Logical database models. Logical Data Models

Logical models are implemented using the so-called predicate logic.

Predicate – a function that takes only two values – “true” and “false” and is intended to express the properties of objects and the relationships between them.

An expression that confirms or denies the presence of any properties in an object is called. statement.

Predicate logic constants are used to name objects subject area.

Logical expressions (or statements) form atomic (simplest) formulas.

Interpretation of predicates– the set of all admissible associations of variables with constants. At the same time tie up I - substitution of constants instead of variables.

The statement logically follows from the given premises. It is true whenever the premises are true.

Most in simple language Logic is the calculus of statements in which there are no variables. Each statement can be assigned the meaning “true” or “false”. Individual statements can be connected by connectives “and”, “or”, “not”, which are called boomy operators.

The basis of propositional calculus is the rules for the formation of complex propositions from atomic ones.

Example of complex statements.

A is true and B is false.

A and B are true.

A and B are logical statements that can be said to be true or false. Propositional calculus is not enough means of expression for knowledge processing, since it cannot represent expressions that include variables with quantifiers.

Predicate calculus with quantifiers (predicate logic) is an extension of propositional calculus, in which sentences including not only constants, but also variables can be used to express domain relations.

Predicates: clear (a), clear (c), ontable (a), ontable (c), on (c,b), cube(a), cube(b), pyramid.de(c).

In general, models based on predicate logic are described by a formal system, which is defined by the four:

M = (T, P, A, P)

T – set of basic elements (alphabet)

P – a set of syntactic rules on which you can build syntactically correct sentences

A – a set of axioms or several syntactically correct sentences, given a priori

P – production rules (inference rule or semantic rule with which you can expand set A by adding syntactically correct sentences to it

The main advantage of logical models: the ability to directly program the mechanism for outputting logically correct sentences. However, with the help of the rules that define the syntax of a language, it is impossible to establish the truth or falsity of a particular statement. This applies to all programming languages that implement predicate logic.

A statement can be constructed syntactically correctly, but turn out to be completely meaningless.

Logical models for representing and manipulating knowledge were especially popular in the 70s of the 20th century, especially with the advent of the prologue language.

As more and more new intellectual problems came into the field of view of researchers, it became clear that it was possible to talk about demonstrative inference in a small number of cases when the problem area in which the problem was being solved was formally described and fully known. But in most problems where human intelligence allows one to find a solution related to areas where knowledge is fundamentally incomplete, inaccurate and incorrect. Under such conditions, we can only talk about a plausible conclusion, in which the final result is obtained only with some assessment of confidence in its truth.

Therefore, the further development of knowledge bases using logical models followed the path of work in the field of so-called inductive logics, “common sense” logics, “faith” logics and other logical systems that have little in common with classical logic.

FRAME

Frame – data structure for representing stereotypical situations. The frame-based data representation model uses the concept of organizing the memory of human understanding and learning, proposed in 1979 by M. Minsky.

Frame (frame) – a unit of knowledge representation, the details of which may change according to the current situation. The frame can be supplemented at any time various information concerning the methods of its use, the consequences of this use, etc.

Frame structure – characteristics of the described stereotypical situation and their meaning, which are called slots And slot fillers .

Structure:

(Frame name: Slot1 name (slot1 value); Slot2 name (slot2 value); ... SlotName (slotN value))

The value of a slot can be almost anything: numbers, formulas, natural language texts, programs, inference rules, or a link to other slots in a given frame or other frames.

The slot value can be a slot value greater than low level, which makes it possible to implement the “matryoshka principle”.

Frame – a data structure representing a stereotyped situation. Each frame has several types of information attached to it. Some of this information is about how to use the frame, another part is about what to expect next, and another part is about what to do if expectations are not confirmed.

The frame can be represented as a kind of table.

In the table, additional columns are intended to describe the way a slot receives its value and the possible attachment of special procedures to a particular slot, which is allowed in frame theory.

The slot value can be the name of another frame. This is how networks of frames are formed.

There are several ways for a slot to receive a value in a frame instance:

1) default from sample frame;

2) through inheritance of properties from the frame specified in the ACO slot;

3) according to the formula specified in the slot;

4) through the joining procedure;

5) clearly from the dialogue with the user;

6) from the database.

The most important property of frame theory is the so-called inheritance of properties. This inheritance occurs through AKO connections. A KIND OF (AKO)

The ACO slot points to a frame at a higher level of the hierarchy, from which they are implicitly inherited, i.e. the values of similar slots are transferred.

