What type of language does marine flag belong to? Artificial and natural languages

Question 11. An information model that has a tabular structure is:

Answer 2. flight schedule;
Answer 3. family tree;
Answer 4. functional diagram of a computer.

Question 12. An information model that has a network structure is:
Answer 1. computer file system;
Answer 2. family tree;
Answer 3. model of the Internet computer network;
Answer 4. train schedule.

Question 13. Full-scale modeling is:
Answer 1. creating mathematical formulas that describe the form or behavior of the original object;
Answer 2. modeling, in which a separate feature of the original object is recognized in the model;
Answer 3. a set of data containing text information about the original object;
Answer 4. modeling, in which the model has a visual similarity to the original object

Question 14. The following cannot be considered an information model of an object:
Answer 1. description of the original object using mathematical formulas;
Answer 2. description of the original object in natural or formal language;
Answer 3. another object that does not reflect the essential features and properties of the original object;
Answer 4. a set of formulas written in the language of mathematics that describe the behavior of the original object.

Question 15. A mathematical model of an object is:
Answer 1. a set of formulas written in the language of mathematics that reflect the properties of an object;
Answer 2. description in the form of a diagram of the internal structure of the object being studied;
Answer 3. a set of data containing information about quantitative characteristics;
Answer 4. a model created from any material that accurately reflects the external characteristics of the object.

Question 16. In the “object-model” relationship there are
Answer 1. a country is its capital;
Answer 2. bolt - drawing of a bolt;
Answer 3. chicken - chickens;
Answer 4. spacecraft - the law of universal gravitation.

Question 17. Documents that represent an information model of government management include:
Answer 1. The Constitution of the Russian Federation;
Answer 2. geographical map of Russia;
Answer 3. Russian dictionary of political terms;
Answer 4. list of deputies of the State Duma.

Question 18. Information models describing the organization of the educational process at school include:
Answer 1. cool magazine;
Answer 2. list of visual teaching aids;
Answer 3. list of school students;
Answer 4. lesson schedule.

Question 19. Mark the true statement:
Answer 1. direct observation is the storage of information;
Answer 2. The request to information systems is the protection of information;
Answer 3. building a graphical model of a phenomenon is the transfer of information;
Answer 4. Reading reference books is a search for information.

Question 20. Drawings, maps, drawings, diagrams, diagrams, graphs represent:
Answer 1. tabular information models;
Answer 2. mathematical models;
Answer 3. graphical information models;
Answer 4: hierarchical information models

What is the essence of the alphabetical approach to measuring information?

How to determine the information volume of a message represented by symbols of some natural or formal language?
An information message with a volume of 650 bits consists of 130 characters. What is the information weight of each character of this message?

PLEASE HELP ME MAKE A PLAN FOR THIS PARAGRAPH! § 2.2. Information models The original object can be replaced by a set of its properties: names (values)

and meanings. A set of properties containing all the necessary information about the objects and processes under study is called an information model.
In table Figure 2.1 shows an example of an information model of a country house - a card from a catalog, from which a customer of a construction company can select a suitable project. Each card in the catalog contains the names (values) of house properties (on the left) and the values of these properties (on the right).

Table 2.1

Appearance
Length 10 m
Width 8 m
Number of floors 1
Wall material Brick
Wall thickness 0.6 m
Interior wall decoration Board
Roof material Slate

All names of properties in information models are always symbolic elements, because the name can only be expressed by signs. But the values of quantities can carry both symbolic and figurative information. For example, in table. 2.1, the value of the quantity “appearance” is expressed by a figurative element (drawing), and the values of the remaining quantities are expressed using signs (numbers, words, commas).
The figurative element of the information model can be not only a drawing or photograph, but also a three-dimensional layout or video recording. However, it must be possible to connect this element with the characteristics of a specific object. For example, the “Exterior” line in a house catalog may contain a layout code. And in order for the layouts themselves to be elements of the information model, and not decoration, they need to be provided with labels with codes.
Information models represent objects and processes in figurative or symbolic form. According to the method of presentation, the following types of information models are distinguished - Fig. 2.1.

