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COMPUTER SYSTEMS FOR SIMULATION OF COGNITIVE MAPS: APPROACHES AND METHODS
A.A. Kulinich
Decision support systems in poorly defined dynamic situations based on modeling expert knowledge presented in the form of cognitive maps are considered. Using the example of cognitive map modeling systems developed in Russia, an overview of methods for implementing the main functional subsystems of decision support systems of this class is given.
Key words: cognitive map, “soft” system analysis, architecture of modeling systems, parameterization, verification, adjustment.
INTRODUCTION
In management processes, there is a need to make decisions in weakly structured dynamic situations, when parameters (values of variables), laws and patterns of development of the situation are described qualitatively. These are unique situations in which the dynamics of the parameters of the situation are accompanied by difficult to predict changes in its structure.
To make decisions in the face of a lack of accurate quantitative information, experts and analysts are forced to rely on their own experience and intuition, using a subjective model based on expert assessments of analysts, i.e., on their knowledge, to make decisions as a model of a dynamic situation. A subjective model of a semistructured dynamic situation is called a cognitive map.
The activities of experts and analysts aimed at studying the situation and making decisions with the help of cognitive maps is a methodology - a logical-time structure of the use of various methods and techniques: constructing a cognitive map, its parameterization, obtaining forecasts for the development of situations, verification, adjustments of the cognitive map and decision making .
Over the past twenty years, a large number of publications have been presented in foreign scientific journals and in the proceedings of international conferences,
devoted to theoretical studies of cognitive maps and methods of their analysis. Often theoretical studies are accompanied by examples of analysis of cognitive maps that confirm the validity of the proposed methods. However, the software used to obtain confirmatory results is scientific articles is not described and is not intended for a wide range of users. Numerous studies of cognitive maps and methods of their analysis have laid the theoretical foundation for the creation of applied commercial systems for modeling cognitive maps and created the necessary conditions for their emergence. A sufficient condition for the emergence of such systems is their demand by end users for solving pressing problems under conditions of uncertainty.
Note that the composition of methods for analyzing cognitive maps embedded in software systems is determined by the nature of the actual problems for which they were created. For example, foreign systems for modeling cognitive maps Decision Explorer (see http://www.banxia.com/dexplore/index.html) and FCMapper (see http://www.fcmappers.net/joomla/) in to a greater extent are focused on analyzing the structure of cognitive maps, and not on analyzing the dynamics of the development of situations modeled by cognitive maps.
In Russia, in the context of socio-economic and political transformations, systems for modeling cognitive maps are mainly
focused on analyzing the dynamics of situation development.
Russian research teams actively involved in the use of cognitive maps to support decision-making and situation analysis have created their own software products to automate various stages of the decision-making process. Over the past decade, a number of computer decision support systems in dynamic situations based on modeling cognitive maps have been described in the domestic scientific literature. These are systems developed at the Institute of Management Problems. V.A. Trapeznikov RAS: a system for modeling signed and weighted digraphs, created by a team led by V.V. Kulby; system “Situation”, integrated system “KURS”, which includes the systems “Situation”, “Compass-2” and “KIT”, created by a team under the leadership of V. I. Maksimov and
ON THE. Abramova; systems "Compass" and "Canva", created by a team under the leadership
O.P. Kuznetsova. Systems for modeling cognitive maps were also developed in various regions of the Russian Federation: a cognitive modeling system created by the scientific team of the Southern Federal University under the leadership of G.V. Gorelova; "IGLA" system, Bryansk State Technical University, developers D.A. Korostelev and others; system "Strategist", Volgograd State Technical University, developers M.A. Zabolotsky and others. Among the systems created outside the Russian Federation, we mention the Cosmos system, developed by the Data C company (Ukraine, Sevastopol) under the leadership of V.B. Silova.
With such a variety of systems for modeling cognitive maps for decision making, their comparative analysis is relevant. In this work, a comparative analysis of computer systems for modeling cognitive maps is carried out from the point of view of their usefulness for automating various stages of the methodology (logical-temporal structure) of decision making in semi-structured dynamic situations.
The purpose of this work is to review possible methods and approaches for implementing various stages of decision-making methodology in semi-structured dynamic situations. The different combinations of methods and approaches for implementing the stages of the decision-making methodology in various computer systems listed above determine the boundaries of their effective use.
Some of the listed systems are positioned by the developers as systems for laboratory
extensive research into problem situations and therefore have no detailed description interfaces, nor a description of the mathematical apparatus used to obtain forecasts for the development of situations (at best, there is a link to a well-known mathematical apparatus).
Therefore, for the analysis of computer systems for modeling cognitive maps, a number of systems were selected (“Situation”, “Compass”, “Canva”, “Cosmos” and “NEEDLE”), for which the mathematical apparatus used in the systems is described in sufficient detail. In addition, the listed systems are positioned as commercial products. This means that demo versions of these systems may be of interest to readers for their own studies of semi-structured dynamic situations.
1. METHODOLOGY FOR MODELING DYNAMIC SITUATIONS USING SUBJECTIVE MODELS (COGNITIVE MAPS)
In the general theory of systems, two directions of its development are distinguished: the theories of “hard” and “soft” systems. The theory of “hard” systems requires strict quantitative constructions based on the deductive method. To describe “hard” systems, strict formalized descriptions are used, and the modeling results are explained by strictly proven causal relationships. The formalization of “soft” systems is based not on precise quantitative measurements, but on qualitative, fuzzy and hypothetical ideas about the system in the form of expert assessments and heuristic reasoning. The theory of “soft” systems considers systems that are capable of adapting to external conditions, while possessing the ability to develop. These are biological, psychological, social systems. Methods for modeling and analyzing “hard” systems are not always suitable for analyzing “soft” systems. The methodological basis for decision-making in a poorly defined dynamic situation is considered to be the methodology of “soft” system analysis.
To analyze “soft” systems, P. Cheklad proposed the methodology of “soft” system analysis, which is a system-oriented guide that helps the analyst cope with the analysis of a complex situation. This methodology is a systematically organized research process poorly a certain system, which includes a number of sequentially performed stages: structuring problematic situation; conceptualization, which consists in constructing an abstract model of observation
Example of a cognitive map
my system; verification of an abstract model - comparison of an abstract model with the real world; adjusting the abstract model, and finally, using the adjusted model, making decisions to manage the situation.
The task of supporting decision-making to manage the situation in a “soft” dynamic situation is defined as the task of developing a strategy for transferring the situation from the current state to the target state based on a subjective model of the situation, which includes expertly measured values of the factors of the situation and a model of its functional structure that describes those known to the analyst laws and patterns of the observed situation. This subjective model is recorded in the form of an oriented sign graph - a cognitive map. An example of a cognitive map of an economic situation is shown in the figure. Here the vertices of the graph are the factors of the situation, and the arcs are the cause-and-effect relationships between them.
The plus sign on the arcs between the factor vertices means that an increase in the value of the cause factor leads to an increase in the effect factor, and a minus sign means that an increase in the value of the cause factor reduces the value of the effect factor. The cognitive map reflects the functional structure of the analyzed situation, since a change in the value of any factor of the situation leads to the emergence of a “front” of changes in the values of factors associated with it. This “front” of changes is called an impulse process in the cognitive map and allows us to obtain forecasts of the development of the situation.
Within the framework of the methodology of “soft” system analysis, the construction of a cognitive map is an iterative process of generating and testing hypotheses about the functional structure of the situation until a structure is obtained that can
clearly explain the dynamics of its development and includes three main stages:
Construction of a hypothetical cognitive map (generation of a hypothesis about the functional structure of the situation);
Verification of the cognitive map (checking the plausibility of the hypothesis about the functional structure of the situation);
Correction of the cognitive map (functional structure) of the situation.
Iterative process of “generation, verification,
adjusting the model (generating a new hypothesis)” is repeated until a functional structure is obtained that plausibly explains the behavior of the observed situation. In the process of constructing a cognitive map, the intellectual abilities of experts or analysts are used - their knowledge, which is structured in this iterative process.
With the help of a well-founded cognitive map, the problem of developing a strategy for managing the situation is solved, capable of transferring it from the initial state to the target state. Moreover, the validity of the strategies being developed is determined by the validity of the cognitive map obtained in the process of its generation.
Thus, when making decisions to manage a poorly defined situation, based on modeling cognitive maps, the knowledge and intelligence of the analyst are directly involved in the decision-making process and largely determine its quality. It can be said that decision support systems in poorly defined situations produce positive results only in tandem with the analytical abilities and creativity of the analyst.
This circumstance imposes certain requirements on the architecture of a computer decision support system based on modeling cognitive maps, which should be reflected in the subject-oriented architecture of the system.
2. COMPUTER SYSTEMS FOR SIMULATION OF COGNITIVE MAPS
There is a fairly diverse set of computer simulation modeling tools in a variety of subject areas and activities. Currently, there are more than 50 different computer simulation systems on the software market. They all work with numerical data that reflects the characteristics of the systems being modeled, and simulation models
systems are built within the framework of the concept of analysis of “hard” systems.
Computer knowledge modeling systems operating within the framework of the concept of “soft” system analysis include expert systems that model the knowledge and behavior of experts when solving problems for which significant decision-making experience has been accumulated. However, this experience is difficult to formalize within the framework of the theory of “hard” systems.
Computer systems for modeling cognitive maps form a special class of simulation systems, which, in terms of functionality and organizational principles, can be positioned between simulation systems and expert systems. In terms of software architecture, cognitive map modeling systems inherit the properties of simulation modeling systems of “hard” systems in terms of organizing simulation modeling processes and expert systems in terms of extracting and presenting expert knowledge, as well as their processing. All of these systems are equipped with ergonomic, convenient multi-window interfaces, but do not support expert work on the development of cognitive maps. The computational forecast of the development of the situation is mainly automated. At the same time, the results of modeling a dynamic system using cognitive maps are inaccurate and allow multiple interpretations. The inaccuracy and qualitative nature of the modeling results are largely determined by the roughness of the expert procedures that are used to build and configure the cognitive map, the level of knowledge, misconceptions and errors of the analyst or expert building the model.
The methodology of “soft” system analysis assumes the presence of expert errors and provides for getting rid of them within the iterative process of “generation - verification - adjustment” of the cognitive map. It is obvious that a computer decision support system that implements the methodology of “soft” system analysis will eliminate many expert errors and improve the quality of decisions made. The software architecture of a decision support system, focused on supporting the “generation - verification - adjustment” cycle of a cognitive map, can be considered a certain ideal, against which we will further analyze the previously listed software systems for modeling cognitive maps.
Idealized architecture of a decision support system based on modeling
The development of cognitive maps should include functional subsystems that support the following stages of model construction and decision-making to manage the situation: generation - verification - adjustments of the cognitive map and decision-making itself - development of a strategy for transferring the situation from the current state to the target one. Let us consider the content of each functional subsystem from the point of view of the user of the decision support systems selected for analysis.
3. GENERATION OF A HYPOTHETICAL COGNITIVE MAP
At this stage, a hypothesis is put forward about the functional structure of the situation based on the knowledge and experience of the subject - his intellectual abilities, imagination and intuition. Hypothesizing is an expert procedure for identifying the basic (most significant) factors of the situation. Based on the set of identified factors of the situation, the expert puts forward hypotheses about the existence and strength of the cause-and-effect relationship between any pair of situation factors. The result of this stage is a subjective model of the situation, represented by a signed weighted oriented graph - a cognitive map.
Generating a hypothetical cognitive map consists of two stages:
Creation of an abstract cognitive map;
Its parameterization.
Let's look at each of them.