In the network of frames in the figure, the concept “student” inherits the properties of the frames “child” and “person”, which are more high level hierarchy. Thus, to the question “do students like sweets”, the answer is “yes”, since all children have this property, which is indicated in the “child” frame.

Inheritance may be partial, since the age of the students is not inherited from the “child” frame, since it is specified explicitly in its own frame.

There are static and dynamic frame systems.

IN static frame systems frames cannot be changed in the process of solving a problem, and in dynamic systems frames this one is acceptable.

Frame-based programming systems are said to be object-oriented. Each frame corresponds to some object of the subject area, and slots contain data describing this object, i.e. slots contain the values of object attributes.

A frame can be represented as a list of properties, and if you use database tools, then as a record.

Most brightly advantages of frame systems knowledge representations appear when generic connections change infrequently and the subject area has few exceptions.

In frame systems, data on generic relationships is stored explicitly like values of other types.

Slot values are presented in the system in a single copy, since they are included in only one frame that describes the most general concepts from all those that contain a slot with a given name. This property of frame systems ensures economical placement of the knowledge base in computer memory.

Another advantage of frames– the value of each slot can be calculated using appropriate procedures or found by heuristic methods. Frames allow the manipulation of both declarative and procedural knowledge.

Disadvantages of frame systems: relatively high complexity.

A logical data model is a visual graphical representation of data structures, their attributes and relationships. The logic model represents data in a way that is easy to understand for business users. The design of the logical model should be free from the requirements of the platform and implementation language or the way the data will be further used.

Development uses data requirements and analysis results to form a logical data model. The logical model is reduced to third normal form and checked for compliance with the process model.

The main components of a logic model are:

Entities;

Entity attributes;

Relationships between entities.

Essence.

The entity models the structure of similar information objects(documents, data warehouses, database tables). Within a data model, an entity has a unique name, expressed as a noun. For example: student, invoice, product_reference book.

An entity is a template on the basis of which specific instances of an entity are created. For example: an instance of the student entity is Ivan Ivanovich Ivanov.

The entity has the following properties:

Each entity has a unique name, and the same interpretation must be applied to the same name;

An entity has one or more attributes that are either owned by the entity or inherited through a relationship;

An entity has one or more attributes that uniquely identify each instance of the entity;

Each entity can have any number of connections with other entities in the model.

On a diagram, an entity is usually depicted as a square divided into two parts.

Rice. 40 The essence of the data model.

An entity in the IDEF1X methodology is independent if each instance of the entity can be uniquely identified without defining its relationships with other entities. An entity is called dependent if the unique identification of an instance of the entity depends on its relationship to another entity.

The dependent entity is represented by a rectangle with rounded corners rice. (benefits entity dependent on the resident_biysk entity)

Attribute- any characteristic of an entity that is significant for the subject area under consideration and intended for qualification, identification, classification, quantitative characteristics or expressions of the state of an entity. An attribute represents a type of characteristics or properties associated with a set of real or abstract objects (people, places, events, states, ideas, pairs of objects, etc.). An attribute instance is a specific characteristic individual element multitudes. An attribute instance is defined by the type of the characteristic and its value, called the attribute value. In the ER model, attributes are associated with specific entities. Thus, an entity instance must have a single defined value for its associated attribute.

An attribute can be either mandatory or optional (Figure 2.23). Mandatory means that the attribute cannot accept null values. The attribute can be either descriptive (i.e., a regular descriptor of an entity) or part of a unique identifier (primary key).

Unique identifier (key)- This minimum set attributes designed to uniquely identify each instance of this type essence. Minimality means that excluding any attribute from the set will not allow identifying an entity instance by the remaining ones. In the case of full identification, each instance of a given entity type is fully identified by its own key attributes, otherwise its identification also involves the attributes of another parent entity through a relationship.

The attributes included in the key must be mandatory and will not change over time. The attributes included in the key must be mandatory and will not change over time. For example: we have the entity Resident_Biysk.

The age attribute cannot be part of the key, since it changes annually; the passport number cannot be part of the key, since the instance may not have a passport. It is better to use the insurance certificate number as a key here.

Relationship- a named association between two entities that is significant for the subject area under consideration. A relationship is an association between entities in which, typically, each instance of one entity, called a parent entity, is associated with an arbitrary (including zero) number of instances of a second entity, called a child entity, and each instance of a child entity is associated with exactly with one instance of the parent entity. Thus, an instance of a child entity can only exist if the parent entity exists.

