare the reader off with the volume of material and unnecessary explanations.

How can we explain the deductive way of constructing semantic structures? You can select the attributes and try to multiply them by selecting the options. Only the result will be almost unpredictable. Example:
Literate – Ignorant,
Polite-Impudent.
Now we multiply these pairs:
The Teacher is Competent and Polite,
A Friend who is Literate and Impudent,
The Disciple is Rude and Polite,
A fool is an Ignoramus and an Impudent Person.

I must say that in this example, the projection is ambiguous. To meet this condition, you need to specify one more attribute. Then you can get a rank 3 tensor.

Psychology of relationship perception and the relationship tensor.
When considering different-sex relationships, the following axes play a key role: Past-Future, Reality-Fiction, Friend-Foe, Profit-Loss.

Cube of a woman's relationship to a man (5.31):
1. Ideal, Father,
2. Former, Brother,
3. Spare, Son,
4. Real, Husband;
Here the axes are Past - Future, Reality-Fiction.

Male-to-male Relationship Cube (5.32):
1. Mentor, Father,
2. Comrade, Brother,
3. Subordinate, Son,
4. Friend, Uncle or Nephew;
Here the axes are Mentor – Subordinate, Friend-Foe.

Cube of a man's relationship to a woman (5.33):
1. Sponsor, Mother,
2. Stranger, Sister,
3. Consumer, Daughter,
4. Lover, Wife;
Here, the axes are One's Own and Another's, and the Sponsor is the Consumer.

Female-to-female Relationship Cube (5.34):
1. Older, Mother,
2. Other, Sister,
3. Younger, Daughter,
4. Friend, Aunt or Niece;
Here the axis Is The Oldest – Youngest, The Other-Similar.

For girls, the ideal is to dominate, show your superiority on all issues and crush fools. These are the qualities of a caregiver. For men, the ideal is simply the one who knows how to do something better than anyone else. These are the qualities of a master.
Here you should use the semantic multiplication operation to construct a c-matrix:

1. Female image and female values-Housewife,
2. Female image and male values – Teacher,
3. Male image and male values-Master,
4. Male image and female values – Warrior;

Semantic tensor of different-sex relationships by kinship (rank 4). Here the rule of reasoning is: - What is the name of a Man who behaves like a Father in relation to another Man? - (Mentor).
M-M, M-W, W-W, W-M,
Dad, Mentor, , , Ideal,
Mom, , Sponsor, Senior, ,
Brother, Comrade, , , Former,
Sister, , Alien, Other, ,
Son, Subordinate, , , Spare,
Daughter, , Consumer, Younger, ,
Husband, Friend, , , Real,
Wife, , Lover, Girlfriend, ;

This table shows only the verbal relationship system.
Hidden positions are a nonverbal relationship called a wrong transaction. See Eric Berne's "Games that People Play".
The table is very useful if you interpret this semantic convolution correctly. For example, girls often play the role-playing game "Daughters-Mothers", just sliding along the age scale. For boys, such a game is impossible, because in practice it turns out to be such shoals as: begging, insubordination, snitching or something even worse. However, girls often look for friends among the guys for practice (they just need a psychological simulator).

Perhaps, in addition, we will get a semantic tensor of relations (rank 5): Here the rule of reasoning is: - What is the name of a Man who behaves like a Mother in relation to another Man? - (Preacher).
M-M, M-W, W-W, W-M,
Dad, Mentor, Customer, Educator, Ideal,
Mom, Preacher, Sponsor, Senior, Boyfriend,
Brother, Comrade, , , Former,
Sister, Believer, Stranger, Other, ,
Son, Subordinate, , , Spare,
Daughter, Parasite, Consumer, Younger, ,
Husband, Friend, , , Real,
Wife, Sycophant, Lover, Girlfriend, ;

Here is another semantic tensor responsible for the psychological difference between the male and female genders. Here you can see the difference in relationships to a number of items (5.35):
Relation: For women: For men:
1. Tool, personal, general,
2. Person, personal, general,
3. Home, Personal, General,
4. Food, personal, general,
5. Work, General, personal,
6. Animal, general, personal,
7. Clothing, general, personal,
8. Money, general, personal;

This tensor has 3 axes:
Personal, General,
Means, Purpose,
Profit, Achievement.

This is an unusual tensor, since it is formed from a system of 4 equations of dynamic semantics.
Vehicle type:   Goal:
Tool – Work, Experience – Knowledge,
Animal – Human, Training -Benefit,
Clothing – Home, Protection -Comfort,
Food – Money, Resources – Assets,


For women , the other person is a part of themselves - this is a part-whole relationship (aggregation). For example: "car-body".
For a man-the other person is a kind of self-it is a combination or variation type of relationship. For example: "Christmas tree-birch".

A woman perceives a man as a manifestation of a certain quality. This corresponds to the first semantic relation of the quality type: "silence – sound".
A man sees a woman as his complement. This corresponds to the 6th semantic relation of the type: "form-content".

Continuing the analogy, it should be said that parents perceive children as an inheritance relation of the type: "pond-pond".
And children perceive their parents through a signal-to-noise transgression relationship.
Semantic relations of opposites and comparisons are typical for the perception of inanimate nature.

If you are familiar with the commandments of the Old Testament and the Beatitudes from the Gospel, then you may be interested in the version from semantic algebra.
Here is my opinion (5.36, 5.37):
1. Don't gloat, Don't be ashamed,
2. Do not insult, Do not swear,
3. Don't mock, Don't take revenge,
4. Don't force, Don't give in,
5. Do not do evil, Do not tempt,
6. Do not offend, Do not pretend,
7. Do not abuse, Do not be deceived,
8. Do not exalt yourself, Do not humiliate yourself.


Semantic tensor of psychological states (5.38). Constructed on the axes: "Calm - Excitement", "Internal - External" or "One's Own-Another's", "Constructive - Destructive" or "Rational - Irrational". It is constructed as follows: a person gains or loses access (ownership) to information or a resource. How can he behave and how can he feel?

Consider the pairs constructive or virtue – destructive or sin.
Concern – Concern,
Irritability – Interest,
Carelessness – Sobriety, (Absent-Mindedness-Mindfulness),
Indifference – Contemplation.

The same psychological states can be attributed to the components of socionics:
Intuition: Anxiety and Irritability,
Ethics: Carelessness and Indifference,
Sensors: Concern and Interest,
Logic: Sobriety and Contemplation.

Consider the dynamics of psychological states.
This tensor is formed from semantic gradients (5.39):
1. Worry – Anxiety -Panic,
2. Irritability – Anger – Rage,
3. Carelessness -Melancholy -Apathy,
4. Indifference – Envy -Suicide attempt (?),
5. Concern -Activity -Result,
6. Interest – Participation – Experience,
7. Sobriety -Reflection – Inference,
8. Contemplation -Teaching -Knowledge;

The quality of a person's life can be determined by 8 pairs of criteria, where each pair requires a compromise (5.40):
1. Comfort and Safety,
2. Cleanliness and Order,
3. Prosperity and Care,
4. Growth and Reproduction,
5. Selfishness and Altruism,
6. Necessity and Desire,
7. Reflection and Communication,
8. Training and Upbringing;

It is necessary to speak about the purpose of human existence from the point of view of analytical semantics: it is the accumulation of knowledge and experience, its improvement for transmission to the next generations.
There are 4 phases of this process:
"Perception, Comprehension, Application, Transfer of knowledge and experience".
 


5.6. System-forming structures
Cubes of roles and functions of system elements (6.1, 6.2):
1. Administrator, Solution,
2. Sensor, Perception,
3. Yandex. Explorer, Exchange,
4. Filter, Selection,
5. Effector, Impact,
6. Analyst, Classification,
7. Controller, Approval,
8. Expert, Memory;

Cases represent the faces of a cube (6.3, 6.4):
Nominative, Relation, Observer,
Genitive, Match, Period,
Dative, Addition, Line,
Accusative, Juxtaposition, Plane,
Creativity, Similarity, Volume,
Prepositional, Projection, And Movement.


Hyperword of thought development (6.5, 6.6, 6.7, 6.8):
1. Subject, Content, Topic, Question,
2. Suspicion, Hypothesis, Guess, Assumption,
3. Idea, Thought, Concept, Concept,
4. Axiom, Lemma, Theorem, Statement,
5. Fact, Argument, Argument, Thesis,
6. Discussion, Dispute, Dispute, Analysis,
7. Comparison, Juxtaposition, Analogy, Similarity,
8. Conclusion, Conclusion, Summary, Summary;

Hyperword for system properties (6.9, 6.10):
1. Type, Form,
2. Image, Model,
3. Property, Feature,
4. Character, Direction,
5. State, Value,
6. Position, Value,
7. Method, Function,
8. Behavior, Action.

Hyperword of wave characteristics (6.11, 6.12):
1. Rhythm, Attack,
2. Dynamics, Amplitude,
3. Smoothness, Smoothness,
4. Chaos, Surprise,
5. Cycle, Periodicity,
6. Size, Duration,
7. Progress, Uniqueness,
8. Structure, Similarity.
Hyperword of system-forming characteristics (6.13-6.16):
1. Order, Row, Plan, Justice,
2. Action, Deed, Activity, Reality,
3. Harmony, Law, Equality, Full Rights,
4. Chaos, Chance, Precedent, Opportunity,
5. Limit, Norm, Bound, Equality,
6. Degree, Measure, Level, Dignity,
7. Development, Will, Perfection, Independence,
8. Organization, Way Of Life, Law, Legality;

Hyperword for event characters (6.17, 6.18):
1. Target, Side Event,
2. Main, Additional,
3. General, Private,
4. Global, Local,
5. Natural, Random,
6. Rule, Exception,
7. Cause, Effect,
8. Primary, Secondary;

Cubology for evaluating statements (6.19):
1. Probable,
2. Valid,
3. Defined,
4. Unambiguous,
5. The exact,
6. Correct,
7. Possible,
8. True value.

Comparison Cube tree (6.20):
1. Identical,
2. Similar,
3. Equivalent,
4. The same value,
5. Identical,
6. Similar,
7. Original,
8. Something similar.