3.1. Creating an Abstract Cognitive Map
This stage consists of identifying many factors that describe the situation and determining the cause-and-effect relationships between them. This is an expert procedure, highly dependent on the level of knowledge and preferences of the expert. Different experts, observing the same situation, can identify different factors that are significant for them and the connections between them, thus obtaining different models of the situation and, consequently, different strategies for managing the situation.
The subjectivity of this stage can be reduced using various approaches and methods for organizing intellectual activity in the processes of structuring a poorly defined situation, such as: structural-functional approach; SWOT, PEST, object-structural approach, etc.
The methodological basis for structuring a situation to present it in the form of a cognitive
The map is based on a systematic approach, which is based on considering an object or situation as a system. The main concepts of the systems approach are the concepts of element, structure, and function. The focus of the systems approach is the study of the structure of an object or situation and the place of elements in it. The specificity of the systems approach is determined by the fact that it focuses research on revealing the integrity of the object and the mechanisms that provide it, identifying the diverse types of connections of a complex object and bringing them together into a single theoretical picture. The systems approach is aimed at studying the integrity and establishing the composition of the whole and its elements, studying the patterns of connecting elements into a system, i.e. the structure of the system, studying the functions of the system and its components, i.e. structural-functional analysis of the system.
Recently, in the modeling of cognitive maps, methods of structuring SWOT and PEST, known from the methodology of strategic management, have been used. In works at the stages of structuring the situation, it is proposed to use the model situational analysis SWOT (Strengths - strengths, Weaknesses - weaknesses, Opportunities - opportunities, Threats - dangers, threats) to identify the strengths and weaknesses of the situation (problem characteristics) and build the so-called problem field of the situation. Defining the problem field of the situation allows you to clearly formulate the goals and objectives of modeling cognitive maps and finding a strategy for resolving the problem situation.
To analyze the external environment of the observed situation, the work proposes to use the PEST model of external environment analysis (Policy - politics, Economy - economics, Society - society, Technology - technology). According to this model, four main groups of factors are identified, through which the political, economic, sociocultural and technological aspects of the external environment around the object under study are analyzed.
The methodology for structuring expert knowledge in the form of a so-called knowledge field is also of interest. Here, an object-structural approach (OSA) to knowledge structuring is proposed, according to which the analysis and presentation of knowledge is carried out in strategic, organizational, conceptual, functional, spatial, temporal, causal and economic aspects (strata).
The use of these approaches allows us to somewhat reduce the subjectivity of cognitive
maps, but in any case, cognitive maps constructed at the early stages of situation analysis are characterized by incompleteness and fragmentation, reflecting the incompleteness and fragmentation of the subject’s knowledge about the situation.
The incompleteness and fragmentation of the selected factors leads to mistakes that the expert makes at the stage of determining the cause-and-effect relationships between the selected factors. Typical errors of this stage: establishing a non-obvious connection, errors in determining the sign of influence, establishing transitive closures of connections between factors.
The listed methods are not included in computer decision support systems designed for modeling cognitive maps, but are selected based on the personal preferences of the analyst and are performed manually.
The input interfaces for cognitive maps in the listed systems are either graphic editors or tabular forms reflecting the adjacency matrix of the cognitive map. For example, in the Canva system, the graphic editor provides: construction and editing of a cognitive map (directed sign graph), reflecting the functional structure of the situation; introducing a new factor; establishing a causal relationship between factors; determining the direction and type of connection (positive, negative); removing a factor, removing a connection. By using graphic editor the cognitive map (D M) is determined by expert means, where I is the set of vertices-factors of the situation, F = | -
adjacency matrix of a directed graph.
To reduce the subjectivity of constructing a cognitive map in the IGLA system, a method of its collective creation is proposed. Here, a cognitive map is created by many experts, presenting their opinions on factors and connections between them for approval by the coordinator. The coordinator coordinates the opinions of different experts and corrects it. This method is supported by a “client-server” architecture, ensuring independent work of experts.
3.2. Parameterization of the cognitive map
As a result of parameterization, the abstract cognitive map built at the previous stage turns into a model of a specific dynamic system. In the process of parameterizing the cognitive map, the following scales are determined:
factor values and current factor values;
the strength of influence of a factor on a factor and their values.
3.2.1. Determination of scales of factor values and current factor values
When determining the weaving factors, it is important to determine the type of cognitive map modeled by a specific computer system, i.e., to determine how the values of the factors and the strength of the connection between them are interpreted. The paper examines two possible interpretations of cognitive maps - non-deterministic and deterministic.
In non-deterministic cognitive maps, the weight of the arc and the values at the vertices are interpreted as confidence coefficients, characterizing, respectively, the expert’s confidence in the existence of a connection between factors, and the confidence that a factor characterizing an event will take place.
In deterministic cognitive maps, the value of the factor at the vertex is interpreted as its absolute value, expressed in the corresponding units of measurement (rubles, kilometers, etc.) or linguistic estimates (“Big”, “Medium”, “Small”), while the weight of the arc is interpreted as a transmission coefficient connecting the change in the absolute values of the factors of the sign and the cause.
Based on this criterion, the “Cosmos” and “IGLA” systems should be classified as systems focused on modeling non-deterministic, and the “Situation”, “Compass”, “Compass-2” and “Kanva” systems - deterministic cognitive maps.
In modeling cognitive maps, the dominant approach is aimed at studying the system’s response to some initial disturbance (increment) of the values of its factors.
Confidence scale. Scales of increments of factor values for non-deterministic cognitive maps characterize the increment of the uncertainty (confidence) indicator of the factor value and are presented on numerical intervals [-1, 1]. Interpretation of negative values of the confidence indicator is difficult and little understandable for an expert.
In his work, B. Kosko proposed solving this problem by supplementing any factor of the situation with a factor that has the opposite meaning, i.e. /. . This approach is convenient for describing systems that model multipolar increments of factor values. The expert sets two uncertainty indicators: uncertainty indicator
positive increment p+ e for factor ^ and the uncertainty indicator for its negative increment p- e . With this definition of the increment of the indicator, the
lenience, it is possible to represent uncertainty in the so-called “gray” scales, for which the normalization condition is not satisfied
p+ + p- = 1. It is believed that “gray” scales better reflect expert assessments under conditions of uncertainty. The conflict between the assessments p+ and p- is determined using the cognitive consonance indicator c. = | р+ - р-1/(р+ + р-) .
Degrees of confidence are represented as an ordered set linguistic meanings confidence Zp = (“Impossible”, “Weakly possible”, “Almost possible”, “Possible”, “Very possible”, “Almost certain”, “Reliable”). The confidence scale is represented as a mapping φ: Zp ^ onto a segment of the numerical axis.
The expert procedure for determining uncertainty indicators on the interval of values for positive and negative increments is understandable to the expert and is interpreted as follows: 0 as impossible, and 1 as a reliable increment.
Estimation scales for increments of factor values. The expert procedure for determining factor increment scales for deterministic cognitive maps is somewhat more complex and more subjective.
In the “Situation” and “Compass” systems, it is believed that an expert, having some intuitive understanding of the current values of all factors, which in reality are measured in absolute numerical values or in evaluative linguistic scales, can represent the change in the value of factors in terms of an evaluation scale of increments in factor values from the current value.
An example of such a scale is a bipolar rating scale of increments, represented by an ordered set of linguistic values Z = (“Grows strongly,” “Moderately grows,” “Grows slightly,” “Does not change,” “Falls slightly,” “Falls moderately,” “Strongly”). falls").
The evaluation scale of increments in factor values is constructed as a mapping of the elements of set 2 onto a segment of the numerical axis in the form of equidistant points, i.e. φ: 2^ [-1, 1].
The rating scale of increments has a high level of subjectivity; the expert may make mistakes, since the expert does not explicitly record the current absolute value of the factor and does not clearly represent the various estimates of the degree of increment of factor values on the absolute scale.
Scales with “absolute” linguistic meanings. In the Kanva system, to reduce the subjectivity of factor scales, a linguistic scale with “absolute” linguistic values is used. Here, when determining linguistic values, “absolute” linguistic values of the factor are used, rather than subjective assessments of the factor such as “Large”, “Medium”, “Small”. For example, the linguistic meaning of temperature might be the linguistic meaning of “so hot that you can barely lay your hand on it” or the rating “so cold that your hand immediately freezes,” rather than simply “Very hot” or “Very cold.” With this determination of the linguistic values of the factors of the situation, the expert sets the “absolute” linguistic current value of the factor, which facilitates the work of experts in determining the strength of influence of factors and reduces expert errors.
An ordered set of linguistic values 2. = (gg1, ..., ggt) is defined for the factor. Moreover, for elements of a set of linguistic meanings, not only a strict order of meanings is defined< гй < ... < гт, но и равенство интервалов между лингвистическими значениями. Равенство интервалов между значениями устанавливается с помощью экспертного метода деления отрезка пополам Торгерсона .
The factor scale is defined as a mapping of each linguistic value of the factor to a point on the numerical axis, φ: 2.. ^ X, X = (xl, ..., x.n),
x1..., Xn e.
The inverse mapping φ x is also defined: x ^ , x e , allowing the interpretation
convert any value of x into the linguistic meaning of the factor g, g. e 2..
In terms of scales of factors and increments, the initial state of the situation is defined in the linguistic form 2(0) = (r1k, r2е, ..., rn1) and, accordingly, in the numerical form X(0) = (x1k, x2c1, ..., xn1 ) as a vector of initial values of factors. The initial vector of increments of situation factors P(0) = (р1, р2, ..., рп) is also determined.
The increment of the factor value is determined for the current value of the factor and is characterized by the direction of the increment - positive, negative increment and increment value. For a given current state, the elements of the set gHc+F gKc+2^ ..., gy e 2 6udut
characterize a positive increment, and negative increments are characterized by elements
The current state on the interval corresponds to point xjc. Positive increments are defined as intervals (segments) of the numerical axis:
P+1 = X(c +1) - P +2 = X(c + 2) - Xc; ...; P+n- c) =
X. - x. , and negative increments are
numerical axis intervals: p-1 = xic - x;(c- p-2 =
Xic - xi(c- 2); -; PTc = xic - xi.
Increments of factors in the Kanva system obtained when calculating forecasts for the development of a situation are verbalized, i.e., presented in the form of statements of the form: “The value of factor f has increased (decreased) from the current value Zic = 9-1(xic) to the value zin = 9_1 (xin)". This approach allows us to reduce the subjectivity of expert assessments.
3.2.2. Factor influence scales
When determining the strength of influence of factors, the expert determines the weight of the arc connecting the cause factor and the effect factor. Influence scales for deterministic and non-deterministic cognitive maps interpret the value of the arc weight of the sign digraph differently.
Influence power scale in non-deterministic cognitive maps. In non-deterministic cognitive maps, the weight of the arc determines the confidence in the existence of a connection between the vertices and is represented by a number in the interval [-1, 1]. The specificity of representing increments in non-deterministic cognitive maps as a pair of values -
positive p+ and negative increment of p- factor leads to the following representation of factor connections. For a cause-and-effect relationship w.. e [-1, 1] between the cause factor f e F and the effect factor f e F is positive
connection connects positive increments with positive ones, and negative ones with negative ones
increments, i.e. w+ : p+ ^ p++ .
A negative connection, respectively, positive increments with negative ones, and negative ones with positive increments, i.e.
ij ■ i"i " i"J ’ "ij- pi ^ PJ
This leads to
tami zi(c -1), Zi(c-2),
depending on the size of the adjacency matrix of the cognitive map, but at the same time all elements of the matrix that determine the uncertainty indicator of the existence of a connection are positive and defined on the interval .