A relationship is represented by a line drawn between a parent entity and a child entity, with a dot at the end of the line at the child entity.

The connection can be given a name, expressed by the grammatical turn of the verb and placed near the connection line. The name of each relationship between two given entities must be unique, but the names of relationships in the model do not have to be unique. The name of a relationship is always formed from the point of view of the parent, so that a sentence can be formed by combining the name of the parent entity, the name of the relationship, the degree expression, and the name of the child entity.

For example, the seller's relationship with the contract may be expressed as follows:

the seller can receive compensation for 1 or more contracts;
the contract must be initiated by exactly one seller.

The relationship can be further defined by specifying degree or cardinality (the number of instances of a child entity that can exist for each instance of a parent entity). The following link powers can be expressed in IDEF1X:

Each parent entity instance may have zero, one, or more child entity instances associated with it;
each parent entity instance must have at least one child entity instance associated with it -P;
each instance of a parent entity must have no more than one instance of a child entity associated with it - Z;
Each instance of a parent entity is associated with some fixed number of instances of a child entity.

If an instance of a child entity is uniquely identified by its relationship with the parent entity, then the relationship is called identifying, otherwise it is called non-identifying.

The identifying link is depicted as a solid line,

Rice. 43

Non-identifying is depicted with a dashed line.

Fig.44.

In an identifying relationship, the key of the parent entity is transferred to the key region of the dependent entity, indicating in parentheses (FK) - foreign key. In a non-identifying relationship, the key of the parent entity is transferred to the attribute area of the child entity, indicated in parentheses (FK) - external.

Rice. 45 Identifying connection.

Rice. 46 Non-identifying connection.

On initial stages modeling can reveal many-to-many relationships. The presence of such connections indicates that the analysis is incomplete. Typically, such relationships are converted into identifying and non-identifying relationships.

Rice. 47 Many-to-many communication.

In the process of data modeling, entities can be identified, some of whose attributes and relationships are the same. To model such cases, a hierarchy of categories is used. All common attributes are separated into an entity called a supertype. The remaining attributes are placed into entities called subtypes. And they are connected to the supertype by a connection called DISCRIMINANT.

For example:

Rice. 48 Example of category hierarchy.

Annotation

In this course work describes the design of a central city hospital database and its implementation in Oracle Datebase. The subject area was presented, conceptual, logical and physical data models were developed. The necessary tables, queries, and reports were created using Oracle Datebase tools. Coursework consists of:

Introduction 3

1. Subject area 4

2. Conceptual model 5

3.Logical database model 7

4. Model of physical organization of data 9

5.Implementation of databases in Oracle 9

6.Creating tables 10

7.Creating queries 16

8. Conclusion 27

References 28

Introduction

A database is a single, capacious repository of various data and descriptions of their structures, which, after being defined separately and independently of applications, is used simultaneously by many applications.

In addition to data, the database may contain tools that allow each user to operate only with the data that is within their competence. As a result of the interaction of the data contained in the database with the methods available to specific users, information is generated that they consume and on the basis of which, within their own competence, they enter and edit data

The purpose of this course work is to develop and implement a database for the central hospital to ensure storage, accumulation and provision of information about the activities of the hospital. The created database is intended mainly to automate the activities of the main departments of the hospital.

Subject area

A subject area is a part real system, which is of interest for this study. When designing automated information systems The subject area is represented by data models of several levels. The number of levels depends on the complexity of the problems being solved, but in any case it includes conceptual and logical levels.

In this course work, the subject area is the work of the central hospital, which treats patients. The organizational structure of the hospital consists of two departments: the registry and the reception area. At the reception desk, appointments are made, referrals are issued, patients are assigned to wards, and insurance numbers are recorded. The emergency room, in turn, keeps records of admission and discharge, patient diagnoses, and medical history.

The database is designed to store data about patients, their placement, prescribed medications and attending physicians.

Conceptual model

The first phase of the database design process is to create a conceptual data model for the part of the enterprise being analyzed.

A conceptual model is a model of a domain. The components of the model are objects and relationships. The conceptual model serves as a means of communication between different users and is therefore developed without taking into account the specifics of the physical representation of data. When designing a conceptual model, all efforts of the developer should be aimed mainly at structuring data and identifying relationships between them without considering implementation features and processing efficiency issues. The design of the conceptual model is based on an analysis of the data processing tasks being solved at this enterprise. A conceptual model includes descriptions of objects and their relationships that are of interest in the subject area under consideration. Relationships between objects are part of the conceptual model and must be shown in the database. A relationship can span any number of objects. On the other hand, each object can participate in any number of relationships. Along with this, there are relationships between the attributes of an object. There are relationships of the following types: “one to one”, “one to many”, “many to many”.