Types of information models

Figurative Mixed Iconic
models models models

Maps Graphs Flowcharts

Figurative models (drawings, photographs, etc.) are visual images of objects recorded on some information medium (paper, photo and film, etc.).
Specialists receive a lot of information from satellite photographs of the Earth’s surface (Fig. 2.2)

Rice. 2.2 Satellite photograph of the territory in the Black Sea region<

Figurative information models are widely used in education (illustrations in textbooks (Fig. 2.3), educational posters in various subjects) and sciences, where classification of objects according to their external features is required (in botany, biology, paleontology, etc.).

Rice. 2.3 Formation of the Roman legion in three lines

Sign information models are built using various languages (sign systems). A signed information model can be presented in the form of a text in natural language or a program in a programming language, a formula (for example, the area of a rectangle S = ab), etc.
Many models combine figurative and iconic elements. In Fig. Figure 2.4 shows an example of a model of the unicellular alga Chlamydomonas. The drawn parts of the seaweed are figurative elements of this model, and the inscriptions below and to the right of the drawing are symbolic elements. Rice. 2.4

Examples of mixed information models include geographic maps, graphs, diagrams, etc. All of these models use both graphic elements and symbolic language at the same time.

i Briefly about the main thing
The original object can be replaced by a set of its properties: their names and values. A set of properties containing all the necessary information about the objects and processes under study is called an information model.
Information models represent objects and processes in figurative or symbolic form. According to the method of presentation, figurative, symbolic and mixed information models are distinguished.

“Natural” and “artificial” are the division of languages by origin.

Natural language- in linguistics and philosophy of language, a language used for human communication and not created artificially (unlike artificial languages)

Natural languages are audio (speech) and then graphic (writing) information sign systems that have historically developed in society. They arose to consolidate and transfer accumulated information in the process of communication between people. Natural languages act as carriers of centuries-old culture and are inseparable from the history of the people who speak them. The vocabulary and grammatical rules of natural language are determined by the practice of use and are not always formally recorded.

Natural language features:

· communicative:
- ? stating (for a neutral statement of fact),
- ? interrogative (to ask about a fact),
- ? appellative (to encourage action),
- ? expressive (to express the mood and emotions of the speaker),
- ? contact-establishing (to create and maintain contact between interlocutors);
metalinguistic (for interpretation of linguistic facts);
· aesthetic (for aesthetic impact);
· function of an indicator of belonging to a certain group of people (nation, nationality, profession);
· informational;
· cognitive;
· emotional.

Properties of natural language:

· unlimited semantic power - the fundamental limitlessness of the noetic field of language, the ability to transmit information regarding any area of observed or imaginary facts;
· evolvability - unlimited ability for endless development and modifications;
· manifestability in speech - the manifestation of language in the form of speech, understood as specific speaking, occurring over time and expressed in audio or written form;
· ethnicity is an integral and two-way connection between language and ethnic group.

An essential property of language is its duality, which is expressed in the existence of the following linguistic antinomies:

· antinomy of objective and subjective in language;
· the antinomy of language as an activity and as a product of activity;
· antinomy of stability and variability in language;
· antinomy of the ideal and material nature of language;
· antinomy of the ontological and epistemological nature of language;
· antinomy of the continuous and discrete nature of language;
· antinomy of language as a natural phenomenon and an artifact;
· antinomy of individual and collective in language.

Human everyday reasoning is conducted in natural language. This language developed with the aim of simplifying the process of communication, the exchange of thoughts at the expense of clarity and accuracy. Natural languages have enormous possibilities of expression - you can express any feelings, experiences, knowledge, emotions.

Natural language performs the main functions - representative and communicative. The representative function is derived from the fact that language is a means of expression through symbols or representation of an abstract nature (for example: knowledge, concepts, thoughts) accessible through thinking to specific intellectual subjects. The communicative function is manifested in the fact that language is the ability to transmit an abstract character from one intellectual person to another. The symbols themselves, letters, words, sentences form a material basis. It implements the material superstructure of language, that is, it is a community of rules for the construction of words, letters and other language symbols, and only with this superstructure does this or that material basis form a specific natural language.