The elements of the double positive definite adjacency matrix Ж = \м>У |2пх2п define
are obtained from the adjacency matrix Ж = \м(\пх_п as follows:
esoi > 0, then C>(2.- 1)(2]- 1) = , ™2Ш = Pu,
eshoi< 0, то ^2/(2]- 1) = -^цр ^21 - 1)(2ц) = -^у.
In this case, the degree of confidence in the existence of a connection is represented as an ordered set of linguistic values of confidence 2Р™ = (“Impossible”, “Weakly possible”, “Almost possible”, “Possible”, “Very possible”, “Almost certain”, “Reliably” "). The scale of confidence in the existence of a connection is presented as a display φ: ^ .
The expert procedure for determining uncertainty indicators of factor connections on an interval of values is understandable to the expert, since 0 is interpreted as impossible, and 1 as a reliable connection.
Scale of the strength of influence of factors in deterministic cognitive maps. The situation is more complicated when determining the weights of connections in deterministic cognitive maps. Here the weight of the connection determines the transmission coefficient. When determining this coefficient, the expert must answer the question: “How does the factor influence the factor /. and with what force? In the “Situation” and “Compass” systems, the answer can be selected from an ordered set of linguistic values of influence ratings:
2№ = (“Strongly increases”, “Medium increases”, “Weakly increases”, “Does not affect”, “Weakly decreases”, “Medium decreases”, “Strongly decreases”).
Each element of the ordered set 2rZh is mapped onto a segment of the numerical axis [-1, 1] in the form of equidistant points, φ: 2№ ^ [-1, 1].
This scale of the influence of factors has high level subjectivism. The fact is that cognitive maps, as a rule, model nonlinear dynamic systems in which the strength of influence between factors depends on the current values of the cause factors. Linear cognitive map approximates the area nonlinear system close to the current value of the cause factor, and if the current value of the factor in the expert determination of the strength of influence is determined implicitly, then this leads to significant distortions in the assessment of the strength of influence of the factors in their expert determination.
In the “Situation” and “Compass” systems, the values of arc weights that determine the interval of influence force values are limited by the interval w е [-1, 1]. However, here the weight is interpreted as a transmission coefficient and therefore its values may be outside the designated interval. Numerous
Complete examples of cognitive maps for which W .. £ [-1, 1] can be found in the work of Roberts.
Parameterization of the strength of influence of factors of an abstract cognitive map using rating scales of factors in which the current state of the factor is not explicitly defined has a high level of subjectivity and leads to many errors caused by incorrectly posed questions to the expert.
If the cognitive map is parameterized using the described incremental rating scales and scales of influence, then difficulties arise in its verification.
Indirect methods for determining the strength of influence of factors. To reduce subjectivity in determining the strength of influence of factors in the Canva system, indirect methods are used to determine the strength of influence. The expert determines the strength of influence by answering questions about a possible change in the value of the effect factor with a fixed change in the cause factor. This procedure makes it possible to determine the strength of influence taking into account the current state of the cause factor, which reduces the error of expert assessment. Generation of questions for an expert to determine the strength of influence between characteristics is automatically carried out in two modes: direct assessment and paired comparison.
In the direct assessment mode, the strength of influence is determined as the transmission coefficient calculated from the increments of the cause factor and the effect factor specified by the expert in linguistic form. Increments can be specified exactly or as a fuzzy set.
When accurately specifying the values of factor increments, the expert answers the question: “Estimate,
how does a change in the value of the factor from r0 to r(P affect the change in the value of the consequence attribute /", determining the plausible, from his point of view, "absolute" linguistic meaning of the factor
w^s = p. 1р1 , (1)
where p. = (x. - x.)/x. - value deviation
factor-cause, and p[ = (x0 - x[)/x0 - deviation
factor-consequence, x0 = f.(g0) and x0 = fD g0) initial values respectively, factor-cause and factor-effect; хр = f.(gr) and x[ = fD gG) values of factors after expert determination
nia of the increment of their values, r^ and r5 - the initial linguistic values of the factors u, gr.
and r^ - linguistic meanings of factors and after increment, f. and f^ - mappings of ling-
istic values of g., g5, g. and g5 factors and on a segment of the numerical axis.
Specifying deviations in the values of cause or effect factors in the form of a fuzzy set is used in cases where the expert finds it difficult to accurately determine the deviation of the factor-effect caused by the deviation of the factor-cause. The membership function of the factor-consequence deviation value is represented in a triangular or trapezoidal form and is specified by a fuzzy set:
^(^)= (xG1 xG2 \v2,..., x1k Kb
where x^1,..., x[H are the values of the factor after the increment, y1,..., are subjective assessments of the possibility
corresponding increments of the effect factor for a given increment of the cause factor.
The deviation value of the factor specified by the membership function C(xr):
x = E x^ V Ey»-
After dephasification, the strength of influence of features wis is determined using relation (1).
The paired comparison mode is used in cases where it is easier for an expert to order factor-causes from the set = (/(,/5, ..., according to the strength of influence on the factor-effect. Factor-causes are ordered using the method of paired comparison, the meaning of which is expert determination: a change in which of the two factor-causes proposed for assessment has a stronger effect on the change in the value of the factor-effect. The expert determines his preferences using the ranking scale proposed by T. Saaty. A necessary condition for the correct ordering of factors from a set is the transitivity of the expert’s assessments A violation of transitivity is considered a contradiction in the expert’s preferences that needs to be detected and corrected. The Kanva system automatically detects this
what kind of contradictions and allows the subject to correct them. There are two modes for adjusting expert contradictions: manual and automated. In manual mode, the expert has the opportunity to redefine his preferences specified at the previous step of the paired assessment, and in the automated mode, a heuristic adjustment algorithm is used, which allows replacing the intransitive assessment with the closest transitive one.
In the Canva system, all interfaces for setting up a cognitive map are designed in the form of convenient interfaces that allow you to reduce the complexity of setting up a cognitive map.
The use of “absolute” linguistic scales of factors and indirect methods for determining the weights of arcs allows us to reduce the subjectivity of setting up a cognitive map. The reduction in subjectivity is primarily due to the use in the Canva system of automatically generated questions for an expert in limited natural language, in the form of standard question templates. In the question for indirectly determining the strength of influence of factors, the following are explicitly defined: “absolute” values of the current state of the assessed factors of cause and effect; “absolute” values of the estimated deviations of the values of cause and effect factors that determine the strength of influence. Explicit indication of the “absolute” values and deviations of factors in the assessment question leads to the expert’s understanding of the essence of the expert assessment of determining the strength of influence of factors, which reduces the subjectivity of the assessment.
4. VERIFICATION OF COGNITIVE MAP
Verification of a cognitive map (testing a hypothesis about the functional structure) consists of obtaining a forecast of the development of a situation using a model and explaining it based on available data and common sense. Modeling the situation allows us to identify the discrepancy between the forecast of the development of the situation, obtained using a cognitive map, and the actual development of the situation in the past. The identified discrepancies indicate the analyst’s erroneous ideas about the laws and patterns of the development of the situation embedded in the subjective model, and serve as incentives for the expert or analyst to search for a new or adjust the current functional structure of the observed system.
At the stage of verification of a cognitive map, the expert tries to understand how correct the cognitive map he has constructed is, and whether it is possible to
the power to develop solutions to manage the situation?
We will consider two approaches to performing verification of a cognitive map: direct and reverse verification. Reverse verification is based on establishing the plausibility of forecasts for the development of a situation obtained using a cognitive map by comparing them with the known dynamics of the situation in the past. Direct verification is based on an analysis of the plausibility of the processes leading to changes in the values of factors in the forecast.
Verification of a cognitive map is based on the analysis of forecasts for the development of the situation, which are different in different systems. Therefore, we will consider methods for obtaining forecasts in different systems.
4.1. Methods for obtaining situation development forecasts
The general formulation of the problem of obtaining forecasts for the development of the situation is as follows.
A set of factors of the situation F is given, scales of factors are defined (see section 3.2) and the cognitive map is given by the adjacency matrix Ж of the oriented graph. Let the factors of the situation be characterized by some initial value, presented in the form of an initial state vector X(0) = (x1(0 ), ..., hp(0)). The expert can increase or decrease the initial values of any factors X(1) = (x1(1), ..., xn(1)). The increment in the value of the factor p.(0) = x.(1) - x.(0) is called the initial impulse, and the vector of increments P(0) = (p1(0), ..., pn(0)) is called the initial vector increments. It is required to obtain a forecast of the development of the situation.
To obtain a forecast of the development of the situation in the modeling of cognitive maps, a system of finite-difference equations of the form is written
r a + 1) = zr (o, (2)
where Р(?) and Р(? + 1) are vectors of increments in factor values at points in time? And? + 1 (pulse vectors).
State of the situation at a point in time? + 1 is determined from the relation X(? + 1) = X(?) + P(? + 1), where X(?) is the state of the situation at time?.
The set of increment vectors P(?), P(? + 1), ..., P(? + n) at successive discrete moments in time is called an impulse process, and the states of the situation X(?), X(? + 1), . .., X(? + n) characterize the dynamics of its change under control influences P(?).
4.1.1. A method for obtaining a forecast of the development of a situation when modeling non-deterministic cognitive maps
The Cosmos and IGLA systems use a method for obtaining forecasts based on the theory of fuzzy sets. To calculate the predicted values of situation factors, the rule max-rgooiL - (multiplication and taking the maximum) and the double positive definite adjacency matrix W" = |w"ij |2пх2п are used.
The forecast for the development of the situation is determined using the matrix equation:
Р"(п) = РШ°ж" *, (3)
where ° is the max-rgoulL rule: p\ (n) =
max(рЦ (0) w"ij), р. (п) e Р"(п), р. (0) e P"(0), uA e
Ж"*, Ж"* - transitive closure of the adjacency matrix of the cognitive map.
In the initial P(0) and forecast P(n) vectors
increments of dimension 2n (p-, p+, ..., p-, p+), the value of the factor /" is characterized by two elements: the element with index 21 characterizes positive p+, and with index 21 - 1 - negative p-increment of the factor This makes it possible to model cognitive consonance in the subject's ideas about the meaning of the factor and characterize the subject's confidence in the modeling results.The degree of cognitive consonance c.(?) is determined from the ratio:
с(п) = 1р+(п)-р"(п)1, 0< с(п) т 1. (4)
p I (p) + p I (p)
When c (n) * 1, i.e. p+ (n) >> p- (n) or p- (n) >>
> p+ (n) the subject’s confidence in the increment of the factor p(n) is maximum, and with c(n) * 0, i.e.
p+ (n) * p- (n), minimal.
The transitive closure of a positive definite cognitive map is determined from the co-
tgl* ^ / TT7G\k
relationship: F = ^^ x (F).
Taking into account the cognitive consonance of the factor value of the component p(p) e P(p) of the vector for forecasting the development of the situation, it is represented by a pair (p(p),
s.(p)), where p(p) = 81bp(p+ (p) - p-(p))max(p+ (p), p- (p)) - value of the factor increment, s(p) - consonance of the factor value.
The sign of the increment p(n) is positive if
p+(n) > p- (n), and negative if p+ (n)< рI (п).
In this case, the forecast state of the situation will be determined by the pair
(X(n), C(n)), (5)
where X(n) = X(0) + P(n) - vector of the state of the situation (its component x.(n) = x.(n) + p.(n)), cognitive consonance of the value s.(n) e S(n).
From the transitive closure matrix Ж" * =
= [^]2пх2п teach matrices C5 = [su]пхп -
mutual consonance, = [yu]php - mutual dissonance, = 1 - su, Ud, P5 = [rts]php - mutual positive influence, N = [p.] ^ - mutual
7 o 1 y php
a lot of negative influence.
