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STRUCTURIZATION OF KNOWLEDGE ARRAYS USING COGNITIVE MODELING
TOOLS
S.N. Larin, Candidate of Technical Sciences, Leading Researcher E.Yu. Khrustalev, Doctor of Economic Sciences, Chief Researcher Central Economics and Mathematics Institute of the Russian Academy of Sciences (Russia, Moscow)
DOI:10.24412/2411-0450-2024-5-1-262-268
Abstract. The article presents the results of research and modeling of the structuring of knowledge sets. Finding a solution to this pressing problem is especially important in the current period of development of our country. To achieve this, it is proposed to use cognitive modeling tools. A knowledge representation model has been developed. It is an extension of the existing model in cognitive modeling in the form of a signed digraph and is based on a conceptual model of knowledge representation in the form of a knowledge field. The novelty of the research results lies in the description of the studied bodies of knowledge in structural and functional aspects. The cognitive map of the body of knowledge is described in the functional system of the knowledge field, and the results of its structural and functional decomposition are described in the conceptual system of the knowledge field.
Keywords: knowledge arrays, structuring, cognitive modeling, structural-functional decomposition.
The information revolution has significantly changed the spheres of cognition, perception and human activity. Its result at the current stage of social development is the digital-ization of all significant areas of life, including the education system. Building a digital educational environment is one of the key tasks within the framework of the implementation of the national projects "Education" and "Science", and is also an integral condition for the successful implementation of the Strategy for Scientific and Technological Development of Russia.
The exponential growth of the volume of information, the speed of its perception, problems of synthesis and analysis of new information, problems of the adequacy of educational technologies, the level of digitalization of the individual and the depth of digital experience determine the need to solve the problems of structuring bodies of knowledge in the context of digitalization. Since in conditions of high information saturation, the acquisition of knowledge through the "screening out" of insignificant information becomes a fundamental factor, "cognition" is currently becoming the leading characteristic and basic resource of the individual. Modern cognitive methodology is a complex of scientific
knowledge based on the study and knowledge of the essential characteristics and internal connections of psychological and pedagogical objects, phenomena and processes and contributing to the implementation of the key idea - the idea of personal, organizational, pedagogical, systemic development, influencing the development of society and the country's economy. Cognitive modeling reflects subjective perceptions (individual or collective) of the problem under study. And the cognitive model is intended to identify the structure of causal relationships between the elements of a system, a complex object, and assess the consequences that occur under the influence of influence on these elements or changes in the nature of the connections.
Purpose of the study
The purpose of this article is to substantiate the legitimacy of using cognitive modeling tools for structuring bodies of knowledge.
Materials and methods
The most effective approach for modeling complex systems that take into account cause-and-effect relationships between its elements is the use of a fuzzy cognitive map (FCM -Fuzzy Cognitive Map). The advisability of using such an approach as a tool for modeling intelligent control systems is indicated in their
works by E.Yu. Khrustaleva [1], Kulba V.V. and others [2], Ginis L.A. [3], Butenko E.D. [4], Kosko B. [5], Tsadirasa A.K. [6] and other authors. The cognitive modeling methodology was proposed by R. Axelrod [7] and is used to study unstructured or weakly structured complex systems that can be represented as a fuzzy weighted directed graph, the vertices of which are concepts that describe the main characteristics of the system's behavior. Weighted graph arcs characterize causal relationships between concepts, which can be described using linguistic terms that take values from 0 to 1.
The methodology of cognitive modeling is based on a model representation of subjective opinions of experts about a certain body of knowledge and includes: a methodology for structuring the body of knowledge; model for an expert's representation of an array of knowledge in the form of a signed digraph (cognitive map) (F, W), where F is the set of graph vertices (factors of the knowledge array), W is the set of arcs (cause-and-effect relationships between factors of the knowledge array); methods for analyzing a body of knowledge - forecasting development and searching for control actions that transfer the body of knowledge to the desired state. However, an analysis of existing cognitive modeling systems (Data Mining systems, simulation modeling systems, expert systems, etc. [8]) revealed a significant drawback, which is that the interfaces of these systems poorly take into account the leading role of the expert in cognitive modeling and are not focused on meeting the needs of experts (users) at the stages of building, setting up a model, analyzing modeling results, explaining and interpreting them.