Based on the semantic status of natural language, we note the following:

Based on the fact that language is a set of rules, therefore, there are a huge number of natural languages. The material basis of any language of natural origin is multidimensional, which means that it is divided into visual, verbal, tactile types of signs. All these varieties are independent of each other, but in a large number of languages existing today they are inextricably linked, with verbal symbols being the main ones.

The material basis of language, of natural origin, is studied only in two dimensions - verbal and visual, or writing.

Due to the differences in the superstructure and the basis, a separate natural language shows the same abstract content unique, unique. On the other hand, in any given language, abstract content is also shown that is not shown to us in other languages. However, this does not mean that each individual language has its own special sphere of abstract content. For example, “Man”, “Man” explains to us one abstract content, but the content itself does not belong to English or to the Russian language. The scope of abstract content is the same for different natural languages. That is why translation from one to another natural language is possible.

The object of logical analysis of language is abstract content, while natural languages are only a necessary condition for such analysis.

The sphere of abstract content is the structural region of various objects. Objects base a unique abstract structure. Natural languages show elements of this structure, as well as some fragments. Any natural language in some sense reflects the structure of objective reality. However, this description shows a superficial and contradictory character.

During its formation, natural language changed - this is due to the interaction of cultures of different peoples and technological progress. As a result of this, some words lose their meanings over time, while others, on the contrary, acquire new ones.

For example, the word “satellite” - previously only one meaning was used (fellow traveler, comrade on the road.), but today it has another meaning - space satellite.

Natural language takes on a life of its own. It contains many features and nuances that make it difficult to express thoughts in words. The presence of a huge number of hyperboles, figurative expressions, archaisms, idioms, and metaphors does not help this either. In addition, natural language is full of exclamations and interjections, the meaning of which is difficult to convey.

Historically, the formation of language took place in various forms, different languages created various groups, and the cultural features of the various structural components of the language have been preserved to this day.

All languages are usually divided into 2 large groups: natural and artificial languages.

Natural languages arose in the conditions of human development in various natural-geographical and socio-historical conditions. Being one of the main ethnic characteristics (common territory of residence, language, culture, mentality), natural language became a means of integration of people in the first stages of the formation of human society. With the increasing complexity of social life and the settlement of people across vast areas of the globe, linguistic differences arose, which led to the formation of many national languages. Currently, there are about 5,000 languages on the globe, spoken by residents of just over 200 countries.

Historical features of the formation of natural languages have led to the fact that the same language
People living in different countries and even on different continents, for example, the British, Americans and Australians, consider them native. Russian is the native language for many people born during the Soviet Union in national republics. Their number includes Belarusians, Ukrainians, and representatives of various ethnic groups of vast Russia, etc.
Natural languages have different forms. The main ones are:

1 dialects, including social dialects,
2 professional speech,
3 vernacular,
4 literary language.

Dialect is a language consisting of local names of objects and phenomena of everyday life, verbal designations of everyday actions, simple concepts known to every person from birth. Different ethnic groups, and even people belonging to the same ethnic and national entity, can speak different dialects. In addition to differences in conceptual structure, dialects are often built on different phonetic bases (the same letters and syllables are pronounced differently). Each locality may have its own dialect.

Dialects are not part of the literary national language, since they are not used everywhere, but only in a certain territory. Under the influence of changing living conditions and the spread of linguistic literacy cultivated by the media, dialect words are gradually falling out of use. Some are replaced by the words of the literary language, others are forgotten as the phenomena and objects denoted by them disappear from everyday life.