4.1.2. A method for obtaining a forecast of the development of a situation when modeling deterministic cognitive maps
In the considered systems for modeling deterministic cognitive maps, two different methods obtaining a forecast of the development of the situation - with and without summation of increments of factor values.
A. The method of obtaining a forecast of the development of a situation with the summation of increments in the values of factors is used in the “Situation” system. This model was proposed in the work of Roberts, then analyzed and modified in the works. To calculate the components р.(? + 1) of the vector of forecast increments Р(? + 1) in equation (2), the following relation is used:
p(+ 1) = E Y^. at
The forecast for the development of the situation is presented as a vector of values of all factors (x1(n), ..., xn(n)),
where x(n) = x.(0) + E r.(?), x.(0) e - initial
state of the simulated situation.
Since in this method the current values of factors are specified abstractly (without reference to specific values of factors), we can consider the initial state of all factors to be zero x(0) = 0, / = 1,..., n, and the forecast vector of values
of all factors x(n) = E p(?) is determined by the accumulation
measured increments of factor values per cycle of operation of the modeling complex.
In this case, the components of the forecast vector x(n) e [-1, 1] can be represented in linguistic incremental rating scales.
B. The method of obtaining a forecast of the development of a situation without summing up increments is used in the Compass and Kanva systems.
The method of obtaining a forecast of the development of a situation in the Compass system differs from the forecast method of the Cosmos and IGLA systems in the deterministic interpretation of the cognitive map.
To calculate the components p(n) of the vector of forecast increments P(n) in equation (2), the following relation is used:
p(n) = max WijPj(0).
In the Compass system, which models deterministic cognitive maps, evaluation scales of increments are used to determine the values of factors, without fixing the current value of the factors, i.e. X(0) = 0. Forecasts of the development of the situation are represented by a pair (X(n), C( n)), where the value X(n) = P(n) is obtained using relation (3), and the consonance of C(n) values is calculated using relation (4).
The components р.(п) e Р(п) of the forecast vector are defined on the interval [-1, 1] and can be presented in terms of the rating scale of increments “Growing strongly”, ..., “Falling strongly”.
The Canva system is also focused on modeling deterministic cognitive maps. It uses the method of calculating forecasts of the Cosmos and IGLA systems in a deterministic interpretation of cognitive maps. Unlike the Compass system, the Kanva system uses “absolute” linguistic scales, therefore the initial state of the situation is explicitly defined here as a vector of values of all factors of the situation in the linguistic
D0) = (r1,..., r°) and in numerical form X(0) = (x° ,..., x°n), as well as the initial vector of factor increments p(0 = (p^..^ rt).
The forecast for the development of the situation is also determined by the pair (X(n), C(n)), where X(n) = X(0) + P(n) are obtained using relations (3) and (5) consonance of C(n) values - using relation (4).
The forecast for the development of the X(n) situation in the Kanva system is verbalized using inverse mappings of scales φ 1: X(n) ^ 2(n) and is presented to the user in “absolute” linguistic values.
4.2. Reverse verification of a cognitive map
Predictions obtained using one of the described methods serve as the basis for the verification process of a cognitive map. Reverse veri-
The creation of a cognitive map is based on an analysis of the plausibility of forecasts for the development of a situation and is presented as an expert procedure for comparing the obtained forecast values of factors with known values of factors in the past, obtained under the initial conditions of the past. The correctness of such a verification procedure depends on a number of objective difficulties in formalizing a poorly defined dynamic situation and, accordingly, simplifications made at the stage of constructing a cognitive map.
Let us highlight two main simplifications.
Poorly defined nonlinear dynamic systems are modeled, in which the parameters of connections between factors (weight of arcs) depend on the current state of the system Ж(Х(?)). The dynamics of changes in the state of such a system is defined as the mapping Х(Х(?)): Х(?) ^ Х(? + 1) of the current state Х(?) into the future Х(? + 1). Cognitive maps approximate a nonlinear dynamic system linear in the E-neighborhoods of the current state X(0), considering the weights on the arcs unchanged Ж(Х(0)) = sot! The dynamics of changes in the state of the situation are determined in this case from the relation Ж(Х(0)): Х(?) ^ Х(? + 1), ? = 0, ..., p.
The dynamics of the development of processes in the model of the situation, represented by a cognitive map, occurs in discrete model time, which does not take into account the delays in the propagation of influences between factors that exist in the real modeled system.
Due to the first simplification, verification of linear cognitive maps based on comparison of forecasts for the development of a situation with the dynamics of the development of a nonlinear situation in the past may be useless due to the nonlinearity of the situation itself. Due to the second simplification, the short cycles that exist in the cognitive map, subject to the accumulation of increments in factor values, can greatly distort the predictive values of the factors. In addition, the model forecast reflects the established values of the factors, but it is difficult to state the established values of the factors of the real situation at the time of its observation and verification.
Therefore, determining the proximity of the forecast values and the actual values of the parameters of the dynamic situation turns out to be incorrect. Indeed, the actual development of the situation is usually accurately recorded in absolute values or relative increments of these values (for example, in percentages), and their comparison with the predicted values presented using intuitively derived incremental rating scales.
This does not allow us to speak either about the rigor of such a comparison or about the confidence in the results of such a comparison.
In this case, verification is carried out by analyzing trends in forecasts for the development of the situation by determining their plausibility. The plausibility of forecasts is checked by comparing trends in changes in the values of factors in the forecast, obtained using a cognitive map, and the known dynamics (trends) of the development of the situation in the past. The trend in the development of the situation in the forecast and the actual development of the situation in the past in this case is formalized by the direction of change in the values of the factors, selected, for example, from a variety of linguistic meanings of trends: (“Grows”, “Does not change”, “Falls”) without indicating the degree of growth or decline factor values.
If, to perform such a comparison, forecasts obtained in incremental rating scales (“Grows strongly”, ..., “Falls strongly”), obtained with an intuitive understanding of the current knowledge of factors, are used, then the complexity and incorrectness of the process of verifying forecasts for the development of the situation greatly increases.
It is possible to reduce the subjectivity of this stage by reducing expert errors in modeling systems in which the parameterization of the cognitive map is carried out using linguistic scales with “absolute” linguistic values, and a method without summing up increments is used as a forecast model. Forecasts of the development of a situation obtained using cognitive maps are presented in “absolute” increment scales, i.e., the exact current value and a possible increase or decrease in the value of the factor in the forecast are indicated in linguistic form, indicating the confidence that such a change will occur. Since there is no summation of increments, the predicted values of the factors are considered the lower guaranteed limit of the forecast.
When using linguistic scales with “absolute” linguistic values, the forecast for the development of a situation can be presented in the form of relative changes, indicating the certainty of their change (consonance). This presentation of the predicted value facilitates its comparison with real changes in the values of situation factors, represented by absolute values or relative changes.
Computer support for the verification process in all systems discussed in this article is carried out expertly based on graphical visualization of development forecasts.
tion of situations and their verbalization in incremental rating scales or in scales with “absolute” linguistic meanings.
In direct verification, the plausibility of a forecast is verified by methods other than the method by which it was obtained. Direct verification of a cognitive map is based on an analysis of the plausibility of the processes in the situation and is closely related to the analysis of the structure of the cognitive map. Indeed, the structure of the cognitive map determines the processes that change the values of factors in predictions. When analyzing the structure of a cognitive map, “structural pictures” of the interaction of factors are important. One of the non-strict criteria for the plausibility of the structure of a cognitive map was considered in the works of Eden. He believes that the structure of a cognitive map that is simple and understandable to the subject, which allows one to explain the processes occurring in reality, is plausible. This simple and understandable structure in psychology is called the Gestalt image of the observed situation, represented by a cognitive map. Unfortunately, it is quite difficult to formalize the Gestalt image of a cognitive map, due to its subjectivity, and therefore it is impossible to use it as an objective criterion for verifying a cognitive map based on an analysis of the plausibility of processes. All this leads to the fact that the process of verifying cognitive maps based on process analysis is quite subjective and contains many errors and misconceptions associated with the individual characteristics of experts and the peculiarities of parameterization of the cognitive map.
The works propose an approach to the verification of cognitive maps, based on the analysis of typical systematic errors committed by their developers. Two types of risks have been identified that lead to errors in cognitive maps:
The risk of false transitivity associated with the representation of concepts as factors in a cognitive map different levels generality (false transitivity arises when establishing a cause-and-effect relationship between concepts (factors) of different levels of generality);
The risk of misunderstanding the mathematical meaning of the connections, which leads to a distortion of the substantive meaning of the connections of the cognitive map relative to their mathematical interpretation
and, accordingly, to errors in determining the strength of connections.
It is proposed to reduce the risks of the first of these types by applying the criterion of proportionality.
these factors in terms of the volume of concepts, which makes it possible to detect concepts that are disproportionate in terms of volume and reduce the level of generality by splitting the vertices of the cognitive map into concepts of more low level. It is proposed to detect risks of the second type using the criterion of understandability of the mathematical meaning of map structures based on a verbal template and reduce them by using certain templates to determine the strength of the connection.
Another method of direct verification of cognitive maps involves the use of so-called “how-to-explain” subsystems of forecasts for the development of a situation. In the Cosmos, Compass, and Canva cognitive map modeling systems, support for the process of verifying the structure of a cognitive map is carried out using built-in subsystems for explaining forecasts for the development of a situation. Subsystems for explaining forecasts of situation development in cognitive maps describe the sequence of the process of obtaining forecast values of factors in the form of a chain of rules triggered at the vertices of the cognitive map. Explanatory chains describe processes that change the predictive values of factors, verbalizing them and thus facilitating the understanding of the processes in the cognitive map and, accordingly, verification of its structure.
In the Kanva system, the block for explaining the forecast of the development of a situation provides automatic generation of a report, which includes a description of the successive steps (cause-and-effect chains) of obtaining the forecast value of any factor in the situation. The report contains positive and negative cause-and-effect chains. A positive chain explains the reason for the increase in the value of the attribute, and a negative chain explains the reason for its decrease. The Kanva system proposes a method for finding explanations for forecasts of the development of a situation, based on an analysis of the forecast matrix for the development of a situation. The proposed method makes it possible to obtain explanations for forecasts of the development of a situation in large cognitive maps.
Based on explanatory subsystems, the user expertly determines the plausibility of the processes described in the situation model, and thus determines the plausibility of the cognitive map.
5. COGNITIVE MAP ADJUSTMENT
Correcting the cognitive map consists of changing it based on the results of the verification stage. During the adjustment process, the scales of factors, strengths, and
connections between factors, new factors removed or added, and cause-and-effect relationships. The adjustment process is subjective, relying on the intuition and imagination of analysts or experts creating a cognitive map.
Since a cognitive map is, as a rule, a strongly connected oriented graph, and any arc is included in many processes that determine the predictive values of many factors of the situation, deleting (adding), changing the sign or weight of the influence can completely change the previous forecast for the development of the situation. Computer systems for supporting correction of the cognitive map are unknown to the author of this work. However, there are a number of theoretical developments of methods to support the processes of updating the cognitive map.
Most known method based on the analysis of the so-called structural stability of cognitive maps. A cognitive map (digraph) is presented in the form of a generalized symbolic “rose” that connects its stability with structure. Analysis of the generalized “rose” allows you to find changes in the structure of the map that make it possible to achieve its stability. This method does not provide unambiguous solutions and is aimed at stimulating the intellectual activity of the analyst in searching for possible changes in the digraph. Moreover, formally obtained structural solutions require subjective interpretation in the subject area in which the cognitive map was built and are not always possible. The method allows you to correct the cognitive map, i.e., identify the expert’s mistakes that led to its instability, as well as find structural solutions, i.e., solutions aimed at changing the structure of the map in order to ensure its stability.
