V.S. Vykhovanets1

1 Bauman Moscow State Technical University (Moscow, Russia)
1 Institute of Control Scienses of the Russian Academy of Sciences (Moscow, Russia)

The article is devoted to the analysis of complex subject domains for the creation of notional models. The main problem is that the notion is not just a static representation of reality, but a complex cognitive phenomenon that varies depending on the cognitive goals of the subject and on the available knowledge about the subject domain. The objective of the work is to develop and study the methodology of notional analysis based on the use of notions, not concepts, as is done in other methodologies. Notions differ from concepts. A concept is an abstract objective notion, and a notion is a concrete subjective concept. For this reason, there are many formal notions that have the same name, but different structure and content in different problem areas (aspects). The concept is defined as the union of notions with the same name in all aspects. The notional analysis is based on three notions operations on concepts, on the operations of identification, generalization and association. These operations are considered as mental operations necessary and sufficient to isolate and transform into notions the existing representations from the described subject domain. During the identification operation, the entity of the subject domain is mentally replaced by a notion-sign, as a result of which a one-to-one correspondence is established between entities and notion-signs. The notion-generalization is formed when combining entities of generalized notions (union sets of entities). The notion-association is formed when connecting entities of associated notions, when each entity of the notion-association includes one entity of associated notions (a subset of Cartesian production of sets of entities). The notional operations have the opposite operations of them, namely: interpretation, specialization and individualization, respectively. The notional analysis consists in identifying notions and their ways of formation. The main objective of the notional analysis is the multidimensional structuring of the subject domain in the form of its notional structure. The notional structure defines each notion as the result of generalization or association of other notions. To complete the description of the subject domain, a national model is built. A notional model consists of a notional structure and a description of the entities of all notions belonging to it (a description of the content of notions). As in descriptive logics, the content of notions is given by enumerable or solvable sets of entities in the pure monadic predicate calculus. The pure monadic predicate calculus is complete, consistent and solvable, which makes it possible to build effective notional models of the subject domain. The main difference between notional and conceptual analysis is the refusal to describe the association of notions in the form of a relationship of notions. In the notional model, associations are the same notions as generalizations, which makes it possible to form new notions from associations. Another difference of the notional analysis is the multidimensional expression of notions. The use of the methodology of the notional analysis makes it possible to improve the expressiveness and visibility of notional models to increase the efficiency of the presentation and processing of knowledge.

Vykhovanets V.S. The methodology of notional analysis of complex subject domains. Science Intensive Technologies. 2022. V. 23.
№ 8. P. 60-68−13. DOI: https://doi.org/10.18127/j19998465-202208-07 (in Russian)

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