Hyperword for property checks(6.21, 6.22, 6.23, 6.24):
1. Reality, Fiction, Imaginary, Apparent,
2. True, False, Imagination, Fantasy,
3. Presence, Absence, Replacement, Change,
4. Excess, Need, Exchange, Transfer,
5. Many, Few, Equality, Identity,
6. Completeness, Scarcity, Level, Degree,
7. Frequent, Rare, Period, Cycle,
8. Constant, Intermittent, Stable, Stable;

Kubalogo of standards (6.25):
Standard, Comparison,
Original, Approval,
Original, Unique,
Standard, Verification.

Kuboslovo of rules (6.26):
1. Universal,
2. Generally accepted,
3. Traditional,
4. Installed,
5. Recommended value,
6. Agreed,
7. Standard,
8. Standard;

System Character hyperword (6.27, 6.28):
1. Conservative, Variable,
2. Stable, Variable,
3. Stationary, Floating,
4. Static, Dynamic,
5. Stable, Mobile,
6. Hard, Soft,
7. Reliable, Deceptive,
8. Solid, Temporary;

Cubology of concepts (6.29):
Object + Phenomenon = Body,
Property + State = Spirit,
Request + Rating = Soul,
Question + Answer = The mind.

This is where dynamic operation occurs. Semantic addition implies some process.
It can be read like this:
The body operates with objects and phenomena,
The spirit operates with properties and states,
The soul operates with queries and ratings,
The mind operates with questions and answers,


Factorization of global semantic groups.

Matching the main parts of speech and their attributes:
Noun, Subject, Main, Static,
Verb, Action, Basic, Dynamics,
Adjective, Property, Additional, Static,
Adverb, State, Additional, Dynamics,

Hyperword for global semantic groups (6.30):
Material:
Objects = Form * Matter
Actions = Function * Matter
Properties = Form * Difference
States = Function * Difference

Ideal ones:
Words = Form * Meaning
Signals = Function * Value
Attributes = Shape * Similarity
Positions = Function * Similarity

Objective data:
Creatures = Reproduction * Growth
Phenomena = Result * Process
Behavior = Reproduction * Process
Ability = Result * Growth

Subjective:
Entities = Reproduction * Quality
Miracles = Result * Effect
Character = Reproduction * Effect
Skills = Result * Quality


In Russian, even punctuation marks form a tensor (6.31):
( , ) – ( ; ),
( ! ) – ( ? ),
( . ) – ( … ),
( «» ) – ( - ).

Kuboslovo biznes (6.32):
1. Product — Service,
2. Resource-Work,
3. Money-Obligations,
4. Rights — Responsibility.

So. It turned out to be 32 system-forming cubes.
I notice two things about them.
Some of these structures are similar to synonyms, but they are not gradients. Some are grouped in pairs to form hypercubes. This suggests that there are signs for such concepts with a fine line of differences.
Some of the above structures do not look like cubes, as if orthogonality is violated here. This is a problem of linguistic projection. Russian has a lot of borrowed words from Greek, French, German, English, and other languages.

System attributes:
1. It consists of the following parts:
2. It has sensors and effectors,
3. Has feedback,
4. Safety margin,
5. Autonomy,
6. Mobility,
7. Adaptability,
8. Manageability,
9. Growth (Regeneration),
10. Reproduction,
11. Learning rate,
12. Awareness;

On the issue of system-forming processes:
1. The system consists of elements. The system-forming process is structuring , i.e. establishing hierarchical relationships between system elements.
2. The system is growing, using new elements, including them. This process is called integration.
3. The system is being improved and adapted. This is an optimization (automation) process.
4. The system interacts with other systems and subsystems. This process is called specialization (symbiosis).

Total: structuring, integration, optimization and specialization-these are the 4 main system-forming processes.

Sources of reaction in the history of civilization:
State,
Nature,
People,
Church.

Social functions:
1. Treatment,
2. Protection,
3. Education,
4. Insurance,
5. Everyday life,
6. Food,
7. Transport,
8. Communication.


5.7. Organization, activity, creativity, etc.

Examples of types of organizations, their goals and leaders (7.1, 7.2, 7.3):
1. Class, Training, Teacher,
2. Family, Upbringing, Mentor,
3. Office, Job, Boss,
4. Team, Achievements, Coach,
5. Society, Recreation, Observer,
6. Club, Cult, Idol,
7. Church, Ministry, Shepherd,
8. Army, Victory, Commander;

Hyperword of impact methods for leaders (7.4, 7.5, 7.6, 7.7):
 Manager, Humanitarian, Scientist, Social Worker,
1. Prove, Present, Communicate, Entertain,
2. Compel, Summon, Exhort, Punish,
3. Indicate, Address, Direct, Lead,
4. Encourage, Encourage, Question, Help,
5. Customize, Inspire, Criticize, Tempt,
6. Signal, Distract, Advise, Mine,
7. Proclaim, Frighten, Bless, Serve,
8. Inspire, Win, Command, Command;

Kubalogo of the scope of activity (7.8):
1. Company,
2. Group,
3. Firm,
4. Community,
5. Production,
6. Organization,
7. Company,
8. A corporation.

Kuboslovo of participants in the activity (7.9):
Customer, Performer,
Employee, Colleague,
Superior, Subordinate,
Sponsor or Benefactor.

Hyperword for evaluating performance and capabilities (7.10, 7.11):
1. Effect, Chance,
2. Achievement, Circumstances,
3. Result, Situation,
4. Benefits, Potential,
5. Value, Stock,
6. Quality, Resource,
7. Record, Conditions,
8. Rating, Opportunity.

Hyperword for activity stages (7.12, 7.13, 7.14, 7.15):
1. Goal, Problem, Question, Task,
2. Work, Work, Business, Occupation,
3. Experiment, Test, Practice, Research,
4. Exercise, Training, Task, Lesson,
5. Finding, Reception, Means, Method,
6. Skill, Experience, Skill, Knowledge,
7. Earnings, Payment, Reward, Bonus,
8. Income, Revenue, Prize, Profit;

Hyperword of relationship participants (7.16, 7.17):
1. Friend, Enemy,
2. Brother, Sister,
3. Wife, Husband,
4. Parent, Child,
5. Employee, Competitor,
6. An Ally, A Rival,
7. Friend, Opponent,
8. A Citizen Or A Foreigner.

Hyperword of communication forms (7.18, 7.19):
1. Monologue, Dialogue,
2. Message, Communication,
3. Report, Meeting,
4. Speech, Meeting,
5. Speech, Negotiations,
6. News, Conversation,
7. Notification, Conversation,
8. Report Or Consultation.

Tensor of creative stages (7.20, 7.21):
Idea, Image, Figure, Motif,
Plan, Project, Sketch, Chant,
Model, Prototype, Sample, Melody,
Product, Product, Creation, Work;

Self-organization scale tensor (7.22):
Family, Existence,
Enterprise, Growth,
State, Reproduction,
Civilization, Development;

Tensor of means of expression (7.23, 7.24):
Digit, Sign, Note, Color,
Number, Letter, Sound, Light,
Equation, Word, Melody, Color,
System, Alphabet, Octave, And Palette.


Kuboslo for evaluating actions (7.25):
1. Entity,
2. Yandex. Tolk,
3. Fortunately,
4. Gift,
5. Benefit,
6. Meaning,
7. Help,
8. Meaning.
Hyperword for Teaching and Upbringing (7.26, 7.27):
1. Contest, Search,
2. Selection, Selection,
3. Motivation, Incentive,
4. Training, Education,
5. Obstacle Course, Training Session,
6. Overcoming, Learning,
7. Verification, Control,
8. Exam, Test;

Criteria for the power of the state are all that strengthens, strengthens, unites, inspires and makes the people of the country happy.
If monetary returns are the measure of decisions, then these decisions will lead to degradation. The true measure is God. However, as they say – hope for God, but do not be bad yourself. I am sure that each State needs to have its own self-assessment tool. And in this case, we will not be able to escape from the complexity. Simple solutions will cost more.
I got 32 criteria that should be included in the calculation of the State's rating (7.28, 7.29, 7.30, 7.31):
1. Demography, Health, Housing, Ecology,
2. Territory, Communications, Transport, Supply,
3. Goods, Products, Resources, Energy,
4. Law, Police, Weapons, Army,
5. Education, Education, Inventions, Research,
6. Religion, Tradition, History, Art,
7. Work, Leisure, Recreation, Medical Treatment,
8. Management, Services, Production, Sports;
Each of these criteria represents a spectrum that can be reduced to quantitative and qualitative indicators.
Kuboslovo complicity-counteraction (7.32):
1. Counteraction,
2. Resistance,
3. Non-resistance,
4. Complicity,
5. Organization,
6. Incitement,
7. Agitation,
8. Order.

Digit-number hyperword (7.33, 7.34):
1. Digit, Number,
2. Letter, Word,
3. Sign, Expression,
4. Value, Suggestion,
5. Calculation, Result,
6. Reflection, Idea,
7. Problem, Solution,
8. Work, Meaning;

Hyperword Man-House, (7.35, 7.36):
1. Food, Medicine,
2. Hygiene, Cleanliness,
3. Clothing, Underwear,
4. Dishes, Furniture,
5. Heat, Cold,
6. Water, Sewerage,
7. Light, Electricity,
8. Communications, Transport;

Hyperword for business processes (7.37, 7.38):
1. Product - Service,
2. Real - Placebo,
3. Single – Replicated,
4. Social – Commercial,
5. Approved – Disapproved,
6. Legal - Criminal,
7. Help - Satisfaction,
8. Paid - Free Of Charge.
Now about the organization of business processes. They are based on the following matrix:
Customer, Performer,
Client, Manager;
Now it is interesting to look at the business development.

The Customer-Client pair. Earned – share! (7.39):
"Friends", Raiders,
Scammers, the Church,
"Doctors", Sorcerers,
Restaurants And Casinos.
Total – spent time and money.

The Manager-Executor pair. Return money to your business! (7.40):
Sociality, Security,
Advertising, Employees,
Technologies, Equipment,
Turnover, Premises;
Total – received profit and respect.


Now about the technological processes:

Material tech-process (7.41):
Material, Effect,
Form, Subject,
Part, Assembly,
Verification And Acceptance.

Ideal Tech Process (7.42):
Task, Analysis,
Project, Plan,
Development, Testing,
Implementation And Support.