The paper proposes a method for searching for structural solutions based on the presentation of alternatives for managing the situation in a model of a cluster conceptual system of a subject area. The search for a structural solution is based first on the search for a class of admissible interpretations, and then on the search for a structural solution (structure changes) that falls into this class.
CONCLUSION
The systems for modeling cognitive maps developed in Russia are considered. Methods and approaches for presenting a cognitive map in different systems, issues of its parameterization and adjustment are reviewed and analyzed in detail.
When choosing a system for modeling a poorly defined situation, the analyst has to solve a compromise problem, choosing between the accuracy, adequacy (plausibility) of the situation model and the time and complexity of its creation.
The “Situation”, “Compass”, “Cosmos” and “IGLA” systems provide short time and labor-intensive creation of models of complex subject areas. This is due to the fact that the systems use the same standard incremental rating scales for all factors and the forces of influence of the factors. As was shown in this article, you have to pay for the low labor intensity and time with the accuracy and adequacy (plausibility) of the model. With the help of these systems, it is advisable to create abstract models that are not tied to the specific state of the simulated situation. Naturally, the results of modeling abstract models will be abstractly expressed in terms of rating scales.
The time and labor required to create situation models in the Canva system, despite good interfaces and user support, is greater than in the mentioned systems. Here, scales with “absolute” linguistic values are created for each factor; in addition, the weight of the connection is adjusted individually, based on indirect characteristics. However, such additional expert work makes it possible to reduce the subjectivity of the cognitive map, turning it from an abstract model of the situation into a model that reflects the features current moment its development.
Forecasts of the development of the situation obtained in the Kanva system are easier to verify, since they are presented in terms of “absolute” linguistic meanings, which facilitates analytical work. This system is advisable to use in decision support situations, when it is important to take into account the current state of the situation.
The considered systems can be used for conceptual analysis and modeling of complex and poorly defined political, economic or social situations, development of management strategies and mechanisms for their implementation, development of program documents for the strategic development of a country, region, enterprise, firm, etc., as well as tools for continuous monitoring of the state of the situation, generating and testing hypotheses of development mechanisms and mechanisms for managing the situation.
The use of cognitive map modeling systems significantly expands the horizons of the analytical capabilities of experts, freeing their intellect from routine work, stimulating imagination and intuition to generate original solutions and management findings in a confusing situation.
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Kulinich Alexander Alekseevich - Ph.D. tech. sciences,
3.2. Cognitive maps
Cognitive maps belong to the same class of knowledge representation systems as frames. It is interesting that this term appeared long before the emergence of cognitive science in the work of the outstanding American psychologist, representative of neobehaviorism E. Tolman, “Cognitive maps in rats and humans” (1948). Analyzing the behavior of rats in a maze, Tolman came to the conclusion that as a result of running through a maze, a rat forms a special structure, which can be called a cognitive map of the environment. “And it is this approximate map, indicating the paths (routes) and lines of behavior and the interrelationships of environmental elements, that ultimately determines what kind of responses, if any, the animal will ultimately carry out.”
Tolman suggested that cognitive maps also determine people’s behavior, and called for the “expansion” of cognitive maps as a means of combating excess aggressiveness - only in this way, in his opinion, can people be taught to adequately navigate in solving life’s problems.
Thus, a cognitive map can be understood as a schematic, simplified description of an individual’s worldview, or more precisely, a fragment of it related to a given problem situation.
Psychologists have recently used this term in a narrow sense, only to describe spatial relationships. It seems that the term “cognitive map” is much more closely related to the generally accepted understanding of the picture of the world than the concepts of “frame” and “script” introduced by linguists. Therefore, in what follows we will use the term “cognitive map” in a broad sense, as envisaged by Tolman and accepted in applied research.
So, should the birth date of the cognitive approach be placed at 1948? No, the fact is that Tolman’s work was significantly influenced by the ideas of Gestalt psychologists, and it is in their works that the origins of cognitivism should be sought.
One of the founders of Gestalt psychology, the outstanding German psychologist M. Wertheimer, put forward a number of revolutionary ideas for his time, which were realized by other researchers decades later, and some ideas have entered scientific circulation only in recent years. In the introductory article to the classic monograph by Wertheimer V.P. Zinchenko notes: “From Wertheimer’s descriptions of productive thinking, it follows that the main thing in this process is not so much the operational and technical procedures aimed at solving an already formulated problem, but rather the formulation of the problem itself, the formulation of the problem. It is on this side of the thought process that the attention of researchers should be concentrated . Specialists in the field of computer science and artificial intelligence are only now coming to this conclusion. The most insightful of them are beginning to realize that future artificial intelligence systems will be able to solve any problems, but will not be able to pose them. Posing problems is the prerogative of man... Wertheimer's book, undoubtedly , will help, if not overcome computer metaphors in psychology and cognitive metaphors in computer science, then at least significantly enrich their content."
At the conclusion of his monograph, M. Wertheimer provides a number of generalizing provisions that summarize his research into productive thinking. As Wertheimer argues, the analysis of problems and situations requires not just partial, fragmentary factual truths, it requires structural truth. Accordingly, productive thinking consists "... in discretion, awareness of structural features and structural requirements, in actions... in the direction of improving its structure."
Here the emphasis is placed on the fact that unclear places, gaps, and violations should be considered in accordance with their place and function in the structure of the problem situation. The main operations in productive thinking are structural groupings, isolation, centering, and changes in the dynamic structure should be clearly recorded. The role of structural transposition and structural hierarchy is also noted.
Wertheimer believes that a structural understanding of problems and situations is necessary. “At the same time, the transformation of the structure often explodes and completely changes the previous vision of the problem situation. In short, the fact is that in productive processes, structural foundations become efficient causes.” The transition to a new point of view occurs suddenly, as a result of insight.
M. Wertheimer's monograph notes the role of graph theory in the analysis of structures (a structure is also a graph), emphasizing the importance of the process of restructuring graphs, i.e. The problem of information visualization is posed.
Cognitive psychologists believe that a causal schema depicts a person's way of thinking about possible causes in connection with a given consequence. This provides the individual with the means to make causal attributions based on limited information. It is also assumed that each person has a certain repertoire of mental models for analyzing causes (many causal schemes).
As the results of research carried out within the framework of cognitive science show, the human mind uses “universal explanatory schemes, or cognitive clichés,” to understand problems. A striking example of a universal explanatory scheme is a common way of relating to any interaction with a partner, as in a chess game. This is a ready-made scheme for understanding situations that involuntarily impose confrontational relationships (one wins, the other loses or a draw), while they usually forget that other modes of behavior are possible: cooperative actions, negotiations in which both parties win.
V.M. Sergeev notes that during the era of the Great French Revolution, a universal explanatory scheme, according to which difficulties and failures are the result of the machinations of the enemies of the revolution, became an important element of revolutionary political culture.
Cognitive cliche- hard knowledge, which is a collective social product of thinking. One of the main
problems of cognitive science is to find out how universal explanatory schemes are formed. Currently, it is believed that this process occurs as a result of the consistent application of special procedures that certify knowledge, the most important of which are metaphors (for example, the “chess metaphor”), as well as the use of examples, since metaphors that are not explained by examples hang in the air.
A cognitive map can be visualized as a set of vertices, each of which corresponds to one factor or element of an individual’s picture of the world. The arc connecting vertices A and B corresponds to the cause-and-effect relationship A → B, where A is the cause, B is the effect.
The relationship A → B is called positive ("+" sign) if an increase in A leads to an increase (strengthening) in B, and a decrease in A leads to a decrease in B, all other things being equal. The "-" sign above the arc A → B means that the relationship is negative, i.e. other things being equal, an increase in A leads to a decrease (inhibition) in B and a decrease in A leads to an increase in B.
As an example of a cognitive map, consider the ideas of a depressed person (Fig. 3.2).
Shown in Fig. 3.2 picture of the world allows you to analyze the dynamics of the development of depression. Let's assume that the patient's self-esteem has decreased for some reason. This leads to increased depression (the relationship has a negative sign). Increasing depression reduces the ability to cope with the situation on one’s own, therefore, the need for outside help increases, which in turn further reduces self-esteem. The process is repeated over and over again. Things are clearly moving in an undesirable direction. To find a way out of a seemingly hopeless situation, it is necessary to adjust the picture of the world. The patient should be convinced that the help of others testifies to the love of friends and relatives for him, therefore this help
should increase his self-esteem, and the sign of the corresponding causal connection becomes positive. In this case, the loop discussed above gives hope that over time the situation will level out - an accidental decrease in self-esteem due to the action of the loop will be compensated.
Cognitive maps can be a useful tool for forming and clarifying a hypothesis about the functioning of the object under study, considered as a complex system. To understand and analyze behavior complex system, it is advisable to construct a structural diagram of cause-and-effect relationships.
Let's consider an example of a cognitive map for analyzing the problem of electricity consumption in the region (Fig. 3.3).
F. Roberts believes that the problem under study can be described quite fully by seven factors F, J, P, Q, R, C, U. The arcs in Fig. 3.3, significant cause-and-effect relationships are noted; the influence of the rest can be neglected.
The arc (Q, P) has a “+” sign, since an improvement in the environment leads to an increase in the number of residents, and a deterioration in the state of the environment causes an outflow of population. The arc (U, Q) has a “-” sign, since an increase in energy consumption worsens the state of the environment, and a decrease in energy consumption has a beneficial effect on its condition. The arc (P, U) has a “+” sign due to the fact that the increase in the number of inhabitants
causes an increase in energy consumption and, conversely, a decrease in population leads to a decrease in energy consumption.
Let's consider the interaction of factors in the circuit P, U, Q, P. Let's assume that the population has increased. This will lead to increased energy consumption and therefore deteriorate the environment, which in turn will lead to a decrease in the number of inhabitants. Thus, the influence of the impulse at the vertex P will be compensated by the action of the circuit P, U, Q, P, and the behavior of the system will stabilize. Three factors P, U, Q form a circuit that counteracts deviation.
In the contour U, C, F, all arcs have a “+” sign, and it is easy to see that an increase (decrease) in any variable in this contour will be amplified.
The contours in the cognitive map correspond to feedback loops (see § 1.2). The circuit that enhances deflection is a positive feedback loop, and the circuit that counteracts deflection is a negative feedback loop. The Japanese scientist M. Maruyama named these contours accordingly morphogenetics And homeostatic. In the same work, Maruyama proved that a contour enhances deflection if and only if it contains an even number of negative arcs or does not contain them at all, otherwise it is a contour that counteracts deflection. Indeed, in the case of an even number of negative arcs, opposition to the deviation will itself be counteracted. If the number of negative arcs is odd, then the last opposition to the deflection is unopposed.
This analysis scheme largely corresponds to intuitive ideas about causality. It is clear that the interaction of two factors A and B may be subject to more complex patterns, but in this case, languages of functional relationships should be used to describe the process under study.
Experience in using cognitive maps shows that the researcher often over-simplifies the situation due to limited cognitive capabilities, difficulties in simultaneously taking into account large number factors and their dynamic interaction. M. Wertheimer wrote that the researcher often lacks breadth of vision in complex situations involving several subproblems,
understanding of the whole is lost, and a narrow view of the problem is automatically imposed.
D. Hayes's monograph on causal analysis emphasizes that only a few interesting phenomena in the social sciences depend on only one cause. Social phenomena usually include many different events and trends determined by several factors, each in turn influencing a number of other factors. Networks of causal relationships are formed, i.e. Causality is systemic in nature. Causality generates a model of social phenomena, and the study of models provides a deeper understanding of the causal relationships that gave rise to them.
