Methodological Aspects of the Application of Model Theory in Knowledge Engineering and Artificial Intelligence

The paper deals with methodological aspects and methodological problems of applying the Model Theory for solving problems of extraction, formal representation and processing of knowledge, formalization of reasoning about events and situations in various subject domains. Methodological problems associated with the need to use transformations of models of different signatures, such as isomorphic embeddings, submodels and homomorphisms, etc., are considered in the modeling of subject domains. The model-theoretical formalization of subject domain ontologies is considered. Formal glossaries are used as a tool for describing the meaning of concepts. The role of explicit and implicit definitions of key concepts of the subject domain is investigated. Model-theoretical methods are proposed for translating a language containing multi-ary predicates into a language containing only unary and binary predicates. These methods are based on the introduction of special situation-constants. Methodological problems associated with the need to formalize incomplete knowledge about situations and cases of subject domains are considered. For the formal representation of situations, methods of the theory of partial models are studied, submodels and ontological homomorphisms of partial models are considered. Model-theoretical methods for formalizing and automating reasoning based on the use of situation trees are proposed. The model-theoretical methods of knowledge representation and processing considered in the article are used to develop semantic artificial intelligence. These methods are used to solve the problem of explainable artificial intelligence.