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**:** 92
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**:** 2021
**:** .. // . 92. .: , 2021. .64-109. DOI: https://doi.org/10.25728/ubs.2021.92.4

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** (.):** primary mental abstractions, notion, concept, notional analysis, notional model, language of notions, notion calculus, knowledge base, knowledge inference, intelligent system

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** (.):** The article describes notional models that are based on primary mental abstractions: identification, generalization and association. In the process of the notional analysis, a notional model is constructed, which consists of a notional structure and contents of its notions. The notional structure defines each notion as the result of generalization or association of the other notions. The content of the notion is described by enumerable and solvable set consisting of subject domain entities. The main difference between the notional model and the other knowledge models is the refusal to describe the association of the notions in the form of a relationship. In the notional model, the association are the same notion as the generalization, which makes it possible to form the other notions from the associations. All this makes the notional model semantically invariant, i.e. independent in its interpretation from the knowledge of the subject domain. Another difference between notional and conceptual models is the multi-aspect expression of the notions. In order to prove the proposed approach to the representation and processing of knowledge, a formal theory of notions is given. The semantic part of the theory (notional language) proves the methodology of the notional analysis, and its syntactic part (notional calculus) proves the technology of notional modeling. It is proved that the notional language is decidable, complete and consistent, while the notional calculus is decidable and consistent on countable models, but complete only on finite models. The use of the notional analysis improves the expressiveness and clarity of knowledge representation, and the use of the notional models increases the efficiency and reliability of knowledge processing.

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