Matrix of laws (7.43):
1. Laws That Prohibit, this is gratuitous responsibility,
2. Rules that Prescribe, this is rewarded responsibility,
3. Principles that Motivate, these are rewarded obligations,
4. Traditions that Recommend, these are gratuitous obligations.

Kuboslovo del (7.44):
Scale = Amount * Time Frame,
Situation = Personal * Market,
Reputation = Required * Responsibility,
Prestige = Mass Appeal * Attractiveness.

Unrolling divisions into states and characters (7.45, 7.46):
Rich, Poor, Miserly, Wasteful,
Wealth, Need, Debt, Excess,
Reliability, Gratitude, Perspective, Generosity,
Investments, Savings, Charity, Luxury.

Software evaluation criteria (7.47):
1. Open - Closed,
2. Foreign - Domestic,
3. System - Applied,
4. General – Specialized,
5. Free - Commercial,
6. Escorted - Unattended,
7. Interactive - Background,
8. Library -Plugin.

Components of the company's work (7.48):
1. Motivation,
2. Organization,
3. Planning,
4. Control,
5. Group,
6. Tools,
7. Documentation,
8. Realization.

Stages of work or creativity (7.49, 7.50):
Idea, Intention, Goal, Reason.
Idea, Plan, Project, Model.
Process, Development, Debugging, And Verification.
Result, Implementation, Solution, Product.

Stages of attitude change and evaluation (7.51, 7.52):
Premonition, Prophecy, Prediction, Forecast.
Interest, Participation, Cooperation, Help.
Experience, Reward, Damage, Punishment.
Glory, Blessing, Blame, Curse.

5.8. Nature and Metaphysics
Natural quality tensor (8.1, 8.2):
Matter, Solid, Body, Existence,
Energy, Liquid, Soul, Growth,
Space, Gas, Intelligence, Reproduction,
Time, Flame, Spirit, Development;

Tensor of geometric objects (8.3, 8.4):
Point, Line, Area, Volume,
Coordinate, Axis, Plane, Space,
Mark, Tangent, Normal, Projection,
Length, Width, Depth, Height,

Tensor of motions and deformations (8.5, 8.6, 8.7, 8.8):
1. Motion, Radiation, Evaporation, Condensation,
2. Rotation, Torsion, Whirlpool, Vortex,
3. Convergence, Divergence, Jet, Torus,
4. Shift, Shift, Boil, Bubble,
5. Compression, Stretching, Overflow, Flow,
6. Bending, Deflection, Tension, Traction,
7. Impact, Collision, Current, Rush,
8. Stress, Strain, Pressure, And Density.

Carrier tensor (8.9, 8.10):
1. Space, Territory,
2. Material, Property,
3. Energy, Nutrition,
4. Feelings, Emotions,
5. Memory, Savings,
6. Mind, Technology,
7. Consciousness, Ideas,
8. Time, Life;
Cubic aggregate states (8.11):
Sand, Solid,
Gel, Liquid,
Steam, Gas,
Flame, Plasma.

The universe scale tensor (8.12, 8.13):
Particles, Planets, Hormone, Substance,
Atoms, Stars, Cells, Elements,
Molecules, Galaxies, Organ, Detail,
Domains, Universe, Organism, Mechanism;


Interaction level tensor (8.14):
Particle, Attraction – Repulsion,
Atom, Union -Division,
Molecule, Organization -Restructuring,
Bacteria, Replication – Death.

The three-dimensional time tensor and its aspects (8.15, 8.16, 8.17):
1. Lie, Oblivion, Body,
2. Past, Fact, Feeling,
3. Memory, Truth, Soul,
4. Present, Truth, Emotion,
5. Plan, Intention, Reason,
6. Future, Calculation, Thought,
7. Forecast, Assumption, Spirit,
8. Fiction, Design, Thought;

Please note that this section shows how physical processes relate to mental processes. And they relate directly, without chemistry and hormones.

Hyperword for image characteristics (8.18, 8.19):
Transparent, Mirrored, Smoky, Ghostly,
Monochrome, Color, Faded, Toxic,
Pale, Bright, Dull, Sharp,
Blurry, Contrasting, Matte, Glossy;

Cubology of positions in the space (8.20):
Front, Back,
Inside, Outside,
Left, Right,
Top, Bottom.

Kuboslovo of provisions (8.21):
Center, Edge,
Closer, Further,
Left, Right,
Higher, Lower;

Hyperword of Mechanics (8.22):
Rest, Movement,
Oscillation, Rotation,
Attraction, Repulsion,
Acceleration, Deceleration,
Stretching, Compression,
Bending, Torsion,
Sliding, Rolling,
Impact, Tension;

Cubology of physical structures (8.23):
Particle, Wave,
String, Vortex,
Surface, Jet,
Monolith, Void.

Cubology of touch (8.24):
Hardness, Softness,
Roughness, Smoothness,
Dryness, Humidity,
Cold, Heat;

Kuboslovo Razum-Pravina (8.25):
Reason, Truth,
Mind, Experience,
Abstract, Absolute,
Specific, Relative;


Kuboslovo Difficulty levels (8.26):
1. Geometry, Coordinates, Directions,
2. Physics, Inertia, Speed,
3. Chemistry, Elements, Compounds,
4. Bacteria, Absorption, Reproduction,
5. Plants, Growth, Interbreeding,
6. Animals, Feelings, Emotions,
7. Reasonable, Thoughts, Words,
8. God, Invariance, Projection.
5.9. Scanning semantic groups
Based on the semantic groups (from Chapter 3.10), we will do the following sweep.
Stochastic groups (9.1):
Bodies-Mechanisms,
Letters – Words,
Particles – Substances,
Notes – Melodies.

Empirical groups (9.2):
Movement-Tension,
Signals – Messages,
Feelings – Sensations,
Reflexes – Imagination.

Axiomatic groups (9.3):
Digits – Numbers,
Coordinates – Forms,
Operations – Operators,
Equations – Functions,

Mystical Groups (9.4):
Work – Achievements,
Communication – Collaboration,
Experience-Imitation,
Forecasting – Creativity.

You can expand these groups.
This should give a rank 8 tensor (4 * 8 * 8 = 256 words).

Kuboslovo Bodies-Items (9.5):
Natural, Artificial,
Simple, Composite,
The Living, The Dead,
Real, Perfect Ones.

Cubological Mechanisms-Organisms (9.6):
Existing, Fictional,
Primitive, Intelligent,
Dependent, Autonomous,
Individual Or Group Services.

Kuboslovo Letters-Sounds (9.7):
Concrete, Abstract,
Vowels, Consonants,
Single-letter, Multi-Letter,
Monophonic Or Multi-Colored Items.

Kuboslovo Words-Concepts (9.8):
Special, General,
Synonyms, Homonyms,
Unambiguous, Multi-Valued,
Fictional Or Borrowed Items.


Cubist Particle-Elements (9.9):
Atoms, Molecules,
Inert, Active,
Metals, Non-metals,
Regular, Organic Products.

Cubic Description Of The Substance-Compound (9.10):
Stable, Changeable,
Elastic, Ductile,
Hard, Brittle,
Liquid Or Gaseous Substances.

Kuboslovo Sheet Music-Instrument (9.11):
Flats, Sharps,
Pitch, Timbre,
Volume, Duration,
Bass And Treble Instruments.

Kuboslovo Melodii-Muzykant (9.12):
Minor, Major,
Rhythm, Tempo,
Monophony, Polyphony,
Harmony, Improvisation;


Cubology Of Movement-Trajectories (9.13):
Move, Rotate,
Shift, Zoom,
Forced, Own,
Simple, Complex Ones.

Stress – Strain Cubology (9.14):
Stretching, Compressing,
Normal, Tangent,
Temporary, Residual,
Elastic Or Plastic Materials.

Cubic Signals-Values (9.15):
Attenuations, Amplifications,
Stabilization, Switching,
Natural, Anthropogenic,
Regular, Spontaneous Events.

Kuboslovo Messages-Ideas (9.16):
Warning, Incentive,
Independent, Imposed,
Definition, Thesis,
An Assumption Or Conclusion.

Kuboslovo Chuvstviya – Emotsii (9.17):
Nice, Nasty,
Calm, Anxious,
Pleasure, Pain,
Real Or Imaginary Values.

Kubislovo Sensations-Information (9.18):
Gain, Loss,
Your Own, Someone Else's,
Law, Lawlessness,
Adequate, Far-Fetched Ones.

Kuboslovo Reflexes-Habits (9.19):
Current, Outdated,
Congenital, Acquired,
Aggression, Defense,
Successful Or Unsuccessful Ones.

Kuboslovo Imagination-Solutions (9.20):
Individual, Mass Sales,
Original, Template Versions,
Private, General,
Voluntary Or Forced Actions.


Kuboslovo Numbers-Signs (9.21):
Spelling, Pronunciation,
Verbal, Numeric,
Punctuation, Math,
Comparisons And Divisions.

Cubic Numbers-Values (9.22):
Even, Odd Numbers,
Positive, Negative,
Integers, Fractions,
Irrational, Transcendent Ones.


Cubist Coordinates-Measures (9.23):
Scalar, Vector,
Cartesian, Polar,
Absolute, Relative,
Infinite, Finite Values.

Cubological Forms-Images (9.24):
Simple, Composite,
Angular, Smooth,
Dotted Lines, Linear Lines,
Flat, Three-Dimensional Objects.


Cubology Of Comparison Operations (9.25):
Arithmetic, Logic,
Derivatives, Integrals,
Geometry, Trigonometry,
Discrete Or Continuous Operation.

Cubist Transformation Operators (9.26):
Direct, Inverse,
Reversible, Irreversible,
Tensor, Conformal,
Linear Or Non-Linear Items.

Cubist Equations Of The System (9.27):
Relationships, Inequalities,
Defined, Undefined,
Limits, Rows,
Unambiguous, Multi-Valued Ones.

Cubic Functions-Algorithms (9.28):
Numerical, Analytical,
Exact, Approximate Values,
Simple, Parametric,
Cyclic Or Recursive Operations.


Kuboslovo Work-Result (9.29):
Physical, Mental,
Speed, Endurance,
Tactical, Strategic,
Individual Or Collective Work.

Kuboslovo Achievements-Rewards (9.30):
Current And Promising Issues,
In-demand, Spare Parts,
Commercial, Social,
Explicit Or Hidden Ones.