Results and discussion
To eliminate the above drawback, an approach to structuring bodies of knowledge using cognitive modeling tools is proposed. It lies in the fact that the bodies of knowledge under study are described in two aspects: structural and functional.
The description of the body of knowledge in the structural aspect is carried out on the basis of structural-functional decomposition, which consists in identifying the components of the body of knowledge under study in the
form of a "Part-Whole" hierarchy, (D, 0), where, D={di} - set of elements of the body of knowledge - this is the whole and its component parts, 0 - the "Part-Whole" relation on the set D, i=1,..., n.
The description of the body of knowledge in the functional aspect is carried out by determining the main characteristics (features) of all elements of the body of knowledge Fi={fij}, j=1, ■■■, m. Next, on the set of attributes Fi of each element di, a cognitive map (Fi, Wi) is formed by expert means, reflecting the expert's ideas about the laws of operation of this element, where Fi - is the set of vertices, Wi - is the adjacency matrix of the digraph reflecting the functional structure of the knowledge array element di. Cognitive maps of individual elements are combined into a common cognitive map (F, W), where F=uFi - is a set of features that describe the body of knowledge as a whole, and W is an adjacency matrix, including adjacency matrices Wi of individual elements di and describing their interaction. Thus, the cognitive model for structuring an array of knowledge has a block structure.
To facilitate the interpretation of simulation results obtained on the cognitive model (F, W), a knowledge representation model has been developed. It is an extension of the existing model in cognitive modeling in the form of a signed digraph and is based on a conceptual model of knowledge representation in the form of a knowledge field. The latter is used in knowledge engineering to create intelligent systems [9].
The knowledge field is defined by a triple (X, Y, M), where:
X - input data of problems solved by the intelligent system;
Y - output data - the result of solving problems;
M - the operational model on the basis of which the transformation of X into Y occurs.
The operational model M = (Kd, Kf) includes the conceptual system Kd, reflecting the conceptual structure of the body of knowledge, and the functional system Kf, which models the patterns and determines the dynamics of the development of the problem area of the body of knowledge under study.
It is proposed to describe the cognitive map of the body of knowledge (F, W) in the functional system of the knowledge field Kf, and the results of its structural-functional decomposition D, @) - in the conceptual system Kd.
The description of the cognitive map of the body of knowledge in the functional structure of the knowledge field is carried out on the basis of the development of scales for measuring attributes, determining the preferences of the expert to adjust the strength of influence of the characteristics of the situation and choosing methods for predicting the dynamics of the development of the problem area of the body of knowledge under study.
To develop scales for measuring traits, it is advisable to use the method proposed by Torgerson [10]. It is based on specifying reference points (the maximum and minimum values of the attribute) and obtaining new scale values by dividing the segment in half with the interpretation of the midpoint in the subject area. As a result of this procedure, we obtain a linearly ordered set of linguistic values of the j-th attribute of the i-th concept, -Zij={ztjk}, where k - is the number of the linguistic value, the elements of which are mapped onto the segment of the numerical axis [0,1]. For each linguistic value ztjk<Ztj, a point xtjk <[0,1] and its surroundings xjk+s, are defined on the number axis, having the same linguistic interpretation ztjk. Thus, for each attribute of each concept, a numerical scale Xij is defined, each point of which xijeXij has a linguistic interpretation ztjk<Ztj. The initial state of the situation is defined as a vector of values of all its features X(0)=(xn°, ..., including possible positive pij>0 and negative pij<0 deviations of each feature from its current value.