Social dialects- this is the language of various social groups, which, for various reasons, in certain socio-historical conditions, can act as the creators and bearers of a separate subculture. This subculture can take shape in various linguistic forms. The main difference between social dialects and other forms of language is either the use of special words to denote phenomena known only to this social group, for example, the language of criminals, thieves “Fenya”; or in changing the meaning of ordinary words, for example, “laces” - parents in youth slang; in the use of ordinary words in a modified context, for example, in the language of the aristocracy “dinner party, dinner”, etc. are interpreted not as an invitation to a meal, but with the word “specific” (person, man, guy), new Russians (like new Belarusians) call a person who corresponds to their image of a business and successful person.

A type of social dialect is professional language. Its main difference from natural language is that it is the language of a separate socio-professional group, the specialized activities of which are associated with the need to use special terms to designate specific phenomena and objects included in this professional activity.

Depending on the linguistic conditions in which a specific professional activity began to take shape, terminology may develop, which in this case is borrowed in nature. Thus, in the Russian language of sociologists, geneticists, cyberneticists and generally those associated with computer science, there are a lot of foreign language terms, mostly in English, because in the former Soviet Union these sciences were banned for a long time. And classical medicine traditionally operates with terminology in Latin, an already dead language.

Professional language is the means of existence of professional culture. And if it is sometimes deliberately complicated in order to distance professionals from the “uninitiated,” then this may be evidence of a not very high level of professional culture. In the modern “knowledge society”, development is carried out not only by increasing the educational, “knowledge” level of all members of civil society, but also by bringing the scientific professional knowledge base closer to every active member of society, which is also achieved through the openness of professional knowledge in their linguistic design.

Vernacular- this is a special form of natural language, which is characteristic of people who do not know the norms of the literary language. Vernacular speech differs from both the literary language and the dialect. It has a number of typical features in the field of vocabulary, morphology, phonetics, and syntax. For example: words such as “always”, “from there”, “opposite”, “theirs”, etc. are forms of vernacular. Their use in everyday speech is sometimes ironic, sometimes used in literature to express the sociocultural characteristics of a character, sometimes they are used by politicians to get closer to their electorate, who speak the vernacular. However, in general, vernacular is the language of people who are not entirely familiar with the standard language, for various reasons. Nowadays, vernacular language is actively being replaced by literary language. However, some of its features are very tenacious.

Unlike dialects, which are characterized by territorial fixation, vernacular speech is extraterritorial. It does not have its own strictly defined norms, which is why it differs from both the literary language and dialects.

Literary language- the language of official business documents, teaching, science, journalism, fiction, all manifestations of culture expressed in verbal form. The study of a literary language is closely related to the study of literature, the history of language, and the cultural history of the people. It is one of the most effective tools of enlightenment, touching upon the objectives of education.

The main feature of the national literary language is its normativity. Language norm - This is a central concept in defining the national literary language in both its written and spoken form, it means the way it is customary to speak and write in a given society in a given era. Linguistic norms are formed objectively in the process of centuries-old language practice of cultural people. Norms are historically fluid, but they change slowly. If there were no norms, the literary language could not exist. Literary speech would be mixed with streams of dialect speech and vernacular, losing its normative functions.

Constructed languages - These are special formalized languages, constructed according to a specific plan for specific purposes, for example, shorthand, Morse code, computer languages.

World (international) languages- the most common languages used by representatives of different nations outside the territories inhabited by people for whom they are originally native. These are the languages accepted as working languages of the UN and other international organizations. Today these include: English, French, Spanish, Russian, Chinese. The leading place belongs to English, the native language of 350 million people, which is studied in almost all countries of the world.

There are auxiliary international languages, for example Esperanto, an artificial language created in 1887 to simplify communication between people speaking different languages. Esperanto got its name from the pseudonym of its creator: Esperanto means “hopeful.”

The languages used for human communication are called natural languages. There are several thousand of them. The most popular natural language is Chinese. English is one of the most widely spoken languages in the world. Natural languages are characterized by:

Wide scope of application - natural language is known to the entire national community;

The presence of a large number of rules, some of which are formulated explicitly (rules of grammar), others implicitly (rules of meaning and use);

Flexibility - natural language is applicable to describe any, including new, situations;

Openness - natural language allows the speaker to generate new signs (words) that are understandable to the interlocutor, as well as use existing signs with new meanings;

Dynamic - natural language quickly adapts to the diverse needs of interpersonal interaction between people.