Cubological Communication-Empathy (9.31):
Симпатия, Likes and Dislikes,
Encouragement, Excellence,
Understanding, Surprise,
Admiration, Annoyance;

Kuboslovo Cooperation-Competition (9.32):
Exchange, Concealment,
Instruction, Teaching,
Mutual Assistance, Responsibility,
Mutual Assistance, Debt;


Kuboslovo Experience-Purposefulness (9.33):
Attention, Concentration,
Memorizing, Remembering,
Planning, Organizing,
Control And Motivation.

Cubological Imitation-Demonstration (9.34):
Conscious, Automatic,
Rehearsal, Impromptu,
Independent, Motivated,
Control, Arbitrary;

Cubic Prediction-Calculation (9.35):
Intuition, Reason,
Local, Global,
Individual, Group,
Short -Term Or Long-Term Use.

Cubological Analysis-Creativity (9.36):
Emotional, Systemic,
Spontaneous, Prepared,
Inspiration, Skill,
Eclectic, Canonical Content.

Kuboslovo of Development and Design (9.37):
1. Planning, Analysis,
2. Organization, Design,
3. Control, Implementation,
4. Motivation, Optimization,

Software quality criteria (9.38)
1. Focus,
2. Convenience,
3. Functionality,
4. Extensibility,
5. Reliability,
6. Security,
7. Performance,
8. Support,

Now we need to deduce the signs and factors that affect this scenario.
There is an assumption that this is:
1. Technical or Managerial issues,
2. Tactics or Development Strategy,
3. Local or Global policy,

1. Productivity, Tech, Strategy, Global,
2. Convenience, Tech, Strategy, Local,
3. Functionality, Tech, Tactics, Global,
4. Extensibility, Tech, Tactics, Local,
5. Focus, Management, Strategy, Global,
6. Support, Management, Strategy, Local,
7. Security, Management, Tactics, Global,
8. Reliability, Management, Tactics, Local;

Spread quadwords (9.39-9.42):

We deploy 1. Purposefulness (conceptuality):
Solve only your own problem,
Do it best,
Protect the client's interests,
Don't create any restrictions for the client,

Deploy 2.Convenience:
Follow the traditions,
Easily do your main tasks,
Don't impose additional features,
Provide sufficient service,

Deploy 3. Functionality:
Simplicity,
Consistency,
Settings,
Embeddability, export of data and tools,

Deploy 4. Extensibility:
Flexibility, programmability,
Zoom level,
Localization,
Import data and tools,

Deploy 5.Reliability:
Protection against incorrect data,
Overflow protection,
Protection against incorrect hardware,
Protection from the fool,

Deploying 6. Security:
Accuracy of calculations,
Data security,
Confidentiality,
Resistance to hacking,

Deploy 7.Performance:
Optimization of calculations,
Optimization of parallelism,
Memory optimization,
Optimization of data transmission,

Deploy 8. Support:
User-friendly interface,
Textbook,
Answers to questions,
"Hotline".


Dynamic semantics equations:
1. Analysis + Planning = Project.
2. Organization + Motivation = Process.
3. Implementation + Control = Result.
4. Setup + Testing = Escort.

So. The resulting system can be called a classification of classifications. Strictly speaking, this is not a tensor, but a group of c-tensors. Here convolutions are observed for different c-groups. However, this does not mean that it cannot be reduced to an orthogonal form. This is a matter of further research.

5.10. Orthogonalization of semantic groups
Let's create an orthogonal semantic tensor based on the group sweep from Chapter 6.8.  The essence of orthogonalization is that you first need to deduce the general features of terms, and then arrange them according to binary combinatorics.

Real systems, (10.1):
Signs, abstract, artificial,
Movement, Abstract, natural,
Crafts, concrete, artificial,
Organisms, specific, natural.

Ideal systems, (10.2):
Books, developing, passive,
Games, educational, active,
Fishing, applied, active,
Laws, applied, and passive.

Signs, abstract, artificial, (10.3):
Digits, Numbers, axiomatic, passive,
Operations, Functions, axiomatic, active,
Letters, Words, Empirical, active,
Punctuation, Punctuation, empirical, passive.

Motion System, abstract, natural, (10.4):
Notes, Melodies, mystical, passive,
Receptions, Dance, mystical, active,
Sounds, Signals, Stochastic, Active,
Grimaces, Facial expressions, stochastic, passive.

DIY System, concrete, artificial, (10.5):
Buildings, static, passive,
Infrastructure, static, active,
Devices, autonomous, active,
Mechanisms, autonomous, passive.

System Organisms, concrete, natural, (10.6):
Bacteria, collective, passive,
Insects, collective, active,
Animals, individual, active,
Plants, individual, passive.


Ideal systems reduce to a rank 4 tensor. For orthogonalization, refer to the system in Chapter 6.5.
1. Interest, Impression, Soul, Private,
2. Communication, Gratitude, Reason, Privacy,
3. Love, Happiness, Spirit, Private,
4. Freedom, Calmness, Body, Privacy,
5. Affluence, Generosity, Body, General,
6. Influence, Generosity, Spirit, General,
7. Glory, Dignity, Soul, General,
8. Wisdom, Confidence, Reason, General.



Book System, developing, passive, (10.7):
Serious – Funny,
Past – Future,
Love Is Villainy,
Reality – Fiction,
Complex – Simple,
Correct – Ugly,
Beautiful – Scary,
Riddle-Explanation.

Game system, developing, active, (10.8):
1. Process-Result,
2. Collective - Individual,
3. Physical - Mental,
4. Speed – Endurance,
5. Real – Time-Automated,
6. Tactical – Strategic,
7. Cooperation – Competition,
8. Luck – Experience.

Fishing system, applied, active, (10.9):
1. Physical - Mental,
2. Collective - Individual,
3. Mining – Processing,
4. Creation – Maintenance,
5. Commercial – Social,
6. Management – Subordination,
7. Dangerous-Prestigious,
8. Research – Training.

Security system, applied, passive, (10.10):
1. Rights – Obligations,
2. Society-An Individual,
3. Suspicions – Accusations,
4. Evidence – The Court,
5. Suppression – Punishment,
6. Legislative – Executive,
7. Presumption – A Precedent,
8. Administrative – Criminal Cases.

Kuboslovo Activity-Awards, (10.11):
Home economics, Comfort, personal, social,
Household items, personal, commercial,
Enterprise, Impression, general, commercial,
Organization, Honors, general, social.

Kuboslovovo Belonging-Environment (10.12):
Race, Kin, permanent, passive,
Nationality, Friends, Permanent, Active,
State, Neighbors, changeable, active,
Work - Religion, Employees, changeable, passive.
 


5.11. Semantics in biology
Semantics provides a fundamental insight into the structure of the semantic model, i.e., how some knowledge should ideally look.
Consider the subject of biology. To begin with, which semantic vector is the main one in biology? An experienced researcher will immediately start digging in the direction of terminology, he will say-what is biology? This is the science of living organisms! What is alive? - give a definition.
Here you can already use semantic algebra. "Living – inanimate" is a Quality relation that is characterized by a number of characteristics. These attributes are related to each other by the Complement relation. Then you should identify signs of living things.
To simplify this task, I propose to consider the simplest living organism-a bacterium. It is necessary to find at least 2 signs that distinguish the bacterium from inert matter, from the environment. It is advisable to do this yourself. In analytical semantics, such tasks have to be solved regularly. This requires some experience, we can say that over time, a laboratory of meanings should appear in your head. This is very important, because it is necessary to identify only 2 concepts that characterize the whole of biology as a whole.
So. Bacteria grow and multiply. Crystals also grow, but do not multiply. Viruses reproduce, but they don't grow. You can argue a lot about this. However, we already have 4 semantic vectors:
1. Oblique – Live,
2. Medium-Bacteria,
3. Growth – Reproduction,
4. Crystals Are Viruses.
Further, we can distinguish the dynamic semantics equation: "Bacterium = Crystal + Virus". This shows how the functions of Growth and Reproduction complement each other.

Now you should add the rest of the live's paired functions:
1. Growth – Reproduction,
2. Recovery – Development,
3. Division – Merge,
4. Absorption – Self-preservation.
The bottom line is that when considering the types of reproduction or types of existence, it is necessary to determine the control factor (Division - Fusion). Then the hierarchy of biological types is written as a tensor.

In addition, I propose to consider the following tensor:
1. "Growth-Reproduction",
2. "Recovery-Development",
3. "Regeneration-Mutation",
4. "Resurrection-Transfiguration".

Using paired attributes, semantic relations, and operations, you can get a classification of living organisms, their functions, attributes, and properties. This is important because it is based on understanding patterns, not being descriptive.
9. Semantic design
Semantic design is a fundamental discipline-a continuation and development of semantic algebra.
Key concepts:
- semantic element.
- semantic construction,
- semantic template.
- semantic program.

A semantic element is a simple concept that is expressed by a word, signal, sign, image, image, smell, taste, and other manifestations of physical reality through feelings and sensations. Thus, the semantic element expresses feelings and thoughts.
Semantic construction – contains several semantic attributes or elements. It can be a sentence or slogan that carries some idea.
Semantic template-is a special case of a semantic construct. It can be a proverb, anecdote, parable, meme, or comic book.
A semantic program is a structure of semantic constructs and elements that defines behavior until a certain result is achieved. A semantic program contains some moral and idea. In its implementation, a semantic program can be a book, a picture, a movie, a sculpture, or a game.

Classification of semantic elements:
Types of semantic elements are divided according to the complex of feelings and sensations that they affect.
Semantic elements differ from each other in their expressive complexity. For example, the length of a word or the complexity of a sign or signal.
There are a subset of service semantic elements that establish relationships between other elements and constructs – conjunctions and punctuation marks.
Some words are easily confused with semantic constructs. For example, the word "female" refers to a middle-aged human female. This immediately combines several signs: the fact that it is a middle-aged person and a female. Therefore, it is a semantic construct.
There are 2 types of relationships in semantic constructs: sequential and parallel. A serial link is a text or meme. Parallel relationships are tables, lists, and enumerations. Ideally, the parallel relationship should be a semantic tensor. In the text, a parallel relationship is usually highlighted using conjunctions and punctuation.