Currently, to determine the strength of the influence of features, the method of direct expert assignment of the strength of influence is used in the form of a coefficient from the range of values [- 1, 1] or a linguistic value from an ordered set, for example, {"strongly increases", ..., "weakly increases", ..., "does not affect"}. However, the practical application of this method often leads to errors. To reduce errors in determining the strength of
influence of features, methods have been developed for extracting expert knowledge about the strength of influence of features. Three methods of indirectly determining the strength of influence are most often used: direct assessment (clear and fuzzy); pairwise comparison; specifying a functional dependency.
The formulation of the problem of predicting the dynamics of development of the problem area of the body of knowledge under study can be presented as follows.
Let's assume that there are: a set of factors F={Fi}; factor scales Xj; initial state of the body of knowledge under study X(t)=(xu, ..., xnm); adjacency matrix W=\wtjsl\, where indices i,s - concept number, j,l - number of attribute of concept with number i or s; initial vector of factor increments P(t)=(pu,..., pnm).
It is necessary to find the increment vectors of features P(t), P(t+1), ..., P(t+n) and situation states X(t), X(t+1), ..., X(t+n) in successive discrete moments of time t, t+1, ., t+n.
This problem is solved by the method of successive iterations. The vector of increments of feature values at time t+1 is determined from the relation:
P(t+1)=P(t)°W (1),
and the state of the body of knowledge under study at time t+1 from the relation:
X(t+1)=X(t) +P(t+1) (2).
Currently, for qualitatively specified systems (the values of variables and the elements of the adjacency matrix are linguistic values), the operation (°) is defined as max-product -an operation (multiplication and taking the maximum), for which in works [11, 12, 13, 14] Algorithms for obtaining forecasts of the dynamics of development of the problem area of the body of knowledge under study have been developed. However, these algorithms work for positive definite matrices, while in our case the elements of the adjacency matrix and increment vectors can take on both positive and negative values.
To transform an adjacency matrix W=l Wij sllnxn with positive and negative elements to a positive definite double matrix
= lw ij sll2nx2n the following rule is used:
If Wij sl>0, that w\(2j-1) s(2l-1)= Wij sl, w\(2j)
s(2l) = Wij sl
If Wij sl<0, that w\(2j-1) s(2l)= - Wij sl, w\(2j)
s(2l-1) = - Wij sl
The initial vector of increments P(t) and the vector of predicted values of features P(t+1), in this case, must have a dimension of 2n. The rule for obtaining the initial increment vector P (t) of dimension 2n from the initial increment vector P(t) of dimension n is as follows:
If Pij(t)>0, that p\(2j-1)(t)= pij(t), p\(j(t) =
0;
If Pij(t)<0, that p\(2j)(t)= Pij(t), p\(2j-1)(t)=
0;
In the vector Px(t)=(pn-, pn+,..., pnm, pnm+), the value of the feature fij is characterized by two elements: the element with index 2j is characterized by a positive pij+, and with the index 2j-1 - a negative pij- increment of the feature fij. Then, the double increment vector Pr(t+1) for the positive definite matrix W" is determined using the following equation:
P"(t+1)= PYt)°W (3),
where, to calculate the element of the vector P^(t+1), the following rule is used:
p\j(t+1) = max (p\l(t)*w\jsl) (4)
sl
Elements of vectors of increments of feature values obtained at successive moments of time P^(t+1), ..., P"(t+n) after transposition are presented in the form of a block matrix:
P = lP"(t+1)T, ... , P"(t+n)Tl (5)
The rows of this matrix are the increment values of one feature at successive points in time, the columns are the increment values of all features at the time point corresponding to the selected column. The matrix Pt is called the increment matrix and is used in the operation of algorithms for predicting the dynamics of development of the problem area of the body of knowledge under study.
The conceptual system is intended to represent the structural and functional decomposition of the situation (D, 0) and is used to support the processes of interpreting forecasts of the dynamics of development of the problem area of the body of knowledge under study. In the conceptual system of the knowledge field, elements of the knowledge array are represented as specific concepts diGD and are defined by the triple: (di, F(di), V(di)), where di is the name of the concept; F(di) - content of the concept - vector of feature values Fi={fj}, F(di)=(xu, ..., xnm); V(di) - the scope of the concept is an element of the body of knowledge described in the model. The concept di is represented as a point with coordinates of the values of the concepts' attributes (x11, ., xnm) in the space obtained by the Cartesian product of the scales of all attributes of this concept, SS(di) = ^ Xij.
