**1. Introduction**

As Web technologies progress the task of developing tools for the data organization and storage in a web environment assumes ever greater importance [1]. In the pre-network single-user environment, the prevailing way to organize data was a hierarchically organized file structure. Still this method was convenient for not all tasks (in particular, it did not directly provide the possibility of simultaneous classification of various information objects according to various foundations). However, in the whole, it covered a rather wide class of applications.

The situation changed thanks to network technologies, when information objects turned out to be associated with different users, who applied in general different principles for placing, searching, and processing. Thus, the rigidly defined hierarchies were replaced by network structures that determine the connections of information resources set by various ways. The connections may arise due to the different reasons, and this assumes the need, firstly, to process them in different ways and, secondly, to take into account the meaning of the data and their connections when processing. Thus, the data become essentially semantic in nature.

The semantic measurement of data structures leads to the necessity to change respectively the methods of their description, searching in the environment of such structures and manipulating them [2].

this, the description of the user and his view on the subject area using a cognitive map can be considered as a specific instance of the semantic network. The transition from CM to the description in the form of a semantic network can be performed using two basic operations: (1) recovering unclear marks on arcs in CM and (2) deriving semantic network configuration patterns corresponding to the CM fragment.

The interpretation of CM as a special type of semantic network at a conceptual level provides the inclusion of the user in the conceptual model of the domain as part of it. The works on semantically oriented data representation [1, 4] show that the model should include constructions that describe the relationship between the semantics of user characteristics and the semantics of the data being processed. Such model provides the user with data for processing in accordance with the set of

represented as a whole in the form of a semantic network, its considered part can be represented as a control subnet, which provides the computation of query results in

One of the critical tasks in organizing access and processing semantically oriented data is the preservation of semantics while working with resources [5]. The resources, on the one hand, exist for a long time, and this makes their repeated use possible, and, on the other hand, they usually have a dynamic nature, i.e., they can be modified, updated, etc., at any point in time. In this case the change is possible of both the data about separate facts, processes, etc. in the area described by the resource set and the general semantic characteristics of the data. The change is also possible of both the data itself and the links, i.e., the dynamic arising of new links,

The changes in semantics can both save the logical continuity of a network and violate it. This chapter understands the logical continuity as the preservation of a set of general constraints (including informal ones) placed on the contents of the network. Maintaining logical continuity during network modification requires dynamic checking of constraints when performing operations that change the semantics of the network in order to prevent actions that destroy the semantics. For supporting the changes, the most important factor is that the semantics can be changed both unintentionally (by chance) during the work and maliciously. In the latter case, the goal may be to get unauthorized access to information—receiving or changing of the information. For this reason the support of the semantic integrity of the network suggests, in particular, restricting the user's access to information in the network. Such a restriction may include both usual restrictions on writing or reading and more complicated semantically motivated constructions. For example, the possibility to change data in the network only in a strictly determined way or every change must be associated with the information that identifies

The development of tools for supporting the network access operations involves describing the semantics of a system of interconnected resources by a formalized way, which makes it necessary to introduce the concept of a semantic network as a formal analogue of a resource system [6]. The capabilities of network access tools and their restrictions are shown in the form of a model of access tools to the SN. The necessity to implement tools for supporting access operations leads to the fact that the model must be of a computational nature. The development of such a model is expected to provide the ability to construct a semantically correct system of support for access to the SN, including the ability to specify semantically consistent access restrictions, which makes the task of developing a computational model for supporting access operations relevant. The need for data processing, including the

designation of queries, suggests the development of a theoretical basis for constructing a computer information system that provides both the logical

his powers and the nature of the problem to be solved. When the model is

changing the semantics of existing links and other information objects.

accordance with the specified parameters.

*Computational Model for the Construction of Cognitive Maps*

*DOI: http://dx.doi.org/10.5772/intechopen.90173*

the user who made the changes.