By analyzing his own and others' cognitive maps, a researcher can quickly deepen his understanding of a problem and improve the quality and validity of decisions made. In addition, a cognitive map is a convenient tool for changing established stereotypes and contributes to the generation of new points of view. Thus, in the work of M. Maruyama, an example is given of the erroneous belief (cognitive cliché) that trade between two countries is a zero-sum game. If one partner wins, the other loses just as much. This belief is the psychological background of the war of restrictions on the import of goods (imports).
For a country that has a trade deficit with another country, at first glance there are two equivalent ways to improve the trade balance: reduce imports and increase exports. However, the war of restrictions leads to a negative overall effect: due to a reduction in the turnover of capital between the two states and an increase in unemployment, both sides lose. On the contrary, mutual export expansion increases the speed of capital circulation and has a positive effect for both countries.
A cognitive map is especially useful for analyzing the effects of factors that are difficult to formalize, the measurement of which is often a very difficult problem. Thus, the work of R. Axelrod examines the cognitive maps of the experts of the British Committee on Oriental Affairs, taking into account such factors as the presence of consent in society, the degree of British intervention, the elimination of progressive leaders, the degree of unrest, the influence of tribal relations, etc. An example of such a map (Fig. 3.4) is given in the monograph by F.S. Roberts.
The same book discusses about 20 cognitive maps, mainly related to environmental issues and energy consumption.
Designations: sign "+" - positive relationship, sign "-" - negative, zero - indifferent (no relationship), sign Θ - indifferent or positive, sign 0 - indifferent or negative (Axelrod); AA - a policy based on the complete withdrawal of Great Britain from Persia; AB - withdrawal of troops from the northwestern regions; AC - probability of serious unrest in the northwestern regions; AD - degree of unrest; AE - presence of Bakhtiyari; AF - maintaining the role of the Anglo-Persian oil company; AG - availability of telegraph communication; AN - the likelihood of the Bolsheviks participating in the problems of Persia; AI - sympathy of the population of Persia for the Bolsheviks; AJ - degree of security in Persia; AK - extortion in trade caravans; AL - influence of tribal relations; AM - elimination of progressive leaders; AN - the real power of the leaders of Persia; AO - establishment of the Persian Constitution; AR - weakness of the Shah's family; AQ - the ability of the Persian government to maintain order; AR - absence of progressive elements in the parties of Persia (= no progressive elements); AS - the ability to control progressive elements by loved ones; AT - strength of progressive elements; AU - political reconciliation with Persia; AV - cancellation of the treaty with Russia in 1907; AW - revision of customs tariffs; AH - the presence of consent in society; AY - the degree of readiness of Persia to follow the path of independent development; AZ - degree of British intervention in Persian affairs; VA - modern policy of intervention in Persian affairs; BB - the ability of the Persians to continuously receive small subsidies; BC - the amount of Persia's debt to Great Britain; BD - Great Britain's ability to put pressure on Persia.
For sociologists, it will certainly be useful to get acquainted with the cognitive maps given in it: “Science and Society”, “Health Care System”, “Personnel Policy in the Navy”.
The English scientist K. Ideas proposed using cognitive maps for collective decision-making and decision-making. The impetus for building a theory was given to him by reading Kelly's famous work on the psychology of personal constructs. The idea emphasizes the importance of Kelly's position that the effectiveness of interaction in a group of decision-makers depends significantly on the extent to which each participant understands the ways in which situations are interpreted by other group members. An important role in obtaining consensus is played by the achievement by group members of unity in the way of constructing future events, the processes of “strengthening understanding”, “changing symbols”, identifying new points of view. A tool is needed to record and analyze reasons and opinions, which are often based on the experience and intuition of experts. It is important to be able to record the contradictory points of view of experts without losing the richness of the argumentation. A cognitive map makes it possible to trace the relationships between the future, present and past of the process being studied.
It is clear that using cognitive maps for planning in an organization may require recording several thousand interrelated statements. Therefore, to record, store, search and analyze information, it is necessary to use a computer and special software. Currently, a number of commercial packages have been developed for the analysis of cognitive maps (NIPPER, Cope, GISMO).
The computer can be used for the following purposes:
- searching for concepts containing a specific set of keywords;
- searching for clusters in the map, i.e. groups of interrelated concepts that are close to each other;
- finding map outputs (statements without consequences);
- finding statements that are central to a large number of arguments;
- identifying statements with the greatest argumentation;
- analysis of connections between expressed opinions and the structure of the organization.
A cognitive map represents the “synthetic wisdom” of the organization’s team and accumulates the views of people
many of whom have never met. Each participant in the process must be sure that his opinion is taken into account and can influence the organization’s strategy. Therefore, it is desirable that the organization's employees are included in this process on a regular basis, and they should know that other employees are also included in the strategy formation process. With the help of various working groups and committees, individual parts of the strategic plan are refined and, most importantly, feedback effects are monitored.
This approach allows you to get rid of a number of circumstances that impede the making of effective decisions (narrowing view of reality under the influence of habitual experience, boredom and the ritual nature of planning, ossification of organizational structures, the influence of stereotypes, ambitions).
In mathematical language, a cognitive map is called a signed directed graph. A contour in a graph is understood as a closed oriented path, all of whose vertices are different.
Dance therapy is used when working with people who have emotional disorders, communication disorders, and interpersonal interactions.
The use of this method requires quite a lot of preparation from the psychologist, since this type of interaction can awaken strong emotions that are not so easy to find a resolution. Dance movements combined with physical contact and intense interpersonal interaction can evoke very deep and powerful feelings.
The goal of dance therapy is to develop body awareness, positive body image, communication skills, exploration of feelings and group experiences. In the history of the development of dance therapy, K. Rudestam identifies a number of key events.
The first is related to the need for physical and mental rehabilitation of veterans who returned from the fields of the Second World War. Dance therapy became an auxiliary method of rehabilitation for people with disabilities, many of whom either could not speak at all or were not inclined to have verbal influence applied to them. After the dance class, they noted that they experienced feelings of relief and spiritual harmony.
Another factor contributing to the growing popularity of dance therapy was the human relations training movement that emerged in the 60s, which became the basis for the development of new experimental approaches to working with groups and to the development of the personalities of their participants.
Finally, interest in new dance therapy programs has been fueled by research on nonverbal communication, especially the analysis of communicative functions human body. Dance therapy is used primarily in group work.
The main goal of dance therapy groups is to promote spontaneous movement. Dance therapy encourages freedom and expression of movement, develops mobility and strengthens strength both physically and mentally. The body and mind are considered as a single whole.
The main point is formulated as follows: movements reflect personality traits. With any emotional shifts, our well-being changes, both mental and physical, and the nature of our movements changes accordingly.
Dance therapy is aimed at solving the following problems:
1. #Deepening the group members’ awareness of their own body and the possibilities of using it. This not only improves the physical and emotional state of the participants, but also serves as entertainment for many of them. At the beginning of the first lesson, the psychologist observes the participants and evaluates their strengths.
and flaws in each individual's movement repertoire, then determines which movements will work best for each client.
2. Increasing self-esteem among group members by developing a more positive body image. Clients with severe disabilities may have difficulty drawing boundaries between their own body and objects in the environment. In such groups, dance therapy aims to create an adequate body image for participants. Dance allows you to make your body image more attractive, which is directly related to a more positive self-image.
3. Development of social skills through the acquisition of relevant pleasant experiences by participants. Dance movements provide a relatively safe means of connecting with others while learning socially acceptable behavior. Dance therapy creates conditions for creative interaction and allows one to overcome barriers that arise during verbal communication.
4. Helping group members get in touch with their own feelings by connecting feelings with movements. With the client's creative attitude to movements to music, the dance acquires expressiveness, which allows one to release repressed feelings and explore hidden conflicts that can be a source of mental tension. Here the psychodynamic concept of “catharsis” extends to dance, since its movements release hidden feelings, and this has a direct corrective meaning. Dance movements are not only expressive, but also have the ability to release physical tension, especially if they involve swaying and stretching.
5. Creation of a "magic ring". Group classes involve working together participants, games and experiments with gestures, postures, movements and other non-verbal forms of communication. All this as a whole contributes to the participants’ acquisition of group experience, all components of which at an unconscious level form a closed, stable complex - a “magic ring”
Along with those mentioned, the following tasks are also solved:
increasing physical activity; communicative training and organization of sociotherapeutic communication;
obtaining diagnostic material for analyzing the patient’s behavioral stereotypes and self-knowledge;
liberation of the patient, search for authentic paths of development.
Special dance therapy exercises include free swinging, movements that require composure and control of the body, alternating relaxation and composure associated with the breathing cycle, and moving around the room in a strictly defined manner.
In the first phase, which takes a few minutes, dance therapy sessions are typically used as a warm-up to help each participant prepare their body for performance, much as a musician tunes his instrument before a performance. Warm-up exercises have physical (“warming up”), mental (identification with feelings) and social (establishing contacts) aspects.
One of the options for starting classes involves performing spontaneous free-form movements to a medley of different melodies. There are exercises here that include shaking, stretching, swinging, clapping, shaking, which, starting with the hands, spread to the elbow joints, shoulders, and chest. These exercises are repeated until the whole group is properly warmed up.
At the second stage, a group topic is developed. For example, the theme of “meetings and partings” is being developed. At the level of movements, individual parts of the body can “meet” and “separate.” Hands and elbows may “meet” only to “separate” immediately, or they may “meet” to “fight” or “hug” each other. Interaction between group members can be facilitated by the palms of one meeting the elbows of another, etc.
At the final stage of the lesson, the topic is developed using all the space provided to the group, while the speed of movements and their sequence change. The leader either determines the nature of the participants’ movements or repeats them himself.
For diagnostic analysis of movements and to help group members expand their motor repertoire, the “Force Form Analysis System” developed by R. Loban is often used.
R. Loban (1960) developed a system for describing the analysis and diagnosis of movements, known as the “Effort System”, or “Effort Form”, based on the application special characters and designed to describe the dynamic and spatial aspects of movements.
In the “System of Efforts”, according to Loban, the dynamics of movements are described by four parameters:
1. Space.
2. Strength.
3. Time.
4. Current.
Each parameter has two poles: space, which can be direct and multifocal; strength - powerful and light; time is fast and smooth; flow - free and limited.
Each movement can be characterized by any of these dimensions, and their combinations make up the eight basic forces involved in performing movements. For example, the impact force is fast, powerful and direct, while the pressure force is smooth, powerful and direct. Using the Loban system, it is possible to analyze movements in a group, which makes it possible to help group members explore and expand their motor repertoire.
The group leader can be: a dance partner, a manager (organizer), a catalyst for the development of the participants’ personalities through movement.
It creates an atmosphere of calm and trust in the group, allowing participants to explore themselves and others, and reflects and develops the spontaneous movements of group members.
The group leader uses structured exercises in a certain way that promote relaxation, proper breathing, changing the body in space and strengthening self-control.
Dance therapy is used to improve physical condition, release emotions, improve interpersonal skills, to gain positive emotions, expansion of self-awareness. The usual duration of a lesson is 40-50 minutes. Classes can be daily, weekly (over several months or years).
For preventive purposes, it is possible to conduct one-time dance marathons. The optimal size of the group is 5-12 people.
The question of the nature of the musical accompaniment of classes is debatable. Some managers prefer standard tape recordings of folk and (or) dance music, others - their own (or their assistants) improvised musical accompaniment. In all cases, it is emphasized that the individual cultural significance of the music offered to the client should not overshadow the significance and pleasure of one’s own motor activity, therefore it is better to use melodies unfamiliar to the group, moderate sound volume and physiologically oriented rhythms that contribute to the formation of trance states of consciousness.