The space SS(di) in psychology is called semantic space. It can be interpreted as a model of human semantic memory.
In the proposed model of the conceptual system, each concept diGD is represented in its semantic space SS(di), that is the set of semantic spaces SS(D) ={SS(dj), ..., SS(dn)} and the relation 0 ("Part-Whole") between them are defined. The relation 0 between semantic spaces SS(di) 0 SS(dq) means that any two concepts di g SS(di) and dq g SS(dq) are related by the relation 0, that is, di 0dq. Formally, all points of the semantic space with coordinates different from the coordinates of the concept di can be new concepts different from the concept di. This means that when an element of the knowledge array is represented by the concept di in the semantic space SS(di), in the same semantic space concepts will be presented into which the concept di can be transformed by changing the values of its features. However, not all points of the semantic space denote some object that exists in reality and have an interpretation in the subject area of the body of knowledge under study.
To facilitate the search for points in the semantic space that have an interpretation in the subject area of the body of knowledge, it is proposed to structure the semantic space of
each concept di in the form of a conceptual cluster D'. A conceptual cluster is a partially ordered set of concepts of different levels of generality that are connected by the "Class-Subclass" relationship.
The concept di1 is a generalized concept (class) for the concept di2 if two conditions are met:
1) the content F(di1) of the concept di1 is a subset of the content F(di2) of the concept di2, that is (F(d1)^F(dr2));
2) the volume V(di2) of the non-generalized concept di2 is a subset of the volume V(di]) of the concept di1, that is (V(d^)=V(d^)).
To define a conceptual cluster in the semantic space SS(di), the basic concept diB is determined, which defines the class of objects to which the element of the studied body of knowledge di belongs. When determining the basic concept for each attribute of the concept di, which has the value xij, the interval of values XijB=[xijb, Xijc], Xij<XiP, Vj, which defines the boundaries of the class of objects, is determined by expert means. The subspace
T(diB)= x XijB, the semantic space SS(di), is
j
called the domain of tolerance of the basic concept, and XijB is called the tolerance interval of the feature fj.
The basic concept is defined by a triple (diB, F(diB), V(dB)), where diB is the name, F(diB) is the content of the basic concept -this is a vector of tolerance intervals of signs (X11B,..., XnmB), V(diB) - the scope of the basic concept is a set of objects whose feature values belong to the tolerance area of the basic concept T(diB).
Generalization of a basic concept can be performed by removing any of its features or any combination of features. In this case, H=2m-1 generalizations of a basic concept containing m features are possible. Generalized concepts are characterized by a triple: (dBh, F(dBh), V(diBh)): dBh - name, F(dBh) -content and V(diBh) - volume of the generalized concept, h=1,..., H.
The content F(diBh) of the concept diBh, which generalizes the base concept by attribute l and satisfies the nesting condition of the content, is obtained by replacing the intervals of values of the attributes of the base concept XilB with an interval of values equal to the
domain of its definition Xi, XhbgXh. In this case, the domain of tolerance of the generalized concept T(dBh)= x XjBxXii includes the
' J
j *i
domain of tolerance of the base concept
T(diB)= x XijB, and thus the second condition
ij
is satisfied - the condition of nesting the volumes of the base concept in the volume generalizing its concepts, that is, T(diB)aT(diBh) and V(diB) aV(diBh).
The content of the basic concept and all its possible generalizations form a partially ordered set {F(dB), F(diB1), ..., F(dBH)}, which is called the conceptual cluster of the basic concept and is denoted Di. Structuring the semantic space in the form of a conceptual cluster makes it possible to identify and structure easily interpretable subspaces in the semantic space, defined by areas of tolerance and names of generalized concepts.