**141**

The need to use semantically rich network structures requires to develop semantically oriented methods for describing data structures and their processing, in particular, the definition of semantically oriented search methods [3]. Different users must work with different fragments of data, which are determined by the goals of their work, the source data that is necessary to achieve the goals, a set of appropriate access rights, etc. All this raises the problem of providing access to data, which should take into account both the class of the user, getting the access, and its characteristics, as well as the semantics of the data, to which the access is allowed, in particular, providing a user-friendly representation of the data.

The means of describing users and the means of their access to data, considering the specifics of the tasks to be solved, must combine power enough to distinguish the relevant elements of the description and simplicity. It makes it possible to practically use the descriptions without cumbersome instrumental kits. The means of description should fix the user's view on the subject area, which should be sufficiently detailed to describe the classes of problems to be solved, but without redundant detailing that might lead to an increase in the volume and complexity of the description. The use of cognitive maps (CMs) seems promising in this aspect.

Cognitive maps are diagrams used to visually organize information. Various works define the cognitive maps in various ways. For example, CM's can be used to represent spatial relations and determine the mutual position of information elements in a physical environment. CMs also can be used to represent abstract information and to map it to the spatial (usually planar) view. In this case CMs are connected with the presentation of information described as mind maps, which, thus, can be considered as a specific instance of CMs. As a rule, CMs represent information in the form of a hierarchical structure. It is also possible to represent connections between nonadjacent elements of the structure, which brings CMs closer to the network representation of information. The elements of the structure are connected by arcs, which, as a rule, are not specifically marked. The connections represented by arcs can use the order of homogeneous nodes that are on the same level of hierarchy. This allows to provide not only structural information but also, for example, information on the sequence of actions for solving any task.

Using CM to describe the characteristics of the user, including his typical tasks, allows to perform this description in the early stages of designing an information system. The study in the field of cognitive psychology allows us to characterize CM as a means of knowledge structuring, consistent with the human way of thinking in solving practical tasks. For this reason the CM can be used to fix ideas about the user and his tasks up to creating a formal domain model, moreover, as one of the tools for developing such a model.

Semantically oriented structures for data presentation are proposed for solving user's problems. It is worthwhile to choose the representing structure in the form of a semantic network [4]. The semantic network is understood as an oriented graph consisting of nodes and marked arcs. The nodes correspond to concepts, i.e., notions of various degrees of generality, presented in the network. The arcs correspond to the connections of the concepts among themselves, and the marks of arcs determine the way of interpreting the connections. As a rule, arcs are lined not randomly but in accordance with certain patterns representing stereotypical sets of connections (frames).

The semantic network may be of a tree-structured nature or include treestructured fragments in its composition, but it does not mean the network necessarily has this form. Therefore, the semantic network (SN) is actually a more general structure for the representation of knowledge about the domain than CM. Following

#### *Computational Model for the Construction of Cognitive Maps DOI: http://dx.doi.org/10.5772/intechopen.90173*

The semantic measurement of data structures leads to the necessity to change respectively the methods of their description, searching in the environment of such

The need to use semantically rich network structures requires to develop semantically oriented methods for describing data structures and their processing, in particular, the definition of semantically oriented search methods [3]. Different users must work with different fragments of data, which are determined by the goals of their work, the source data that is necessary to achieve the goals, a set of appropriate access rights, etc. All this raises the problem of providing access to data, which should take into account both the class of the user, getting the access, and its characteristics, as well as the semantics of the data, to which the access is allowed,

The means of describing users and the means of their access to data, considering the specifics of the tasks to be solved, must combine power enough to distinguish the relevant elements of the description and simplicity. It makes it possible to practically use the descriptions without cumbersome instrumental kits. The means of description should fix the user's view on the subject area, which should be sufficiently detailed to describe the classes of problems to be solved, but without redundant detailing that might lead to an increase in the volume and complexity of the description. The use of cognitive maps (CMs) seems promising in this aspect. Cognitive maps are diagrams used to visually organize information. Various works define the cognitive maps in various ways. For example, CM's can be used to represent spatial relations and determine the mutual position of information elements in a physical environment. CMs also can be used to represent abstract information and to map it to the spatial (usually planar) view. In this case CMs are connected with the presentation of information described as mind maps, which, thus, can be considered as a specific instance of CMs. As a rule, CMs represent information in the form of a hierarchical structure. It is also possible to represent connections between nonadjacent elements of the structure, which brings CMs closer to the network representation of information. The elements of the structure are connected by arcs, which, as a rule, are not specifically marked. The connections represented by arcs can use the order of homogeneous nodes that are on the same level of hierarchy. This allows to provide not only structural information but also,

in particular, providing a user-friendly representation of the data.