Most popular model conceptual design is the entity-relationship model (ER-model), it belongs to the semantic models.

The main elements of the model are entities, connections between them and their properties (attributes).

An entity is a class of objects of the same type, information about which must be taken into account in the model.

Each entity must have a name expressed by a singular noun. Each entity in the model is depicted as a rectangle with a name.

An attribute is a characteristic (parameter) of an entity.

Domain – a set of values (area of attribute definition).

Entities have key attributes - an entity key is one or more attributes that uniquely identify this entity.

A set of entities for the central hospital (entity attributes are indicated in parentheses, key attributes are underlined):

PATIENTS ( Patient code, last name, first name, date of birth, insurance policy number, department code);

TREATMENT ( Patient code, diagnosis, discharge date, doctor code, cost);

DEPARTMENTS( Branch code, name of department, number of wards);

INCOME ( Patient code date of admission, ward code);

CHAMBERS ( Chamber code, number of places, department code);

DOCTORS(Doctor code, last name, first name, date of birth, personal file number, department code);

Entity-relationship diagram for district hospital shown in Figure 1.

Logical Database Model

The version of a conceptual model that can be provided by a particular DBMS is called a logical model. The process of building a logical database model must be based on a specific data model (relational, network, hierarchical), which is determined by the type of DBMS intended for implementation of the information system. In our case, the database is created in the Oracle environment and will be a relational database.

The relational model is characterized by its simplicity of data structure, user-friendly tabular representation, and the ability to use the formal apparatus of relational algebra and relational calculus to manipulate data.

In relational data models, objects and relationships between them are represented using tables. Each table represents one object and consists of rows and columns. Table in relational model called a relation.

Attribute (field) – any column in the table.

Tuples (records) are table rows.

The tables are linked to each other using key fields.

A key is a field that allows you to uniquely identify a record in a table. The key can be simple (consisting of one field) or compound (consisting of several fields).

IN relational databases data logical design leads to the development of a data schema, which is presented in Figure 2.

Fig.2.
4. Model of physical data organization

A physical data model describes how data is stored on a computer, providing information about the structure of records, their ordering, and existing access paths.

The physical model describes the types, identifiers and bit widths of the fields. The physical data model reflects the physical placement of data on machine media, that is, what file, what objects, with what attributes it contains and what are the types of these attributes.

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To represent mathematical knowledge in mathematical logic, logical formalisms are used - propositional calculus and predicate calculus. These formalisms have clear formal semantics and inference mechanisms have been developed for them. Therefore, predicate calculus was the first logical language that was used to formally describe problem areas related to the solution applied problems.

Logic models knowledge representations are implemented using predicate logic.

Predicate is a function that takes two values (true or false) and is designed to express the properties of objects or relationships between them. An expression that asserts or denies the presence of any properties in an object is called statement. Constants serve for naming objects of the subject area. Logical sentences or statements form atomic formulas. Predicate interpretation is the set of all valid bindings of variables to constants. Binding is the substitution of constants instead of variables. A predicate is considered generally valid if it is true in all possible interpretations. A statement is said to follow logically from given premises if it is true whenever the premises are true.

Descriptions of subject areas made in logical languages are called logical models .

GIVE (MIKHAIL, VLADIMIR, BOOK);

($x) (ELEMENT (x, EVENT-GIVE) ? SOURCE (x, MICHAEL) ? DESTINATION? (x, VLADIMIR) OBJECT (x, BOOK).

Here two ways of recording one fact are described: “Mikhail gave the book to Vladimir.”

Logical inference is carried out using a syllogism (if B follows from A, and C follows from B, then C follows from A).

In general, logic models are based on the concept formal theory, given by the four:

S= ,

where B is a countable set basic characters (alphabet) theory S;

F - subset expressions of theory S, called theory formulas(expressions are understood as finite sequences of basic symbols of theory S);

A is a selected set of formulas called axioms of the theory S, that is, a set of a priori formulas;

R - a finite set of relations (r 1, ..., r n) between formulas, called rules of inference.

The advantage of logical models of knowledge representation is the ability to directly program the mechanism for outputting syntactically correct statements. An example of such a mechanism is, in particular, the inference procedure built on the basis of the resolution method.

Let's show the resolution method.

The method uses several concepts and theorems.