Can be used as an auxiliary or main method of correction in groups of children and adolescents, in sanatorium-resort conditions, in the correction of dysgamy in married couples, for socio-psychological and motor training of people with hearing and visual impairments or in the rehabilitation period (after cardiac surgery, fractures limbs, etc.).
Dance therapy for children is to allow the child to express his emotions through dance, to show his mood and feelings. First of all, dance therapy promotes muscle development, allowing the child to expend energy, which he simply has in abundance. Movements to music not only have a corrective effect on physical development, but also create a favorable basis for improving mental functions such as thinking, memory, attention, and perception.
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Dance therapy
Dance therapy is a type of psychotherapy that uses movement to develop a person's social, cognitive, emotional and physical life. Dance therapy is a new form of treatment for a wide range of illnesses. The treatment is based on the principle that the body and mind are interconnected, and through the movement of the body the most subtle areas of the psyche can be treated.Teachers work with children who have various emotional problems, decreased intellectual capabilities and serious illnesses. They work with children of all ages in group and individual therapy. Some also conduct research. Dance therapists strive to help children develop communication skills, a positive image, and emotional stability. Obviously, dance as a method of treatment belongs to the field of body-oriented therapy, as well as psychology, physical therapy, art therapy and psychosomatic medicine. Dance has long been used as a therapeutic tool. The origins of dance and movement therapy go back to ancient civilizations, in which dance was an important feature of life. It is possible that people began to dance and use body movement as a means of communication before the emergence of language. Experts prove that traditional healers in Indian tribes used dance as a kind of healing art.In China, however, certain movements such as Tai Chi have been added to medical treatment. As early as the 19th century in England, doctors were aware of the effects of movement to treat both physical and mental illnesses. A variety of dance therapy theories were developed in Britain, influenced by American contemporary choreographers such as Martha Graham and Doris Humphrey. Dance therapy emerged as a profession in the 1940s. twentieth century thanks to the work of Marion Chace. She began teaching dance after finishing her career with the Denishawn Company in 1930. She noticed in her classes that some students were more interested in the feelings expressed in the dance and had little interest in the dance technique itself. And then she allowed them to address the freedom of movement rather than the mechanics of dance. Soon local doctors began sending her their patients. These included children with antisocial behavior, adults with motor problems and psychiatric patients. She was the first dance therapist to work in public service. Chace worked with patients who had emotional problems and tried to help them reconnect with others through dance.
Dance therapy with preschool children is a very complex and time-consuming process. The goal is to develop Creative skills children, through the art of dance. The main objectives of dance therapy with children:
- Not only improve the physical and emotional state of children, but also use their body correctly in dance
- Develop social skills through creative interaction
- Relieve physical stress, establish contact with your own feelings; establish a connection between feelings and movements
- Teach children to work in a team
- Increase physical activity
- Liberate the child
- Instill a love of dance
- Develop a wide repertoire of children's dances and dance games
Rhythmics in the teaching system introduces the teaching methods and repertoire of children's dance. In childhood, on initial stage learning, many important skills are laid, therefore the development of the child is largely predetermined by the professionalism of the teacher. Rhythmics helps develop rhythm, the ability to hear and understand music, coordinate movements, develop and train muscle strength of the body and legs, plasticity of the arms, grace and expressiveness. Rhythm creates a physical load for the child’s body equal to the load of several sports. The rhythmic movements used in the lessons, which have undergone long-term selection, certainly have a positive effect on the health of children. In such classes early age posture and muscular skeleton are formed, the development of physical and natural data at an early age helps, like a sculptor, to sculpt simple material unique body. It is necessary to add a play element to the teaching of young children, to make the game the main component of the lesson, which should arise from the game, become its meaning and continuation. Properly selected and organized dance games during the learning process develop the ability to work and arouse interest in the lesson and work. Therefore, it is important for the teacher to carefully select the repertoire for primary school students, constantly update it, making certain adjustments taking into account the time and characteristics of the children being taught, learn independently, create dance compositions and performances taking into account the age, psychological and physiological capabilities of the children.
Methods of teaching rhythm are closely related to constant physical activity and require the choreographer to have perfect performing skills when demonstrating the dance repertoire. By her own exercise stress must be combined with creativity, memory development and emotional expression. The teacher-choreographer must instill in children the desire to creative self-expression, competent mastery of emotions, understanding of beauty. It is necessary to “awaken” children’s interest in classes and acquiring new knowledge, and to set clear goals for children to understand. The choreographer must create conditions for a friendly, purposeful creative process, where both the teacher and the child work equally. In this regard, individual production work brings great success. Children love her, treat preparation with great interest, behave better during rehearsals than in lessons, get involved in the work process, fantasize, and work with great passion and dedication. In the process of preparing for the production, the teacher needs to develop composure, creative activity and artistry, which are required in the future from future performers. They must be able to transform and possess the highest acting skills. Teacher-choreographers, who rehearse clearly and convincingly, achieve high positive results; their students are distinguished by artistry and expressiveness in the performance of complex dance elements. When composing dance compositions for children, it is necessary to strive for the accessibility of the choreographic language. The movements should be simple and at the same time interesting. You should not get carried away by the abundance of various rhythmic figures, changes, technical difficulties - inaccessibility extinguishes the child’s desire to study. If he feels and understands the composition of the dance, then he will no longer give up in the face of difficulties and will work hard. The future specialist must skillfully select dance movements, combining them into interesting combinations, and build choreographic sketches. The technique of preliminary sketch work is useful in working with children specifically when staging story dances and free programs. The most important factor in the work at the initial stage of training is the use of a minimum of dance elements with a maximum possibility of their combinations. Long-term study and repetition of a small number of movements provide the opportunity for high-quality assimilation; practicing it is a solid foundation of knowledge. A different combination of dance movements reveals novelty and develops creative imagination children. Education dance moves occurs through practical demonstration and verbal explanations. There needs to be a clear balance between the combination of these two methods. A detailed verbal explanation leads to students losing attention and losing interest in classes. One cannot limit oneself only to practical demonstration; in this case, the material is perceived imitatively and unconsciously. As you know, a person’s motor skills are formed and developed from the first days of life: a child learns to walk, run, jump, etc. Any movement is a reflex, and it takes time to master it. Choreographic training is a long process of developing a large number of increasingly complex musical and motor skills. Future teachers should remember that teaching motor skills must always be accompanied by a specific emotional mood; one cannot teach only movements; one must reveal the emotional expressiveness of students. At the first stages of training, the teacher introduces children to elementary concepts: the nature of music, tempo, rhythm, time signature, emotional expressiveness. There is an acquaintance with acting skills through game tasks for transmission emotional states. Improvisation must be used in classes. Children's improvisational creativity does not arise on its own; it relies on the perception of music, the child's ear for music and imagination, the ability to change and create something new based on existing experience. Children improvise expressive and visual movements in the nature of the music that they listen to and perform, rhythmize, and participate in games - improvisations based on Russian folk tales and fairy tales of other peoples. Creative tasks of an improvisational nature also include independent selection of the most appropriate names for the music being listened to. Movements to music help to better feel the general character of the work and the tempo of performance. By using their movements in the process of perceiving music, children realize their involuntary desire for motor accompaniment of music. Children really like improvisation, they love to freeze in certain positions, spin around, and love to dance in pairs. Also in game form You can introduce students to anatomy: parts of the body - joints and muscles. This knowledge will help children more consciously learn dance elements and avoid possible injuries. Thus, in the preparation of teachers-choreographers of sports ballroom dance, an important place is given to the subject “Rhythmics”, which lays the creative and professional foundations, teaches how to organize, plan the concert and production activities of a group, be a leader and implement the tasks of nurturing spiritual and moral culture in a modern teenager generations.
Dance therapy for children is to allow the child to express his emotions through dance, to show his mood and feelings. First of all, dance therapy promotes muscle development, allowing the child to expend energy, which he simply has in abundance. Movements to music not only have a corrective effect on physical development, but also create a favorable basis for improving mental functions such as thinking, memory, attention, and perception. In addition, dancing contributes to the development of a child’s aesthetic taste and desire for beauty. This is revealed by the set of dances itself and the most beautiful clothes chosen for the dance. The child also develops an ear for music, which allows him to get in tune with the music. The organizing beginning of music, its rhythmic structure, dynamic coloring, and tempo changes cause constant concentration of attention, memorization of the conditions for performing exercises, and a quick reaction to changing musical phrases. Dance can improve a child's psychodynamic functioning. In fact, rhythmic movements strengthen different muscle groups and improve joint function, as well as affecting abilities such as speed, accuracy and synchronization of movements. It is logical to give preference at the beginning of the correction process motor methods, thereby creating the basic prerequisite for the full participation of mental processes in mastering reading, writing, and mathematical knowledge. This proves the need for special dance classes. Classes in a dance studio help the child and parents have common points of contact, and families have very few of them in the modern world. Therefore, parents should motivate their child’s interest in dancing with their interest, pride in all his small victories, first of all over himself. The child will suffer from colds much less often and will learn to hold his back proudly. All this together allows the child to become a full-fledged person - healthy morally and physically.
Dance and movement therapy
Dance movement therapy (DMT) is a field of psychotherapy. As a separate trend, it took shape around the 50-70s of the 20th century, first in the USA, and then in the 60-80s in Great Britain, Germany and Israel.
In the 80-90s, TDT was developed in other European countries, Asia, Australia and Russia. Official year The birth of TDT in Russia can be considered 1995, when the TDT Association was created in Moscow. It is clear that unofficially everything began much earlier.
Dance movement psychotherapy uses movement and creative expression in the context of a psychotherapeutic relationship that shifts from a purely verbal to a body-oriented approach. The process includes verbal and non-verbal communication, during which creatively actualizes self-expression, self-acceptance,
the ability to make choices, make decisions and consciously develop, making your life more and more fulfilling, creative and meaningful.
TDT is an interdisciplinary field: it exists at the intersection of psychotherapy and dance art. In addition, it is nourished by many other areas of knowledge. Among them: anatomy, physiology, psychophysiology, kinesiology, neuropsychology, a variety of theories of movement and dance, psychology, etc. - i.e. almost everything that can be attributed to the areas of knowledge about the body, movement, dance, psyche, the creative process and creative expression.
MAIN SOURCES OF TDT
It is impossible to understand the essence of TDT without referring to the main sources that feed TDT, such as separate school psychotherapy.
In this regard, four historical aspects should be highlighted:
1. This is the development of science, and primarily of psychoanalytic schools associated with S. Freud’s discovery of mental reality and consideration of the psyche as the dynamics of conscious and unconscious processes in human ontogenesis. S. Freud gave impetus to the development of depth psychology, where three main schools can be distinguished:
Psychoanalysis by S. Freud
- Individual psychology by A. Adler
- Analytical psychology of K. Jung.
By the 40s and 50s, psychoanalytic trends had become quite strong in psychotherapy as an alternative to traditional hypnosis. Many other schools emerged that either refuted or developed these basic theories and practices - thus making invaluable contributions to the general understanding of psychological laws.
TDT was born, already relying on traditions and new psychotherapeutic schools and directions. Dance therapists (depending on their inclinations and general psychotherapeutic training and experience) could use universal language movements to relate and contrast your practice with any psychological concepts. TDT is a kind of meta-level that can draw parallels and combine knowledge, experience and concepts of various psychotherapeutic directions. At the same time, TDT develops its theory based on the idea of psychosomatic unity.
2. The beginning of the century became the era of modernity in art: new forms, new principles were tried. The dance also went beyond the usual. Isadora Duncan is one of the most famous dance innovators in Russia. She was unique as a performer and expressed exactly those ideas that were the banner of modernist art. She didn't leave school behind. The founding of new dance forms of dance pedagogy is associated with other names. And, first of all, it is worth highlighting the Austrian dancer, choreographer and philosopher Rudolf von Laban. He was outstanding teacher and movement and dance theorist.