for example, information on the sequence of actions for solving any task.

of the concepts among themselves, and the marks of arcs determine the way of interpreting the connections. As a rule, arcs are lined not randomly but in accordance

with certain patterns representing stereotypical sets of connections (frames). The semantic network may be of a tree-structured nature or include treestructured fragments in its composition, but it does not mean the network necessarily has this form. Therefore, the semantic network (SN) is actually a more general structure for the representation of knowledge about the domain than CM. Following

Using CM to describe the characteristics of the user, including his typical tasks, allows to perform this description in the early stages of designing an information system. The study in the field of cognitive psychology allows us to characterize CM as a means of knowledge structuring, consistent with the human way of thinking in solving practical tasks. For this reason the CM can be used to fix ideas about the user and his tasks up to creating a formal domain model, moreover, as one of the tools

Semantically oriented structures for data presentation are proposed for solving user's problems. It is worthwhile to choose the representing structure in the form of a semantic network [4]. The semantic network is understood as an oriented graph consisting of nodes and marked arcs. The nodes correspond to concepts, i.e., notions of various degrees of generality, presented in the network. The arcs correspond to the connections

structures and manipulating them [2].

*Cognitive and Intermedial Semiotics*

for developing such a model.

**140**

this, the description of the user and his view on the subject area using a cognitive map can be considered as a specific instance of the semantic network. The transition from CM to the description in the form of a semantic network can be performed using two basic operations: (1) recovering unclear marks on arcs in CM and (2) deriving semantic network configuration patterns corresponding to the CM fragment.

The interpretation of CM as a special type of semantic network at a conceptual level provides the inclusion of the user in the conceptual model of the domain as part of it. The works on semantically oriented data representation [1, 4] show that the model should include constructions that describe the relationship between the semantics of user characteristics and the semantics of the data being processed. Such model provides the user with data for processing in accordance with the set of his powers and the nature of the problem to be solved. When the model is represented as a whole in the form of a semantic network, its considered part can be represented as a control subnet, which provides the computation of query results in accordance with the specified parameters.

One of the critical tasks in organizing access and processing semantically oriented data is the preservation of semantics while working with resources [5]. The resources, on the one hand, exist for a long time, and this makes their repeated use possible, and, on the other hand, they usually have a dynamic nature, i.e., they can be modified, updated, etc., at any point in time. In this case the change is possible of both the data about separate facts, processes, etc. in the area described by the resource set and the general semantic characteristics of the data. The change is also possible of both the data itself and the links, i.e., the dynamic arising of new links, changing the semantics of existing links and other information objects.

The changes in semantics can both save the logical continuity of a network and violate it. This chapter understands the logical continuity as the preservation of a set of general constraints (including informal ones) placed on the contents of the network. Maintaining logical continuity during network modification requires dynamic checking of constraints when performing operations that change the semantics of the network in order to prevent actions that destroy the semantics.

For supporting the changes, the most important factor is that the semantics can be changed both unintentionally (by chance) during the work and maliciously. In the latter case, the goal may be to get unauthorized access to information—receiving or changing of the information. For this reason the support of the semantic integrity of the network suggests, in particular, restricting the user's access to information in the network. Such a restriction may include both usual restrictions on writing or reading and more complicated semantically motivated constructions. For example, the possibility to change data in the network only in a strictly determined way or every change must be associated with the information that identifies the user who made the changes.