8 semantic functions play an important role in semantic constructions:
Explanation (- this),
Enumeration (and, or),
Alternative (either, or),
Contrast (but),
Cause-effect (therefore, for),
Transition (s),
Accent (that's right),
Similarity (as if),
These primary semantic functions correspond to 8 semantic relations. There are also secondary semantic functions:
Time,
Geometries,
Personalities,
Quantity – quality.
They are divided into direct and indirect ones. In addition, they are all paired. Thus, secondary semantic functions form a rank 4 semantic tensor.
Semantic constructs are based on the semantic tensor. Only the semantic tensor is a parallel structure, and the semantic construct has a sequential structure.

Semantic design can be used to analyze linguistic constructs and generate responses. Semantic decomposition should be used for disassembling sentences, and semantic synthesis should be used for assembling sentences.

A good example of parallel semantic constructions is the timbre and intonation of the voice. What information can be extracted from this, even if we don't know the speaker's language? What we define by timbre:
Who's talking.
What condition is it in?
What he wants.
Whether he believes what he says.
This is well understood by all pets. Musical instruments also transmit this information, but you need to be able to listen.
Semantic constructs can be true or false. They can be unambiguous or multi-valued. Summoning-motivators, or distracting-demotivators.
The perception of semantic constructs and programs depends on the characteristics of the mind. Reason always arises where there is some contradiction or conflict.
The mind of dogs arose out of the contradiction in the relationship between the leader and the pack member. The mind of cats arose from the confrontation of predator and prey. The human mind has emerged from conflicts of interest between sexes, generations, and leaders.

5.12. Semantic technologies
This topic began with the fact that I was reproached on one forum – that I do not understand anything in analogies. And it really was. While working on semantic algebra, I overlooked such concepts as analogy, similarity, and similarity. They didn't fit into the semantic relationship tensor in any way.
It turned out that drawing analogies is a side effect of working memory. I will now explain why I came to this conclusion. But to understand this – you need to understand the purpose of semantic technologies. Think about it – why do we need a language at all? Why do you need books, paintings or sculptures, all sorts of diagrams, graphs, maps or diagrams?
Tell me – why is all this necessary?
When I asked myself this question, I realized that the main goal of a person is to accumulate and transfer knowledge and experience about the fundamental laws of the universe, whether spiritual or scientific.
Then I came to the conclusion that the accumulation and transfer of knowledge and experience is a process that has 4 stages:
"Perception, Comprehension, Application, Explanation".
Tell us – what is the most important thing at the stage of perception for successful assimilation of information?
You must be in the present tense – here and now. Your brain should not be distracted by memories or daydreams about the future. It requires extreme attention and concentration on what is happening at the moment around you.
Let's look at the second stage of transferring experience and knowledge – this is comprehension. What should your brain do after you've received new material? What is the purpose of this stage?
I realized this thing – that to do this, you need to learn to remember. Don't try to cram and memorize anything. You need to get used to remembering the right thing at the right time. This is not yet taught at school or at the institute. But it is very important to understand and develop a habit.
What else do you need to do to understand this information? Your brain should integrate, combine all your experience with new knowledge. And to do this, you need to get a good night's sleep.
A person has two hemispheres in his head. These are neural networks. Or you can say systems with feedback, from the point of view of automatic control theory. What is feedback and how does it work?
If you take a receiver with an amplifier and apply an output signal to the input, you will experience reverb. This reverse signal can either amplify or attenuate the original signal. Therefore, feedback is called positive or negative.
In the brain, these phenomena are called the processes of excitation and inhibition. Only the bottom line is that one such system can not work for a long time. Either it burns out from excitement, or it fades out. Therefore, all animals have two hemispheres in their heads. When one hemisphere works in real time, the second hemisphere corrects the operation of the first. And then you need sleep, so that the hemispheres sort of switch roles, to pack all the information and eliminate errors.
Thus, sleep is a necessary process of comprehending new knowledge and experience.

It is said that repetition is the mother of learning. This is a lie. If you don't feel any emotion from the information you receive, your brain will simply block it out like the sound of a rattling car.
They say that faith without works is dead. And it's true. Because if you do not apply your knowledge and experience in practice, and get rewarded and enjoy it, then this knowledge is in vain. But there is another way. You can pass on your knowledge and experience to the younger generation. Only to do this, you need to choose concise phrases, put emotions, and speak in a simple and understandable language.
This is the highest level of professionalism. This is the explanation stage. And practice plays a crucial role here. I will now speak very categorically. I believe that if a person has not written a single story in his life, if he has not composed a single poem, then he has no right to teach literature and the Russian language.

Now let's get back to semantic technologies.
Why did the concept of analogy turn out to be such a difficult topic? The fact is that this is a synthetic concept. It combines the concepts of similarity and similarity.
What is the difference between similarity and similarity?
It's hard to tell. I believe that similarity concerns the external form, and similarity is determined by the internal structure of objects.
Now again about the analogy. This is a multidimensional semantic object. Let's find out – what are the types of analogies?
1. A form analogy, such as an image,
2. Analogies by device, such as voice timbre,
3. Analogies by purpose, such as phrases,
4. An action analogy, such as a gesture.
And the smell, and the sound, and the color and taste-all this also has its analogies. Because the mechanism of information perception is based on fractal packing of data and uses the principle of resonance from the theory of vibrations.
Fractal packaging works based on the similarity of shapes. When this algorithm was tested on different images, we found an interesting side effect.
It turned out that such packaging and unpacking can improve and restore image quality. This is possible because such an algorithm uses the similarity principle to restore missing image details.
Now, based on this principle, neural networks are trained to restore the quality of the video sequence. Progress, just amazing for processing old movies and newsreels. But you can't use such processed materials as evidence. The fact is that neural networks lie a little and fantasize to restore the image.
Our memory works the same way. We also sometimes lie and fantasize when we tell a story. Just to avoid going into too much detail or to intrigue the other person. This is how myths and legends are born.
So what is an analogy? What words can you use to define this? Similarity, similarity, association, resonance, echo, reflection, habit...
Within the framework of analytical semantics, I propose the following definition: analogy is a correspondence between semantic constructions.
The catch is that this definition doesn't match recursion. For example, when a function calls itself. That is, it is necessary to somehow explain that the semantic construct can correspond to itself.
So why is the analogy mechanism so important? The thing is, it doesn't matter what you do – science, dance, or music. They are simply means of understanding the fundamental laws of the universe. And the principle of analogies will help you understand all the issues of life, whether it's psychology or quantum physics.



6. Final part
6.1. Responses to missing words
Flame, Gas, Solid, Liquid.
Home, Work, Family, Organization.
Love, Addiction, Liking, Craving.
Necessary, Sufficient, Need, Excess.
Rule, Often, Exception, Rarely.
Street, Road, Apartment, Corridor.
Street, House, Apartment, Room.
Law, Conscience, Responsibility, Justice.
Head, Beginning, Director, Direction.
Private, General, Supplementary, And Basic.

6.2. Sacrament of the 7th:
Where did the fashion for the number 7 come from? What is the mystery of 7 notes, 7 colors, chakras, etc.?
These categories are signal types or signal sources. Then there should be a general background on which they appear. Such as a blank page or silence. That makes a total of 12 states. These 12 states form a tensor-like basis. This similarity lulls the search for truth, as money lulls, like the sleep hormone. However, no guru will admit that your wallet is the eighth chakra, so as not to lose your income.
It is profitable for a teacher to teach you for as long and as expensive as possible. Only a real Teacher will teach you how to learn on your own.
It is generally accepted that the color spectrum consists of 7 colors. However, there is no word for blue in English. Similar discrepancies can be observed in other languages and cultures. Therefore, the question arises-how many colors and which colors are the main ones? For the answer, you can refer to the technology of color formation on the computer. There is a concept of a color cube, which includes 8 colors:
black, white, red, green, blue, turquoise, purple and yellow. The situation is similar with octave notes (octet-8m). Thus, the choice in favor of a controversial but structured theory has a good reason.

6.3. Logic games to choose from
There are some unusual games in which one player conceives a certain option, and other players must solve it by matching. During the game, you need to build hypotheses and correct them based on the answers of the person who conceived the secret. This principle is similar to how a word is decomposed into attributes in analytical semantics.
Similar games were used in ancient Greece in initiation rituals in the town of Eleusis. The card version is called New Eleusis. The rules of this game are described in the book on entertaining mathematics by Perelman.
The bottom line is this. The game is played with a regular card deck. The leader (god) formulates a RULE according to which the cards should be placed in a row one after the other. It is better to write down the rule on paper. The following attributes are used: color, suit, picture or number, even or odd card. For example:
After red - only pictures,
After numbers-only peaks.
These are single-link rules, but there are more complicated ones:
After the red numbers – only images,
After the numbers of diamonds – black even numbers.
You can also use the parity or odd of the card in the displayed row. For example: every second map should be a picture.
The game process is as follows. When the moderator has written down the rule, the other players in the queue select a card from the deck (you can use 2 decks) and show it to the moderator. He says whether it is the right card or not. The correct card is placed horizontally in a row, and the wrong card is placed vertically. The first card is always considered correct. This is a restriction on the intended rule.
Players try to guess the intended rule. If the player thinks that he has understood the rule, then on his turn he can say - " prophet!". Now it is the prophet who declares the correctness of the cards, but God is silent. If the prophet makes a mistake, God says, " The prophet is cast down." Another player can now become a prophet on their turn. The prophet has several moves to make sure that his hypothesis is correct. Before starting the game, you need to agree on how many moves are given to the prophet to name the rule, for example, 5 moves are enough. If the prophet did not have time to name the rule or called it incorrectly, then God overthrows him. The prophet who correctly named the intended rule wins.
That's about the essence of this wonderful game.
Clear rules of the New Eleusis game can be found on the Internet. I recommend not to bother too much with scoring. The goal-to solve the rule-itself is quite gambling.

You can play a similar game with chess pieces. Only here you can use the following attributes: color, pawn or piece, specific piece, even or odd pieces in a row. Examples of designed rules: after the bishop, only black pawns, after even numbers, only white pieces, after pawns, only black pieces (both pawns and pieces). This can be tried.