Concept tautologies, a logical formula whose value will be “true” for any values of the atoms included in them. Denoted by?, read as “generally valid” or “always true.”

Theorem 1. A?B if and only if?A B.

Theorem 2. A1, A2, ..., An? In if and only if when? (A1?A2?A3?…?An) V.

Symbol? read as “it is true that” or “can be deduced.”

The method is based on the proof of tautology

? (X? A)?(Y? ? A)?(X? Y) .

Theorems 1 and 2 allow us to write this rule in the following form:

(X? A), (Y? ? A) ? (X? Y),

which gives grounds to assert: it is possible to deduce from the premises.

In the inference process using the resolution rule, the following steps are performed.

1. The operations of equivalence and implication are eliminated:

2. The negation operation moves inside the formulas using De Morgan's laws:

3. Logical formulas are reduced to disjunctive form: .

The resolution rule contains a conjunction of disjuncts on the left side, therefore, bringing the premises used for proof to a form that represents a conjunction of disjuncts is a necessary step in almost any algorithm that implements logical inference based on the resolution method. The resolution method is easy to program; this is one of its most important advantages.

Suppose we need to prove that if the relations and are true, then the formula can be derived. To do this, you need to follow the following steps.

1.Bringing premises to disjunctive form:
, , .

2.Construction of the negation of the deduced conclusion. The resulting conjunction is valid when and are both true.

3.Application of resolution rule:

(contradiction or “empty disjunct”).

So, assuming the falsity of the deduced conclusion, we obtain a contradiction, therefore, the deduced conclusion is true, i.e. , is deducible from the initial premises.

It was the resolution rule that served as the basis for the creation of the language logic programming PROLOG. In fact, the PROLOG language interpreter independently implements output similar to the one described above, generating an answer to the user’s question addressed to the knowledge base.

In predicate logic, in order to apply the resolution rule, it is necessary to carry out a more complex unification of logical formulas in order to reduce them to a system of disjuncts. This is due to the presence of additional syntax elements, mainly quantifiers, variables, predicates and functions.

The algorithm for unifying predicate logical formulas includes the following steps.

After completing all the steps of the described unification algorithm, you can apply the resolution rule. Usually this involves negating the conclusion being drawn, and the derivation algorithm can be briefly described as follows: If several axioms are given (TH theory) and a conclusion has to be made about whether a certain formula is deducible R from the axioms of the theory Th, the negation is constructed R and added to Th, giving new theory Th1. After reducing the axioms of the theory to a system of disjuncts, one can construct a conjunction and axioms of the theory Th. At the same time, it is possible to derive disjuncts - consequences - from the original disjuncts. If R is deducible from the axioms of the theory Th, then in the process of derivation one can obtain a certain clause Q, consisting of one letter, and the opposite clause . This contradiction indicates that R deducible from the axioms Th. Generally speaking, there are many proof strategies; we have considered only one of the possible ones - top-down.

Example: let’s imagine the following text using predicate logic:

“If a student knows how to program well, then he can become a specialist in the field of applied computer science.”

“If a student does well on the information systems exam, then he knows how to program well.”

Let us represent this text using first-order predicate logic. Let us introduce the following notation: X- variable to designate the student; Fine- constant corresponding to the level of qualification; P(X)- a predicate expressing the possibility of the subject X become a specialist in applied computer science; Q(X, okay)- a predicate denoting the subject’s skill X program with evaluation Fine; R(X, okay)- predicate specifying the student’s connection X with examination mark in information systems.

Now let's construct a set of correctly constructed formulas:

Q(X, good).

R(X, good)Q(X, good).

Let's supplement the resulting theory with a specific fact
R(Ivanov, good).

Let's perform inference using the resolution rule to determine whether the formula is P(Ivanov) a consequence of the above theory. In other words, is it possible to deduce from this theory the fact that student Ivanov will become a specialist in applied computer science if he passes the information systems exam well?

Proof

1. Let us transform the original formulas of the theory in order to bring them to a disjunctive form:

(X, good) P(X);

(X, good) (X, good);

R(Ivanov, Fine).

2. Add to the existing axioms the negation of the conclusion being drawn

(Ivanov).

3. Let's construct a conjunction of disjuncts

(X, good) R(X)? ? P(Ivanov, good)? ? Q(Ivanov, good), replacing a variable X to a constant Ivanov.

The result of applying the resolution rule is called resolvent. IN in this case the resolvent is (Ivanov).

4. Construct a conjunction of clauses using the resolvent obtained in step 3:

(X, good) (X, good) (Ivanov, good) (Ivanov, good).

