Kolesnikov D. Predicate models of logic-mathematical concepts and their application in the artificial intelligence systems

In the thesis predicate models of the following logic-mathematical concepts are constructed: equality, Cartesian product, belonging, operations of union, intersection and complement of sets, separation of sets, link between mappings and relations, link between separations and equivalences. Obtained models allow to simplify creation of the artificial intelligence systems that are oriented to handling of the appropriate logic-mathematical concepts. The simplification is achieved due to the use of these models as the basic elements during modeling specified systems by the first order predicate calculus. The logic-mathematical tools that are oriented to the building of arbitrary logic-mathematical concepts are developed. The predicate models of logic-mathematical concepts and logical equations solution methods that are constructed in the thesis have been applied at the development of the deductive database management system. The models application has increased abstraction level of the inquiries system; the application of the logical equations solution methods has allowed to efficiently evaluate the inquiries answers that are defined relations in the terms of their negations. The logical equations solution methods have also been applied in the knowledge bases, based on the first order predicate calculus, for solution the character count minimization task of formulas that represent knowledge base fragments.