In connection with the development of science and technology, formal languages have emerged that are used by specialists in their professional activities. Moreover, many formal languages have international use.

A formal language is a language in which the same combinations of signs always have the same meaning. Formal languages include systems of mathematical and chemical symbols, musical notation, Morse code and many others. The formal language is the universally used decimal number system, which allows you to name and write numbers, as well as perform arithmetic operations on them. Formal languages include the programming languages that we will learn about in computer science classes.

A feature of formal languages is that all the rules in them are specified in explicit form, which ensures the unambiguous recording and perception of messages in these languages.

1 .2.4. Forms of information submission

The same information can be expressed in different ways. A person can present information in symbolic or figurative form (Fig. 1.3).

The presentation of information in one form or another is otherwise called coding.

Representation of information using some sign system is discrete (composed of individual values). The figurative presentation of information is continuous.

THE MOST IMPORTANT

To save and transmit information to another person, a person records it using signs. A sign (set of signs) is a substitute for an object that allows the transmitter of information to evoke an image of the object in the mind of the recipient of the information.

Language is a sign system used by a person to express his thoughts and communicate with other people. There are natural and formal languages.

A person can present information in natural languages, formal languages, and in various figurative forms.

Presentation of information in any language or in figurative form is called encoding.

Questions and tasks

1. What is a sign? Give examples of signs used in human communication.

2. What do a pictogram and a symbol have in common? What is the difference between them?

H. What is a sign system? Try to describe the Russian language as a sign system. Describe the decimal number system as a sign system.

4. What type of writing (letter-sound, syllabic, ideographic) does the English writing belong to? Germans; French; Spaniards?

5. Which languages are currently the most widely spoken in the world? (The answer can be found in encyclopedias or on the Internet.)

b. What type of languages (natural or formal) can the naval flag alphabet be classified as?

7. Compare natural and formal languages:

a) by scope of application;

b) according to the rules of operating with language signs.

8. Why did people need formal languages?

9. In what cases can signs of formal languages be included in texts in natural language? Where did you encounter this?

Binary coding

Keywords:

Discretization alphabet

Power of the alphabet

Binary alphabet

Binary coding

Binary code width

Binary coding

5 1.3

1 . Z. 1. Converting information from continuous

Shapes to discrete

To solve his problems, a person often has to transform existing information from one form of representation to another. For example, when reading aloud, information is converted from discrete (text) form to continuous (sound). During a dictation in a Russian language lesson, on the contrary, information is transformed from a continuous form (the teacher’s voice) into a discrete one (students’ notes).

Information presented in discrete form is much easier to transmit, store or automatically process. Therefore, in computer technology, much attention is paid to methods for converting information from continuous to discrete form.

Information discretization is the process of converting information from a continuous form of representation into a discrete one,

Let's look at the essence of the information sampling process using an example.

Meteorological stations have recording instruments for continuous recording of atmospheric pressure. The result of their work is curves showing how pressure has changed over long periods of time (barograms). One of these curves, drawn by the device during seven hours of observation, is shown in Fig. 1.4.

Based on the information received, you can build a table in which the instrument readings at the beginning of measurements and at the end of each hour of observation will be entered (Fig. 1.5).

Rice. 1.5. Table built using a barogram

The resulting table does not give a completely complete picture of how the pressure changed during the observation period: for example, the highest pressure value that occurred during the fourth hour of observation is not indicated. But if you tabulate the pressure values observed every half hour or 15 minutes, the new table will give a more complete picture of how the pressure changed.

Thus, we converted information presented in continuous form (barogram, curve) into discrete form (table) with some loss of accuracy.

In the future, you will become familiar with ways to discretely represent audio and graphic information.

Binary coding

In general, to represent information in discrete form, it must be expressed using symbols in some natural or formal language. There are thousands of such languages. Each language has its own alphabet.