The development of tools for supporting the network access operations involves describing the semantics of a system of interconnected resources by a formalized way, which makes it necessary to introduce the concept of a semantic network as a formal analogue of a resource system [6]. The capabilities of network access tools and their restrictions are shown in the form of a model of access tools to the SN. The necessity to implement tools for supporting access operations leads to the fact that the model must be of a computational nature. The development of such a model is expected to provide the ability to construct a semantically correct system of support for access to the SN, including the ability to specify semantically consistent access restrictions, which makes the task of developing a computational model for supporting access operations relevant. The need for data processing, including the designation of queries, suggests the development of a theoretical basis for constructing a computer information system that provides both the logical

correctness of data interpretation and the construction of appropriate computational procedures. For this purpose this chapter uses the formalism developed on the basis of intensional logic [6]. The computational aspect is ensured, in particular, by the possibility to include the means of a typical lambda calculus into the logical system under consideration.

The necessity to take into account the subjective view on the semantic network requires modeling the dependence of the interpretation of the system's structures on the subject. This requirement is considered in the intensional logic by defining an interpretation structure using a parameter, the assignment point. The value of each construction corresponds to specified parameter value. In this case the constructions of the language of intensional logic are divided into extensional and intensional ones. The value of the composite extensional construction at the specified assignment point is a function of the values of its constituent structures at the same assignment point. The determination of the value of the intensional composite constructions requires determining the values of its constituent constructions on the entire set of assignment points or on some of its subsets.

To take into account the interpretation of various entries of an information object requires the construction of models of interpretation dependence on the context. The context determination can also be performed using intensional constructions. In this case, it is possible to use intensional operators or constants intensions of higher orders.

Regarding this some lines of research in the field of cognitive modeling should be mentioned. The work [13] proposes the most common approach. According to the approach, the cognitive modeling is "a line based on a knowledge-intensive interdisciplinary methodology for solving applied problems through cognitive maps with more or less support to special information technologies." In this case the cognitive map is understood as a formalized model of the situation that reflects the knowledge and/or beliefs of the subject, individual or collective, about the cause–

Within the considered line, the formal models of CMs relate to the questions of

reducing the risk, introduced by the human factor, when solving problems in various subject areas using CMs. The work [13] proposes an option of describing the approaches to the formal definition of the methods of interpreting CMs. This work distinguishes two approaches to the interpretation of CMs: descriptive (pinning methods of understanding the notions of the subject area) and normative (fixing the methods of solving problems in the subject area), which trace back to the approach accepted in the work [14]. The first approach aims to use CMs for developing an internal model of a man's knowledge about a certain situation. The second approach suggests CMs of different types as normative models (schemes or rules)

In general, depending on the objective of the study, the details of the CM's definition differ from each other; in particular, CMs may have a different structure. In the whole within the formal approach, the CM definition is often extended to a cognitive graph. For example, the work [15] considers the structure of spatial knowledge that arises from the study of a new spatial environment and gives grounds for generalizing CMs up to cognitive graphs. The studies of the optimization of CM's representation adjoin the works of this type. Thus, the work [16] proposes a three-dimensional representation of CMs. The representation is based on the selection of the node kernels and daughter nodes, the nodes being located in three-dimensional space and being represented by balls of different radius. The proposed representation, as stated, enhances the cognitive clarity of the represen-

effect impacts between the important factors of the situation.

*Computational Model for the Construction of Cognitive Maps*

*DOI: http://dx.doi.org/10.5772/intechopen.90173*

**Figure 1.**

**143**

*Lines of research and application of CMs.*

for the external presentation of knowledge about situations.

tation, which is interpreted as the ease of its intuitive understanding.

A cognitive map or, with a graph-based approach, a cognitive graph can represent parts of systems with a cognitive architecture and in this way be put in one or another cognitive architecture. The work [17] describes some cognitive architectures, the method of description giving an opportunity to think about the

The applied method of parameterization allows to take into account the semantic characteristics of users of various classes.

This chapter is structured as follows. Section 2 describes some approaches to the definition and construction of cognitive maps; special attention is paid to the degree of use of semantic information. Section 3 contains a statement of the problem of supporting the language of description of cognitive maps and means of its interpretation and offers a solution as a variant of the language of intensional logic. Section 4 describes the use of cognitive maps in the description of the problem area on the example of dependent types. In Section 5 we propose an approach to build a support system of cognitive maps on the basis of adjoint functors. In conclusion, the results are summarized briefly.
