Relations and operations on predicates in the theory of intelligence
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Abstract
Purpose. The purpose of the paper is to develop a formal technique of the theory of intelligence, namely, to develop the model and axiomatics in the language of algebra of finite predicates (AFP); to introduce a system of operations on relations; to construct of the algebra of relations. Methods. The methods of algebra of finite predicates, Boolean algebra and axiomatic method are used in the paper. Results. In the paper the mathematical apparatus of the theory of intellect was further developed. The models and axiomatics of relations in the language of algebra of finite predicates (AFP) are developed, operations on relations such as the injection, equivalence, surjection, quasi-order, partial order, circulation and product of the relation are introduced. The algebra of relations is constructed. The system of operations on predicates in the algebra of finite predicates, namely, the Boolean negation, disjunction, conjunction, implication, equivalence is axiomatically assigned. The basic predicates (predicates of object recognition) are introduced. Conclusions. The predicates of different orders correspond to concepts of a different level of abstraction. The solution of the AFP equations can be interpreted as a creative activity of a person. Due to the presence of such a wide and meaningful interpretation, even the purely mathematical development of the AFP allows at the same time to impel the development of the theory of intelligence. The minimization, decomposition, solution of equations, identical transformation of formulas are important tasks of the theory of intelligence.
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References
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