Alphabet is a set of symbols (signs) distinct from each other used to represent information. The power of the alphabet is the number of symbols (signs) included in it.

Rice. 1.7. Scheme for converting a character of an arbitrary alphabet into binary code

If the cardinality of the original alphabet is greater than two, then to encode a symbol of this alphabet you will need not one, but several binary symbols. In other words, the serial number of each character of the original alphabet will be associated with a chain (sequence) of several binary characters.

The rule for binary encoding of alphabet characters with power greater than two is represented by the diagram in Fig. 1.8.

L L LL

Chains of three binary symbols are obtained by adding two-digit binary codes to the right with the symbol O or 1. As a result, there are 8 three-digit binary code combinations - twice as many as two-digit ones:

Accordingly, a four-digit binary code allows you to get 16 code combinations, a five-digit one - 32, She (UTIZNACHNYY - 64, etc.

Please note that 2 = 2 1, 4 2 2, 8 = 23, 16 = 24, 32 = 25 etc. d.

If the number of code combinations is denoted by the letter N, and the bit depth of the binary code by the letter i, then the identified pattern in general form will be written as follows:

Task. The leader of the Multi tribe instructed his minister to develop a binary code and translate all important information into it. What depth of binary code will be required if the alphabet used by the Multi tribe contains 16 characters? Write down all code combinations.

Solution. Since the Multi tribe alphabet consists of 16 characters, they need 16 code combinations. In this case, the length (bit capacity) of the binary code is determined from the ratio: 16 2 i. From here

To write down all the code combinations of four O and 1, we will use the diagram in Fig. 1.8: 0000, 0001, 0010, 0011, 0100, 0101,

The website http://school-collection.eduxu/ hosts the virtual laboratory “Digital Scales”. With its help, you can independently discover the difference method - one of the ways to obtain the binary code of entire de-

By origin, languages are either natural or artificial.

Natural languages - These are sound (speech) and then graphic (writing) information sign systems that have historically developed in society. They arose to consolidate and transfer accumulated information in the process of communication between people. Natural languages act as carriers of the centuries-old culture of mankind and are distinguished by rich expressive capabilities and universal coverage of the most diverse areas of life.

Natural languages cannot always be used in the process of scientific knowledge due to such features as:

1) polysemy– many words and linguistic expressions of natural language, depending on the context, take on different meanings, which is associated with homonymy, for example the words “world”, “braid”, “sleeve”, etc.;
2) non-compositionality, those. the absence in natural language of rules with the help of which, out of context, it would be possible to determine the exact meaning of a complex expression, although the meanings of all the words included in it are known. For example, the phrase “He sat on a horse with a broken leg for a long time” can be interpreted in two ways: a) the rider’s leg was broken; b) the horse’s leg was broken;
3) self-applicability, those. when expressions can speak for themselves. For example, "I'm lying."

Artificial (scientific) languages are created specifically to solve certain problems of cognition. They appeared as formalized languages of science - mathematics, physics, chemistry, programming. Artificial languages are auxiliary sign systems created on the basis of natural languages for the accurate and economical transmission of scientific and other information. They are constructed using natural language or a previously constructed artificial language.

Scientific languages are subject to normative principles: unambiguity, objectivity and interchangeability.

According to the principle unambiguity the expression used as a name must be the name of only one object, if it is a single name, and if it is a general name, then the given expression must be a name common to all objects of the same class. In natural language, this principle is not always observed, but it must be adhered to when constructing artificial languages, for example, the language of predicate logic.

The principle of unambiguity excludes homonymy, i.e. designation of different objects in one word, which is often found in natural languages (for example, the word “spit” can mean a type of hairstyle, an agricultural tool, or a sandbank).