Another similar game is somewhat simpler. It's called Bulls and Cows. Two people are playing. Everyone writes down a four-digit number on paper. A number without repeating digits is easier to guess than a number with repeating digits. This should be agreed upon in advance. During the game, each player takes turns calling a number to match the opponent's number. The opponent responds like this. If the figure is in the intended number, then it is a cow, and if it stands in its place, then it is a bull. For example: I conceived the number 8130. The opponent tries 1234. I have to answer-1 cow 1 bull. Because 1 is out of place and 3 is out of place. The winner is the one who previously picked up the secret number-4 bulls.
Usually 7-9 steps are enough to solve the number.

6.4. Reflections on Levels of Diversity
I want to share some thoughts about how the universe works. Everywhere we are surrounded by various Levels of Diversity-minds. All minds are mutually different in complexity, spatial scale, and nature.
Natural minds – the process of PERCEPTION:
1. MIND of elementary particles and fields;
2. The MIND of atoms and chemical elements;
3. ANALYSIS of molecules and chemical compounds.
4. SYNTHESIS of alloys and organic molecules;
5. MIND of bacteria and biological cells;
6. The MIND of plants, fish, animals, and birds.
7. The MIND of people and individuals;
8. Support for families, organizations, companies, and nations;
9. VIEW galaxies, stars, planets, moons, comets, and meteorites.
10. THE MIND of the universe, God, angels and demons.

; Minds of language and science – the process of UNDERSTANDING: philosophy, psychology, mathematics, literature, physics, music, chemistry, logic, biology, law, medicine, electronics, programming, architecture, sociology, politics, astronomy, cosmology, esotericism and theology. Basically, it's all about how we understand and express the natural minds given to us.
; Minds of material, artificial, and hand-made objects – the PROCESS OF APPLYING:
1. USE of substances and objects.
2. PRODUCTION of materials, fabrics, compositions and alloys,
3. PURCHASE of food, beverages and medicines;
4. WASHING dishes and food;
5. PURCHASE of clothing and furniture.
6. MIND of things and buildings.
7. MIND of mechanisms and machines;
8. SMART appliances, televisions, phones, and computers.
9. MIND power plants and weapons;
10. THE MIND of spaceships, satellites, and stations.

; Minds of art, spiritual and intellectual values – the process of SELF-EXPRESSION: discoveries, ideas, theories, concepts, prayers, textbooks, books, stories, poems, music, songs, paintings, sculptures, buildings, photographs, films, formulas, drawings, algorithms, programs, viruses, advertising, satire and humor.
; A special place is occupied by the minds of: vices, sins, money, laws, crimes, poisons, diseases, phobias, injuries, garbage, waste, accidents, catastrophes and natural disasters.
Each mind is characterized by the processes of transgression (disintegration and synthesis of a new one), which leads to a combinatorial explosion and an increase in complexity, which only analytical semantics and AI can cope with.
6.5. UNIFIED PHILOSOPHICAL TABLE OF CONCEPTS

God The Holy Spirit God, The Father, God The Son, The Virgin Mother Is
The Word The Letter Offer Letter Number
Word Speech Phrase Sound The Melody Of
The Word Language Idea Business Concept
Word Root Prefix The Ending Suffix For
The Present Time Past Future Fiction
Act Action Cause The Consequence Of The Decision
Device Aggregation Integer Part Detail
Concept Category Abstract Concrete Alternative To
The Phenomenon Of Nature Is A Common Private Miracle
Place Space External Internal Body
Pronoun Verb Noun Adjective Adverb
Knowledge Information Question Answer Faith
Summer Year Spring Autumn Winter
Man Spirit Body Mind Soul
Liquid Substance Firmament Flame Gas
Range Distance Vertical Horizontal Scale
Electron Particle Proton Neutron Photon
Light Color Direction, Brightness, Darkness
, The Sound Of The Tone Direction Loudness The Silence
The Movement Of The Rotation Direction , The Speed Of The Peace Of
The Interaction Of The Body Influence The Dependence Of The Inertia Of
Matter , The Body , The Substance Field Emptiness
Youth Age Childhood Adulthood Old Age

This way the table can be continued. However, it can be seen from the above fragment that vertical associations cannot be unambiguously drawn. From this we can conclude:

Conclusion: in accordance with Godel's theorem applied in semantics, the method of semantic tensors is consistent and incomplete, and the method of the unified philosophical table of concepts is complete and contradictory.
 


7. Articles written using the Yandex Alice AI
7.1. Alice, construct a semantic tensor for the concept of "benefit"
Semantic tensor for the concept of "benefit" (rank 3, 8 elements)
The semantic tensor is constructed on the basis of a binary combination of three semantic axes (features), each of which sets the opposition of two poles. For the concept of "benefit", we will choose three key axes that reveal its multidimensionality.

1. Axis 1: Subjectivity ; Objectivity
Subjective benefit — something that seems useful to a particular subject (person, group) based on their values, preferences, and experience.
Objective benefit — something that is useful regardless of subjective perception, confirmed by facts, norms, and long-term consequences.

2. Axis 2: Short-term ; Long-term
Short-term benefit — a benefit that is tangible immediately or in the near future (satisfaction of a momentary need, instant effect).
Long-term benefit — a benefit that manifests itself over a significant period of time (investment, prevention, strategic development).

3. Axis 3: Individuality ; Collectivity
Individual benefit — what is beneficial to a particular subject (individual, organization) without necessarily considering the interests of others.
Collective benefit is something that is beneficial to the group, society, and the system as a whole, even if it contradicts the short-term interests of individual subjects.

Eight-element tensor (combinations of three axes)
Each of the 8 nodes of the tensor is a unique combination of three features. Below are semantic "coordinates" and examples.

1. Subjective + Short-Term + Individual
Example: eat dessert, despite the diet (nice now, for me personally).
Meaning: momentary pleasure without taking into account the consequences.

2. Subjective + Short-Term + Collective
Example: a team prank at work (fun for the group right now, but pointless in the long run).
Meaning: joint entertainment without a strategic goal.

3. Subjective + Long-Term + Individual
Example: learn a foreign language because you "want to" (personally significant, but the benefits are not obvious to others).
Meaning: personal development based on inner motivation.

4. Subjective + Long-Term + Collective
Example: a volunteer project that seems important to the community (subjective assessment of long-term public benefit).
Meaning: an idealistic social initiative.

5. Objective + Short-Term + Individual
Example: take medication for an illness (proven health benefits here and now).
Meaning: rational personal gain based on facts.

6. Objective + Short-Term + Collective
Example: fire evacuation (definitely useful for everyone at the moment).
Meaning: an urgent, generally useful measure.

7. Objective + Long-Term + Individual
Example: retirement savings (proven personal benefits in the distant future).
Meaning: investing in your own future based on rational calculations.

8. Objective + Long-Term + Collective
Example: introduction of renewable energy (scientifically proven benefits for society in the future).
Meaning: strategic public good.

Visualization (tensor diagram)
You can represent the tensor as a cube, where:
on the X-axis — Subjectivity ; Objectivity,
on the Y-axis — Short-term ; Long-term,
on the Z — axis-Individuality ; Collectivity.
Each vertex of the cube is one of 8 options for "use".

Result. This tensor allows you to:
analyze specific situations through three dimensions of "benefit";
identify conflicts of interest (for example, individual short-term benefits vs collective long-term benefits).
justify decisions based on objectivity and time horizon.
 


7.2. Alice, construct a semantic tensor for the concept of"pleasant"
Semantic tensor for the concept of "pleasant" (rank 3)
A semantic tensor is a multidimensional structure where each axis defines a binary opposition of semantic features. For the concept of "pleasant", we will highlight three key axes that allow us to cover the main dimensions of the experience of pleasure.

Tensor axes
The Subjectivity axis ; Objectivity"
Subjectively pleasant — something that is perceived as pleasant by a particular subject based on their tastes, preferences, and context.
Objectively pleasant — something that is considered pleasant within the framework of generally accepted norms, cultural codes, or biologically programmed reactions (for example, the sweetness of food).

The "Short-term ; Long-term"axis
Short-term pleasant — pleasure that occurs instantly or in the short term (the taste of ice cream, a compliment).
Long-term pleasant — satisfaction associated with promising results, meaningful efforts, or sustainable states (goal achievement, harmonious relationships).

The "Individuality ; Collectivity" axis
Individually pleasant — something that brings pleasure to a personal subject without necessarily involving others (reading a book, walking alone).
Collectively pleasant — pleasure that occurs in social interaction or through participation in a group (holiday, team victory).

Eight tensor nodes (combinations of axes)
Each node is a unique combination of three attributes. Here are some examples and semantic accents.

1. Subjective + Short-Term + Individual
Example: listen to your favorite song with headphones.
Meaning: momentary personal pleasure based on individual preferences.

2. Subjective + Short-Term + Collective
Example: sharing memes in a chat.
Meaning: short-term group entertainment that is meaningful to participants because of their shared interests.

3. Subjective + Long-Term + Individual
Example: mastering a hobby that is "addictive" (drawing, programming).
Meaning: long-term personal satisfaction from the process, meaningful only for the subject.

4. Subjective + Long-Term + Collective
Example: participation in a long-term volunteer project that "warms the soul".
Meaning: sustained group pleasure based on the subjective value of the case.

5. Objective + Short-Term + Individual
Example: a sweet fruit that quenches thirst.
Meaning: Biologically determined instant gratification, universal for most people.

6. Objective + Short-Term + Collective
Example: fireworks at a city festival.
Meaning: generally recognized short-term pleasure, accessible to all present.

7. Objective + Long-Term + Individual
Example: regular physical activity that improves your well-being.
Meaning: Science-based long-term enjoyment of health and tone.

8. Objective + Long-Term + Collective
Example: improvement of a park that will be used by generations.
Meaning: A socially recognized long-term benefit that brings sustainable pleasure to the community.

Visualization (tensor diagram)
The tensor can be represented as a cube, where:
on the X-axis — " Subjectivity ; Objectivity";
on the Y-axis — "Short-term ; Long-term".
on the Z-axis — "Individuality ; Collectivity".
Each vertex of the cube corresponds to one of the 8 nodes.

Interpretation and application
The tensor shows that "pleasant" is not uniform: its perception depends on a combination of three dimensions.
Allows you to analyze rating conflicts (for example, subjectively pleasant for one person may be objectively harmful).
It helps differentiate the types of pleasure: from instant sensory responses to long-term socially significant experiences.
It can be used in psychology, marketing, and experience design (UX) to predict responses to stimuli.