5. Let us write the conjunction of the resulting resolvent with the last disjunct of the theory:

(Ivanov, good) (Ivanov, good)(contradiction).

Therefore, the fact P(Ivanov) deduced from the axioms of this theory.

To determine the order of application of axioms in the inference process, the following heuristic rules exist:

At the first step of inference, the negation of the deduced conclusion is used.
Each subsequent step of derivation involves the resolvent obtained at the previous step.

However, using the rules that define the syntax of a language, it is impossible to establish the truth or falsity of a particular statement. This applies to all languages. A statement can be constructed syntactically correctly, but turn out to be completely meaningless. A high degree of uniformity also entails another disadvantage logical models- the difficulty of using heuristics that reflect the specifics of a particular subject problem when proving. Other disadvantages of formal systems include their monotony, lack of means for structuring the elements used and the inadmissibility of contradictions. Further development knowledge bases followed the path of work in the field of inductive logics, “common sense” logics, logics of faith and others logic circuits, which have little in common with classical mathematical logic.

1.1 Logic models

The logical (predicate) model of knowledge representation is based on the algebra of statements and predicates, on the system of axioms of this algebra and its rules of inference. Of the predicate models, the most widespread is the model of first-order predicates, based on terms (arguments of predicates - logical constants, variables, functions), predicates (expressions with logical operations).

Example. Let’s take the statement: “Inflation in the country exceeds last year’s level by 2 times.” This can be written in the form of a logical model: r(InfNew, InfOld, n), where r(x,y) is a relation of the form “x=ny”, InfNew is the current inflation in the country, InfOld is inflation last year. Then we can consider true and false predicates, for example, r(InfNew, InfOld, 2)=1, r(InfNew, InfOld, 3)=0, etc. Very useful operations for logical inferences are the operations of implication and equivalence.

Logical models are convenient for representing logical relationships between facts; they are formalized, strict (theoretical), and there is a convenient and adequate toolkit for their use, for example, the logical programming language Prolog.

Models of this type are based on the concept of a formal system. The formulation and solution of any problem are related to a specific subject area. Thus, when solving the problem of scheduling the processing of parts on metal-cutting machines, we involve in the subject area such objects as specific machines, parts, time intervals and general concepts of “machine”, “part”, “type of machine”, etc.

All objects and events that form the basis of a common understanding of the information necessary to solve a problem are called a subject area. Mentally, the subject area is represented as consisting of real objects called entities. The entities of the subject area are in certain relationships to each other. Relationships between entities are expressed using propositions. In language (formal or natural), propositions correspond to propositions.

Descriptions of subject areas made in logical languages are called logical models. Logic models built using logic programming languages are widely used in knowledge bases and expert systems.

1.2 Product models

The production model of knowledge representation is the development of logical models towards the efficiency of knowledge representation and output.

A production is an expression containing a kernel interpreted by the phrase “If A, then B,” a name, scope, a condition for the applicability of the kernel, and a postcondition, which is a procedure that should be performed after successful implementation kernels. All parts except the core are optional.

An interconnected set of products forms a system. The main problem of knowledge inference in a product system is the choice of the next product to analyze. Competing products form a front.

Products (along with network models) are the most popular means of representing knowledge in AI systems. Implication can be interpreted in the usual logical sense as a sign of the logical consequence of B from true A. Other interpretations of the product are also possible, for example, A describes some condition necessary for action B to be performed.

If a certain set of products is stored in the system’s memory, then they form a system of products. The product system must be specified special procedures product management, with the help of which products are updated and the implementation of one or another product from among the updated ones occurs.

The product system includes a rule base (products), a global database and a management system. A rule base is a memory area that contains a body of knowledge in the form of IF - THEN rules. The global database is a memory area containing actual data (facts). The control system generates conclusions using a rule base and a database. There are two ways to form conclusions - direct inferences and inverse inferences.

In direct inferences, one of the data elements contained in the database is selected, and if, when compared, this element agrees with the left side of the rule (premise), then the corresponding conclusion is derived from the rule and placed in the database, or the action defined by the rule is executed, and accordingly The contents of the database change. In reverse inferences, the process begins from the set goal. If this goal is consistent with right side rules (conclusion), then the premise of the rule is taken as a subgoal or hypothesis. This process is repeated until a subgoal match is obtained with the data. With a large number of products in the product model, checking the consistency of the product system becomes more difficult, i.e. lots of rules. Therefore, the number of products they work with modern systems AI, as a rule, does not exceed thousands.

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