According to the principle objectivity statements must assert or deny something about the meanings of the names included in the sentences, and not about the names themselves. It should, of course, be borne in mind that the meanings of some names are the names themselves. Such cases do not contradict the principle of objectivity. For example, in the sentence “Matter is primary, and consciousness is secondary,” the word “matter” is the name of objective reality, and in the sentence ““Matter” is a philosophical category,” the word “matter,” taken in quotation marks, is the name of the name, the name of the category . Such names are called in quotation marks names. Sometimes in natural language there are cases where the name of a name is the original name itself. For example, in the sentence “The word “table” consists of four letters,” the word “table” is the name of the word itself. This use of names, when words designate themselves, is called autonomous. Autonomous use of expressions is unacceptable in scientific languages, since it leads to misunderstandings.

Italics or quotation marks are used to indicate the autonomous use of expressions. Mixing ordinary and autonomous use of expressions leads to logical errors in reasoning. An example of such an error is the following reasoning: “The dog is gnawing on a bone. “Dog” is a noun. Therefore, the noun is gnawing on a bone.”

Principle interchangeability: If in a complex name the part that is itself a name is replaced by another name with the same meaning, then the value obtained as a result of such replacement of the complex name must be the same as the meaning of the original complex name. For example, in the sentence “Aristotle taught philosophy to Alexander the Great,” the word “Aristotle” can be replaced with the words “creator of syllogistics.”

Extensional is called a context relative to those signs, the equivalent replacement of which does not lead to a change in the meaning of the context. The use of these signs is called extensional.

To preserve the principle of interchangeability and avoid antinomies, two ways of using names should be distinguished. The first is that the name simply identifies the item(s). The second is that objects denoted by a name are considered in a certain aspect.

For example: if two expressions have the same meaning, then one of them can be replaced by the other, and the sentence in which the replacement is made retains its true meaning. Thus, two expressions – “Mikhail Yuryevich Lermontov” and “author of the story “Taman”” – denote the same person, therefore in the sentence “Mikhail Yuryevich Lermontov was born in 1814” – the first expression (“Mikhail Yuryevich Lermontov”) can be replaced the second (“the author of the story “Taman””), without any prejudice to the truth of the entire statement: “The author of the story “Taman” was born in 1814.”

Thus, the principle of interchangeability serves to distinguish between extensional and intensional contexts.

A context (complex sign) in which the principle of interchangeability of at least one of the signs included in it is violated is called intensional with respect to this sign, i.e. depending on the intension (meaning) of a given sign.

A context (complex sign), in which equivalent replacement of signs does not lead to a change in the meaning of the context, is called extensional, depending only on the extension (meaning) of the sign.

For extensional contexts, only the objective meaning of expressions (their “volume”) is important, therefore expressions with the same meaning are identified. In intensional contexts, the meaning of an expression is also taken into account, so replacing expressions with the same meaning can make a true sentence false if these expressions have different meanings. If in the true sentence “The student did not know that Mikhail Yuryevich Lermontov is the author of the story “Taman”” the expression “author of the story “Taman”” is replaced by the expression “Mikhail Yuryevich Lermontov”, which has the same meaning, then the result will be an obviously false sentence : “The student did not know that Mikhail Yuryevich Lermontov was Mikhail Yuryevich Lermontov.”

For example, in the expression “Paris is the capital of France,” the names “Paris” and “capital of France” are used extensionally, since only the identity of their meanings is asserted and no replacement of any name with an equivalent one will lead to a change in the meaning of the context. In the sentence “Paris is the capital of France, due to which the French government is located in it,” the name “Paris” is used intensionally, since it is the property of this city to be the capital of France that provides justification for the fact that the government is located in it. If we replace the name “the capital of France” with its equivalent “the city in which the Eiffel Tower is located,” then the true statement will be converted into a false one, since the presence of the Eiffel Tower in Paris is not the reason that the French government is located there, i.e. e. Regarding the name "Paris", the context is extensional, since it simply means a certain city with all its characteristics, and any replacement of this name with equivalent ones will not lead to a change in the meaning of the statement.

Thus, with respect to one sign the context can be intensional, and with respect to another - extensional. The characterization of a context as intensional or extensional is always given in relation to a specific sign.