Key findings
"Pleasant" is always context-sensitive — its meaning is revealed through the interaction of axes.
Objectively pleasant is more often associated with biological or cultural universals, subjectively pleasant-with individual trajectories of experience.
Long-term pleasure requires thinking about the consequences, while short-term pleasure relies on immediate sensations.
 


7.3. Alice, construct a semantic tensor for the concept of "love"
Semantic tensor for the concept of "love"
A semantic tensor (or semantic field) is a system of interrelated semantic components that reveal the multidimensional nature of a concept. Below is a structured model for the concept of" love", grouped by key clusters.

1. Concept core (basic definitions)
Deep emotional attraction
A sense of heartfelt attachment
A state of selfless devotion
Striving for unity with the object of love

2. Types of love (classifications)
Eros (passionate, sensual love)
Filia (friendly love, affection)
Agape (selfless, sacrificial love)
Storge (love-tenderness, family affection)
Mania (obsessive, jealous love)
Pragma (rational, "calculating" love)

3. Subjects and objects of love
To a person:
romantic love
parental love
brotherly / sisterly love
platonic love

Abstract concepts include:
love for the motherland
love of art
love of knowledge

To yourself:
healthy self-esteem vs selfishness

4. Emotional states
Positive ones:
happiness
delight
pacification
gratitude

Negative ones:
sadness
jealousy
despair
fear of loss

5. Behavioral manifestations
Care
Sacrifice
Attention to the needs of the other
Loyalty
Physical intimacy (in a romantic relationship)
Words of recognition (compliments, confessions)

6. Cultural and religious aspects
Christianity: agape as the highest virtue ("God is love" - 1 John 4: 8)
Philosophy:
Plato: Love as the pursuit of an ideal
Fromm: Love as Art

Literature and Art:
Archetypes: Romeo and Juliet, Tristan and Isolde
Symbols: heart, rose, dove

7. Linguistic markers
Synonyms: affection, passion, tenderness, adoration
Antonyms: hatred, indifference, disgust

Phraseological units:
"Love of evil — you will love a goat"
"Out of sight — out of mind"
"Love for real"

8. Psychological mechanisms
Idealizing your partner
Empathy
Attachment (Bowlby attachment theory)
Cognitive dissonance in love conflicts

9. Social functions
Creating a family
Social integration
Transfer of values between generations
Support for psychological well-being

10. Contradictions and paradoxes
Love as freedom vs love as addiction
Love and jealousy
Love for an unworthy object
Mismatch of expectations and reality

Note:
The structure reflects the multidimensional nature of the concept: from intimate experiences to sociocultural norms.
Components may overlap (for example, "sacrifice" refers to both behavior and agape type).
In different cultures, the emphasis shifts (for example, in Eastern traditions, duty in love is more often emphasized, in Western traditions-individual choice).
 


7.4. Alice, build a semantic tensor for the concept of "communication"
Semantic tensor for the concept of "communication"
A semantic tensor is a multidimensional model that reflects the key semantic facets of a concept through interrelated categories. Below is a structured diagram for the concept of "communication", covering its essential characteristics, functions, forms, components, and contexts.

1. Essence and definition
Communication — subject -subject interaction aimed at:
exchange of information;
establishing and developing interpersonal relationships;
coordination of joint actions;
mutual understanding and self-reflection.

Key attribute: bidirectional (dialogic), as opposed to unidirectional communication.

2. Main functions
Informational — transmitting and receiving information.
Regulatory — coordination of actions, influence on the partner's behavior.
Affective emotional — expression and perception of feelings, setting up the emotional background.
Socializing — assimilation of norms, roles, and values.
Expressive — self-expression, demonstration of individuality.
Cognitive — mutual cognition, forming the image of a partner.

3. Structure (according to G. M. Andreeva)
Communication side — exchange of messages (verbal/non-verbal).
Interactive side — organization of interaction (cooperation, competition, conflict).
The perceptual side is the partner's perception, understanding, and interpretation (empathy, attribution).

4. Types of communication (by criteria)
By content:
material (exchange of items);
conditioned (influence on the condition);
motivational (transmission of motivations);
cognitive (knowledge sharing);
activity-based (exchange of skills).

By goal:
biological (satisfaction of vital needs);
social (expanding contacts, personal growth).

According to the form:
direct / indirect;
direct/indirect (technique, text);
mass/interpersonal.


By duration:
short-term (hours, one topic).
long-term (multi-shadow, intermittent/continuous).

By orientation:
socially oriented;
subject -oriented group planning.
personality -oriented.

5. Funds and channels
Verbal: speech, writing, language signs.

Nonverbal:
kinesics (gestures, facial expressions, and posture).
prosody (tone, tempo, volume).
tactile contacts.
spatial organization (proxemics).

Technical: Mass media, Internet, instant messengers.

6. Contexts and spheres
Household (everyday, family).
Business (professional, organizational).
Educational (pedagogical interaction).
Psychotherapy (deep personal communication).
Ritual/ceremonial (normalized forms).
Cross-cultural (taking into account ethno-cultural codes).

7. Barriers and hindrances
Semantic (different understanding of meanings).
Logical ones (argument inconsistencies).
Stylistic (if the form doesn't match the content).
Phonetic problems (speech defects, noise).
Psychological (biases, stereotypes).
Technological (communication channel failures).

8. Results and effects
Mutual understanding (coincidence of meanings).
Coordination of actions (cooperation).
Change of attitudes (persuasion, suggestion).
Emotional release (catharsis).
Formation of identity (self-determination through feedback).
Conflict or dissonance (if expectations don't match).

9. Analysis levels
Micro-level — interpersonal dialogue, small groups.
Meso-level — organizational and institutional communication.
Macro level — mass communications, socio-cultural patterns.

10. Related concepts
Communication (more broadly, includes unidirectional processes).
Interaction (the activity aspect of communication).
Perception (perception of the partner).
Reflection (analysis of one's own participation in communication).
Empathy (emotional empathy).
Feedback (interaction correction mechanism).

Summary: the semantic tensor of" communication " reveals it as a multidimensional sociopsychological phenomenon that combines informational, interactive and perceptual processes in the context of specific goals, means and situations. The model allows you to systematically analyze communication at different levels-from microdialog to macro-social communications.


7.5. Alice, construct a semantic tensor for the concept of "impression"
Semantic tensor for the concept of "impression"
The semantic tensor represents a concept as a multidimensional structure that reveals its semantic facets through interrelated categories. Below is a systematic model for the concept of "impression".

1. Essence and definition
Impression — a subjective mental image that occurs as a result of perception of an external object/event and carries an emotionally evaluative connotation.

Key features:
subjectivity (depends on personal experience and attitudes).
integrity (synthesizes multi-modal sensations).
dynamic (it can be transformed by repeated contact).
evaluation (contains the "like/dislike", "important/unimportant"components).

2. Genesis (sources of formation)
Direct perception (sense organs: sight, hearing, touch, etc.).
Indirect perception (through a story, text, image, or video).
Imagination and fantasy (reconstruction based on incomplete data).
Social influence (other people's opinions, stereotypes, cultural codes).

3. Structure (components)
Sensory layer — primary sensations (color, sound, smell, texture).
Cognitive layer — comprehension, categorization, attribution of values.
Emotional layer — the experience of pleasure/discomfort, interest/indifference.
The evaluation layer is a judgment of value, significance, and attractiveness.
Mnemic trace — fixation in memory (short-term/long-term).

4. Types of impressions (by criteria)
By modality:
visual, auditory, olfactory, gustatory, tactile, kinesthetic.

By intensity:
faint, moderate, bright, stunning.


By valence:
positive, negative, ambivalent.

By duration:
instantaneous (seconds), stable (hours/days), long-term (months/years).

According to the degree of awareness:
explicit (reflexive), hidden (subconscious).

By source:
personal (direct experience), other people's (retold), virtual (media, games).

5. Functions
Tentative — helps you quickly assess the situation/object.
Protective — an alarm about danger/discomfort.
Motivational — motivation to take action (learn, avoid, repeat).
Communicative — transfer of experience to others ("I got this impression...").
Identifying — the formation of the image of "I" through the experienced impressions.
Aesthetic — enjoyment of form, harmony, and beauty.

6. Formation mechanisms
Selective attention (highlighting significant stimuli).
Apperception (the effect of past experience on perception).
Categorization (assignment to known classes).
Emotional coloring (linking an experience to a stimulus).
Reflection (comprehension and verbalization of impressions).
Social verification (comparison with the opinions of others).

7. Contexts of manifestation
Everyday life (impressions of people, places, and events).
Art (aesthetic impressions of music, painting, and theater).
Marketing and design (creating a "consumer experience": packaging, service, brand).
Psychology and psychotherapy (analysis of first impressions about the client / therapist).
Education (impressions of the lesson, teacher, and learning environment).
Tourism (impressions of travel and sightseeing).

8. Factors influencing the impression
Object characteristics: novelty, complexity, contrast, aesthetics.
Subject's state: mood, fatigue, motivation, expectations.
Situation: context, time, presence of other people.
Cultural norms: stereotypes, traditions, symbolic meanings.
Previous experiences: associations, traumas, positive / negative memories.

9. Dynamics and transformation
First impression — an instant assessment at first contact (often stable).

Correction — changes made under the influence of new information.
Consolidation — transition to a stable opinion/attitude.
Forgetting — the fading of a trace in memory.
Reactivation — reactivation when a stimulus or memory is repeated.

10. Related concepts
Perception (the process of image formation).
Image (the result of perception, more stable).
Attitude (stable evaluation position).
Stereotype (a template impression generalized to the group).
Waiting (anticipating an impression).
Emotion (an experience that accompanies an impression).
Memory (storing and reproducing impressions).
Impressionability (individual tendency to vivid impressions).

11. Methods of study and measurement
Self-report (surveys, diaries, interviews).
Observation (for nonverbal reactions).
Psychophysiological methods (ECG, HRG, EEG recording of emotional reactions).
Projective techniques (associations, drawings).
Behavior analysis (choice, time of interaction, repeated contacts).

Bottom line: the semantic tensor "impressions" demonstrates it as a complex psychosemiotic phenomenon that combines sensory, cognitive, and emotional processes in the context of personal and cultural experience. The model allows you to analyze impressions at different levels-from instantaneous sensations to stable personal formations.



Conclusions. What's next?