In the conceptual cluster, transitions from the basic concept diB to the generalized concept diBh are defined. These transitions mean an increase in the generality of the description of the elements of the body of knowledge under study in the conceptual system. To characterize such transitions in the conceptual system, the concept of the state of the conceptual system of the body of knowledge under study is introduced, which is characterized by the triple: (SD(t), SF(t), SV(t)), where SD(t) = (diBh, ..., dnBh), - vector of names of concepts describing the situation; SF(t)=(F(diBh),..., F(dnBh)) - content of the state of the conceptual system, that is concept content vector dBhsSD(t); SV(t)=(V(diBh),..., V(dnBh)) -vector of volumes of concepts diBhe SD(t), Vi.
Let us define a rule for modifying the state of the conceptual system, connecting changes in the state of the body of knowledge X(t) in the functional system with the state of the conceptual system (SD(t), SF(t), SV(t)). It is as follows: if, in the process of obtaining forecasts of the dynamics of development of the problem area of the body of knowledge under study, the value of any attribute of any concept has gone beyond the area of tolerance of their basic concept, then a new concept is formed that generalizes the original basic
concept according to the attribute, the value of which has gone beyond the area of tolerance.
Formally, this rule is presented as a mapping of the state of the functional system X(t) into the state of the conceptual system (SD(t), SF(t), SV(t)) RM: X(t)^(SD(t), SF(t), SV(t)), where RM=(RM) is a vector of rules for modifying the basic concept diB into the generalized concept diBh, Vi.
The proposed rule allows the user to search for an interpretation not for a specific concept with certain feature values, but to determine the name of a generalized concept to the scope of which the object interpreting this specific concept belongs. In this case, it is much easier to determine the name of the generalized concept, the elements of its scope, and interpret a specific concept using the elements of the scope of the generalized concept.
Taking into account the rule of modification of RM concepts, the knowledge representation model in the form of a knowledge field is represented by a triple:
Kd, Kf, RM)
(6),
where Kd - the conceptual system of the knowledge field, (SS(D), 0, D', (SD(t), SF(t), SV(t)));
Kf - functional system of the knowledge field, (F, X, X(0), W);
RM - vector of rules for modifying the state of a functional system into the state of a conceptual system.
Conclusion
As a result of the research, a structured representation of knowledge arrays in the form of a knowledge field was completed. It allows you to describe the studied bodies of knowledge in a conceptual and functional aspect. In a functional system, knowledge arrays are presented in the form of a block cognitive model. In the conceptual system of the knowledge field, the studied bodies of knowledge are represented by many conceptual clusters connected by the "Part-Whole" relationship. They make it possible to describe not only the existing elements of the body of knowledge, but also their possible modifications. Thus, the proposed approach to structuring the studied bodies of knowledge for their representation in the cognitive model of the knowledge field has been
practically implemented.
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СТРУКТУРИЗАЦИЯ МАССИВОВ ЗНАНИЙ ПРИ ПОМОЩИ ИНСТРУМЕНТАРИЯ
КОГНИТИВНОГО МОДЕЛИРОВАНИЯ
С.Н. Ларин, канд. техн. наук, ведущий научный сотрудник Е.Ю. Хрусталев, д-р экон. наук, главный научный сотрудник Центральный экономико-математический институт РАН (Россия, г. Москва)
Аннотация. В статье представлены результаты исследования и моделирования структуризации массивов знаний. Поиск решения этой актуальной проблемы особенно важен в условиях современного периода развития нашей страны. Для его достижения предложено использовать инструментарий когнитивного моделирования. Разработана модель представления знаний. Она является расширением существующей в когнитивном моделировании модели в виде знакового орграфа и основывается на концептуальной модели представления знаний в виде поля знаний. Новизна результатов исследования заключается в описании исследуемых массивов знаний в структурном и функциональном аспектах. Когнитивная карта массива знаний описана в функциональной системе поля знаний, а результаты его структурно-функциональной декомпозиции описаны в понятийной системе поля знаний.
Ключевые слова: массивы знаний, структуризация, когнитивное моделирование, структурно-функциональная декомпозиция.