It was R. Laban who put into practice the principle of the value of individual expression in dance. Having abandoned the usual ballet training, he developed his own approach to teaching and staging movement techniques, which made it possible to maximize individual characteristics expressions of each dancer. In addition, he created a system for recording and describing any human movement(like sheet music for recording music), which is currently theoretical basis and the method of analysis and diagnosis in TDT.
His teaching was continued in the 60-70s by Irmgard Bartenieff, who added a special system of exercises (Bartenieff Fundamentals), harmonizing movement and teaching the correct and economical use of the body in movement. Currently, Labananalysis and Bartenieff's Basics are an integral part of the TDT methodology, as well as its separate direction.
The middle name is the German dancer and choreographer Mary Wigman, the founder of dance expressionism. She was most interested in human affects. Emotional experience gave birth to bodily form and determined the quality of movement. In ballet, on the contrary, a set of certain forms serves to express different contents. Mary Wigman contributed
in dance pedagogy and choreographer's art of improvisation.
Dance improvisation is methods of spontaneous movement. When a person moves spontaneously, he expresses himself very accurately and honestly: in spontaneous movement, unconscious aspects of the personality can materialize. The unconscious can become visible, take shape, thus a person is able to reconnect with lost parts of himself, his psychological resources. And if you realize this, then the opportunity opens up for self-knowledge and gaining greater personal integrity and integration - and this is the main part and goal of the psychotherapeutic process. Those. it turned out that improvisation itself confronted dancers and teachers with the healing power of dance.
It is no coincidence that all the first dance therapists were students of R. Laban and M. Wigman or their followers.
For example, Marian Chace had her own studio. And gradually her interest shifted more and more from performing arts to the process of exploring individuality in dance improvisation. She saw her students open up and change as individuals, becoming more whole, more themselves.
There is a legend that among her students there were people who were simultaneously in psychotherapy. And psychotherapists paid attention to the improvement in the condition of their patients, which was associated with classes with M. Chase. Gradually, some psychotherapists began to refer their patients to dance improvisation classes at her studio. And in 1946, Marian Chase was officially invited to work at the psychiatric hospital. St. Elizabeth in Washington, DC, where her method was born in close collaboration with psychiatrists. Probably, this date can be considered the birthday of TDT.
It should be mentioned that this clinic is one of the most advanced psychiatric hospitals in the United States. She is known for her humanistic approach to psychiatry and remains an innovator in the use of creative expression therapies in psychiatric treatment to this day. Other pioneers of TDT include Trudy Shoop, Mary Whitehouse, and Lilan Espenak.
3. It is worth mentioning separately about Wilhelm Reich and his teaching about muscular-emotional blocks and characteristic armor. He was one of the most talented students of S. Freud, who was the first among analysts to pay attention not only to what the patient says, but, above all, to how he says it. Reich said that unexpressed emotional experiences are not
disappears, but remains in the muscles and “gets stuck” there in the form of muscle blocks. Emotions in the form of muscle clamps, remaining unexpressed and unconscious in the body for years, form a muscular armor, or characteristic armor, which reflects the methods of psychological defenses (often pathogenic) and its character structure, formed under their influence.
V. Reich, being an analyst, proposed not just verbal analysis, but he directly influenced muscle blocks in order to release them and the emotions hidden in them, and on this basis analyze situations, relationships with people that caused these feelings and experiences.
TDT refers to this understanding of psychosomatic mechanisms formulated by W. Reich, but practically does not use his working methods.
4. It is impossible not to mention the original purpose of dance and ancient healing practices, where dance was an integral attribute, and which was completely lost in modern civilization.
Even before the advent of language, movement and gestures were a means of communication primitive people. And in the first human communities, dance was one of the main components of community life: both an individual way of expression (fear, sadness, joy, etc.) and a way of transmitting cultural heritage. Until now, in Aboriginal tribes, instead of asking:
"What tribe are you from?" They ask: “What dance are you doing?”
The dance accompanied all rituals of passage (birth, wedding, death, etc.), all holidays and celebrations, events of everyday life (hunting, fishing, etc.), military campaigns. It was in dance that a person conveyed his relationship with the unknown and unknown, with nature, his connection with the Universe and with gods and spirits. Dance served as a means of spiritual and healing practice. And the basis of this is not an aesthetic form, but an expression of the Innermost in a person.
And TDT, after many, many centuries of treating dance as an elite art form, returns dance to its original meaning: it doesn’t matter how you move, what matters is what you sense, feel and think, what matters is what you express with your dance.
After all, the body is the only thing in a person that does not lie and can help him reveal and express himself in all his fullness and truth.
Abraham Maslow said that "...just as man has instinctual needs that are part of his biological nature, he also has higher needs; for example, the need to be significant, the need for esteem and the need for freedom of expression." If we translate this into the language of dance therapy, it is the need to be visible, which is only possible in movement.
So, to summarize the above, dance therapists turn to the healing power of dance, to the power of creative expression in movement, and also use the achievements of modern dance pedagogy, and turn to movement studies and the experience of various psychotherapeutic schools (primarily psychodynamic, existential, humanistic and transpersonal ).
BASIC PRINCIPLES AND OBJECTIVES OF TDT
1. The body and psyche are inseparably interconnected and have a constant mutual influence on each other. For a dance therapist, it is an axiom to understand that the body is a mirror of the soul, and movement is an expression of the human self. By making the body more flexible, we make the soul more flexible, and vice versa. Therefore, the goal of therapy is to achieve self-awareness by exploring the body's reactions and actions.
2. Dance is a communication that occurs on three levels: with oneself, with other people, and with the world. In this regard, the task will be to create a safe space, a therapeutic relationship, so that, by analyzing the relationship with the therapist, and/or with other people, if this is group work, the person can find more effective ways of interacting in his environment.
3. Holistic principle, i.e. the principle of integrity, where the triad of thoughts - feelings - behavior is considered as a single whole, and changes in one aspect entail changes in the other two.
The task is to find a way to match each other's thoughts, feelings, and actions. Often a person begins to think one thing, feel another and act in a third way, which is a reflection of some kind of internal conflict. It explores how thought, feeling and movement can express one content, and also analyzes what in personal history led to such division within, i.e. to loss of internal integrity.
4. The body is perceived as a process, and not as an object, object or subject. The word process emphasizes that we are not dealing with something given, static, but with something constantly changing. The essence of such a process is best reflected by one of the principles of Tao: the ability to see statics in movement and movement in statics.
We have learned to control the body, give it certain forms, appearance, restrain it, and we think that it will remain unrequited, will not give any backlash. And then inexplicable symptoms and pain arise, a constantly felt tension in the body appears, stiffness appears, and the range of movement becomes more and more limited.
The task, following a person's process (one might say his psychosomatic Tao) of dance - the therapist helps to release and reveal the information that underlies symptoms, pain, various kinds of bodily discomfort and restrictions in movement - the person learns to understand the language of his body and, thus, restores dialogue with yourself. This work also develops the ability to use movement and dance to express a full range of feelings, and to find
constructive ways to deal with your feelings without denial and suppression (the latter is destructive to psychological health).
5. Appeal to creative resources man as an inexhaustible source of vitality and creative energy. Objective: development of self-esteem, self-acceptance and deep trust in oneself and in the life process, development of constant contact with one’s life resources. Here TDT addresses creative dance directly: these are moments of exploration and expression of emotional material (dreams, fantasies, memories) through symbolic movement.
WHO SEEKS A DANCE THERAPIST
These are, first of all, people, they are sometimes called kinesthetics, for whom movement is a way of processing information. To fully understand, they need to feel it in the body and find expression for it in movement. For them, movement is a way of self-expression, self-knowledge and development.
And these could also be people of a different type (you can distinguish the auditory or visual type), who at a certain stage of their lives began to understand that in order to solve their problem, they need to turn to their body, learn to understand its language and enter into communication with it. dialogue.
They can all be united by the fact that at a certain moment these people may feel that they are not whole, have lost contact with themselves, or would like to change the quality of this contact. Psychologically, loss of contact with oneself is identical to loss of contact with the body.
Thus, summing up the above, we can say that TDT is indicated:
For anyone who experiences emotional difficulties, conflicts, or is under stress.
For those who want to develop skills in communication, self-exploration and self-understanding.
For those for whom some feelings or experiences are too strong or so overwhelming that it is difficult to find words to say about them, or for those who avoid their own feelings and cannot find the exact words to verbalize their feelings, desires, needs.
For those whose problems are related to physicality: problems related to body image, difficulties in movement associated with a general feeling of tension and muscle tightness in different parts body, or anxiety about intimacy, physical contact and trust.
For people experiencing a stressful or crisis period in their lives, which is associated with various types of losses (death of loved ones, divorce, etc.) or a radical change in their lives.
For people who are concerned that their problems are not being solved for too long, that life seems to be going in circles, or experiencing a general condition that “everything in life is going wrong.”
General goals may include:
Developing self-awareness, self-esteem and personal autonomy.
Establishing connections between your thoughts, feelings and actions. Working through emotional blocks at the bodily level. Exploring alternative, more constructive behaviors.
Improving adaptive abilities and developing behavioral flexibility.
Expressing and managing overwhelming feelings and thoughts.
Development of communication skills.
Access to inner resources and creative forces.
Development of harmonious and trusting relationships.
WHAT CAUSES LOSS OF CONTACT WITH THE BODY?
As a child, a person seeks the approval and love of his parents, developing a system of “shoulds and shouldn’ts,” often without taking into account his own immediate needs;
Tries to avoid punishment, unpleasant and painful experiences, unbearable feelings and creates basic clamps in the body and in his movements;
He learns to survive in the world around him and, to varying degrees, rejects and cannot accept significant parts of his personality when society does not recognize them, or considers them unimportant, or does not adequately support the manifestations of individuality.
So, TDT as a field is huge. There are no age or nosology restrictions for TDT. The only limitation is the limitations of the dance therapists themselves (i.e., it depends on their specialization).
In Russia, TDT initially developed as a type of personal growth group for adults. Now the range of its application has expanded significantly. There is group and individual work with children and adults, with the help of which you can solve your personal problems related to relationships with other people, anxieties and fears, crisis life situations, loss life meaning, misunderstanding of oneself.
There is also a family TDT where you can decide family problems; There are children's groups for preschoolers and schoolchildren that develop the child's creative abilities and communication skills, helping them prepare and adapt to school. There are unique programs for children (child-parent groups) that correct the disharmonious development of the child (such as delayed mental development, minimal brain dysfunction, etc.); We work in groups and individually with people suffering from eating disorders (anorexia, bulimia, compulsive overeating); with psychogenically caused bodily symptoms and other psychosomatic disorders. TDT is used as a way to prepare couples for parenthood before childbirth, as well as for postpartum support - special groups for babies from 0 to 3 years old and their mothers.
Work with people suffering from post-traumatic disorders, disabled children, and refugees is beginning to develop.
TDT In Russia it is still a very new specialization. The Association of Dance Therapy (ADT) is gradually taking steps to develop this profession with the support of the American Dance Therapy Association (ADTA), the European Dance Therapy Association and the International Association of Creative Expression Therapy (IEATA).
Since 1995, there has been a training program on TDT in Moscow. In January 2005 we celebrate its tenth anniversary. Now this is a 3-year specialization in TDT at the Institute of Practical Psychology and Psychoanalysis with a state diploma of professional retraining.
Irina Viktorovna Biryukova,
e-mail: [email protected]