While working on the monograph, I came across a book – "Practical Psychology of color" by Nadezhda Andre and Svetlana Nekrasova, that's where semantic algebra works 100%. At the same time, I observe the growing interest and number of publications on semantics in general. This is good news.
Here I tried to combine more than 1000 concepts into a system, and gave more than 100 semantic tensors. Here is everything that I considered the main thing and that allowed me to cover my horizons. However, the work cannot be considered completed. The underwater part of the iceberg is a semantic dictionary translator. This is difficult and routine work. It is worth considering – how can this be simplified and optimized?
There is no doubt that the revealed tensor topology of the semantic space is the key to building neuro-processors. Presumably, you can focus on the global semantic tensor of rank 16. This is 65536 semantic units.
As for the prospect of semantic programming of quantum computers, it should be borne in mind that this is already a person who makes his own choice: agrees or rejects, wants or fears. This is a complex spiritual question that still needs to be answered.

What's next? I assume that Semantic physics is a very broad, deep and diverse field of research on such issues as: communication space, semantic body, space of interests, sphere of trust, semantic flows, etc.
Semantic physics is a natural development of semantic algebra, which analyzes and integrates all aspects of the semantic dynamic structure of the Universe, such as: subjects and objects of the communication space; the variety of their interaction; external and internal emotional and logical processes: perception, comprehension, application and self-expression.


Dictionary of terms
SEMANTICS is a branch of linguistics that studies the meaning of language units.

SEMANTIC ALGEBRA is a fundamental analytical discipline that studies the semantic patterns of language, concepts and relations between them. Semantic algebra allows you to identify semantic tensors from a certain domain and perform operations with them according to the rules of linear algebra to build semantic models.

A SEMANTIC RELATION is a relation between two concepts that reveals the essential characteristic (essence) of objects and phenomena. For example: "Black and White, light, color, vision". There are 12 fundamental types of semantic relations that can be used as attributes in obtaining/identifying new concepts.

A SEMANTIC VECTOR is 2 or 4 concepts that are located on the same semantic axis. This is either a semantic relation or a semantic gradient. For example: "Object-Subject", "Rest-Movement", "Life - Death".

A SEMANTIC GRADIENT is a semantic vector of 4 concepts that denote a stepwise change in a certain factor. For example: "Tiny, Small, Bigger, Huge."

SEMANTIC MULTIPLICATION is a procedure for detecting such a concept, the definition of which consists of words corresponding to the concepts being multiplied. Such multipliers play the role of features. For example: "Girl = Woman * Youth", "Woman = Man * Female". So the signs are multiplied and decomposed into other signs in the same way as multiplying prime numbers in mathematics.

A SEMANTIC MATRIX is a table obtained by multiplying a pair of semantic concepts or vectors that are in the same semantic plane. For example: "Childhood, Youth, Maturity, Old Age" * " Man " = "Boy, Boy, Man, Old Man".

A SEMANTIC TENSOR is a multidimensional semantic structure of concepts formed by a binary combination of features. Semantic concepts, vectors and matrices can be considered as tensors of the 0th, 1st and 2nd rank (dimension), respectively. The number of words in the tensor is equal to the power of 2 (i.e. 2, 4, 8, 16, ...). Semantic tensors can be multiplied according to the rules of linear algebra.

A SEMANTIC MODEL is a group of semantic tensors that reflect a particular domain. For example, literature, management, physics, or psychology.

QUALITY (+). This means the appearance of quality, the formation of a semantic axis. Examples: "Peace + Movement", "Silence + Sound", " Darkness + Light".

VARIATION (&). This is a variation. A pair of homogeneous and equal-rank words. For example: "Lake & Pond", "Foliage & Needles", " Table & A chair."

POLARITY ( -). This is mirror antisymmetry, the opposite. For example: "Black – White", "Top-Bottom", "Hot-Cold".

COMPARISON (> or <). This is a gradation. A couple of words denote intensity, strength, degree. For example: "Much > Little", "Strong > Weak", "Bright > Dim", "Chair > Stool".

EXTENSION (#). This is orthogonality. Pairs of words complement each other until the semantic plane appears. One is meant for the other. For example: "Form # Content", " Reason # Investigation", "Man # Woman".

DEVICE (%). These are aggregation, meronym, and holonym. A pair of words like "Part % Whole". For example: "Apartment % House", "Letter % Word", "Detail % Device", "Branch % Tree".

TRANSGRESSION (\ or /). A pair means an asymmetric opposite, which has the character of either decline and damage, or recovery and compensation. For example: "Birth \ Death", "Signal \ Interference", "Building \ Ruins". Or, for example: "Damage / Compensation", "Breakdown / Repair", "Illness / Treatment", "Error / Correction".

INHERITANCE (^). This is a "View" type of relationship. ^ Subspecies". These are hyponyms and hyperonyms. For example: "Road ^ Street", "Building ^ Building", "Reservoir ^ Lake".

MULTIPLICITY (...). This is a "Quantity" type of relationship. … Quality". For example: "Drop-Rain", "Snowflake-Snow", "Shelf-Cabinet", "Book-Library".

NEIGHBORHOOD ( _ ). Indicates the location or location. The neighborhood is specified by prepositions and verbs. For example: "Headscarf", "Carpet is on the Floor", "Bedspread is laid on the Bed", "Towel is hanging on the Hanger", "The page is located on the Site".

AFFILIATION ( @ ). Affiliation or authorship is specified by verbs. For example: "The book was written by the Author", "The Dance was performed by the Dancer", "The music was written by the Composer", "The poems were composed by the Poet".

ASSIGNMENT ( $ ). Binds nouns with verbs. For Example: "Screw-Screwdriver-Twist", "Nails-Hammer-Hammer", "Part-Machine – Process", "Plate-Food-Eat".

QUADWORD-semantic matrix, a rank 2 tensor.
CUBOLOGICAL-semantic tensor of rank 3.
HYPERWORD - semantic tensor of rank 4.
A PENTWORD is a rank 5 semantic tensor.


List of literature

1. Ozhegov S. I., Shvedova N. Yu., Explanatory dictionary,
2. Raymond Lully, Combinatorial Art,
3. Hegel, the Science of Logic,
4. Chelpanov G. I., Textbook of logic,
5. Archimandrite Plato, Orthodox Moral Theology,
6. St. Ignatius (Bryanchaninov), To help the penitent,
7. Archbishop Luka Voyno-Yasenetsky, Spirit, soul and body,
8. Michael Epstein, The Four Sides of Love,
9. Ostretsov I. N., Introduction to the philosophy of nonviolent development,
10. Ausra Augustinaviciute, Model of Information Metabolism,
11. Grigory Reinin, A group of bipolar traits in Jungian typology,
12. Gradi Butch, Object-oriented Analysis and Design,
13. Allan Carter, Programming Stone,
14. Dmitry Anisimov, THE TRUTH about machine translation,
15. Anna Verzhbitska, Metatext in text.
 


Table of contents
Introduction 2
Remarks 3
First acquaintance 3
1. Part One, Introductory 4
1.1. What is semantic algebra and why is it called so? 4
1.2. About the complexity of the material and a number of riddles 5
1.3. Background of issue 5
1.4. Grigory Reinin's priority 6
1.5. Stanislav Taktaev's contribution 7
1.6. Comparison of mathematical and semantic tensors 7
1.7. Why do we need semantic algebra? 8
1.8. On dialectics and axiomatics 9
2. Part Two, Tutorial 10
2.1. Introductory lesson, about antonyms 10
2.2. Lesson on multiplication of features 10
2.3. Lesson on antonyms 11
2.4. Lesson on semantic tensors 12
2.5. Lesson on 12 types of semantic relations 13
2.6. Lesson two, about types of semantic relations 15
2.7. Lesson on semantic models 16
2.8. Lesson on reasoning patterns 16
3. Part Three, Theoretical 18
3.1. Concept 18
3.2. Fundamental semantic concepts 20
3.3. Semantic tensor sweep 21
3.4. Semantic gradients, tensors, and series 22
3.5. Metalanguage and semantic invariance 22
3.6. Classification in semantics and synonyms 23
3.7. Typology of semantic objects 23
3.8. Axioms and theorems of semantic algebra 25
3.9. Static and Dynamic semantics 26
3.10. Global semantic groups 28
3.11. Relationships and groups in a single basis 31
3.12. About the semantic dictionary 32
3.13. Developing triads 34
3.14. Scanning parts of speech 35
3.15. Fundamental axes of c-space 36
3.16. Fundamental planes of c-space 36
3.17. Decomposition of words into attributes 37
3.18. Classification of homonyms 38
3.19. Semantic topology 39
3.20. Dialectics, logic and theology 40
3.21. Fundamental bases of the real and ideal 41
3.22. Fundamental types of transgression 42
3.23. Fundamental types of semantic complementation 43
3.24. Some semantic opposites and additions 44
4. Part Four, Tensor Grammar 46
4.1. Reflections on the grammatical tensor 46
4.2. Intonation, comprehension mechanism, and reverse tense 47
5. Part Five, Appendix 49 49
5.0. Semantic algebra in life 50
5.1. Classification of literary works and speech styles 52
5.2. Classification in music 54
5.3. Classification in literature and structure of myth 55
5.4. Semantic algebra in engineering 57
5.5. Semantic algebra in psychology 59
5.6. System-forming structures 74
5.7. Organization, activity, creativity, etc . 79
5.8. Nature and metaphysics 84
5.9. Scanning semantic groups 86
5.10. Orthogonalization of semantic groups 92
5.11. Semantics in biology 95
5.12. Semantic technologies 97
6. Final part 100
6.1. Responses to missing words 100
6.2. The Sacrament of 7: 100
6.3. Logic games based on option 100 selection
6.4. Reflections on Levels of Diversity 102
6.5. UNIFIED PHILOSOPHICAL TABLE OF CONCEPTS 103
7. Articles written with the help of AI Yandex Alice 104
7.1. Alice, construct a semantic tensor for the concept of "benefit" 104
7.2. Alice, construct a semantic tensor for the concept of "pleasant" 106
7.3. Alice, construct a semantic tensor for the concept of "love" 108
7.4. Alice, construct a semantic tensor for the concept of "communication" 110
7.5. Alice, construct a semantic tensor for the concept of "impression" 112
Conclusions. What's next? 115
Glossary of terms 116
References 118