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Документ Relations and operations on predicates in the theory of intelligence(NTU "KhPI", 2017) Khudhair, Abed ThamerThe 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. The methods of algebra of finite predicates, Boolean algebra and axiomatic method are used in the paper. 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 p redicates 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. 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.Документ The intelligence theory mathematical apparatus formal base(НТУ "ХПІ", 2017) Khudhair, Abed ThamerPurpose. The main task of the theory of intelligence is to describe mathematically the laws governing the intellectual activity of a human. This requires to obtain using physical and objective methods to obtain formal description of the subjective states of a human sufficiently complete for practical purposes. Human thoughts, sensations, perceptions and awareness are all subjective states. This paper is tasked to develop a multidimensional predicate model of comparator identification - the basic experimental method of the intelligence theory and to substantiate the axiomatics of this model. Methods. The comparator identification method developed in this paper provides the possibility of obtaining objective knowledge of subjective states of human intelligence. According to the comparator identification method with his behavior the subject realizes some finite predicate, the properties of which are experimentally studied and mathematically described. The comparator identification method is based on the algebra of finite predicates, Boolean algebra and the axiomatic method. Results. As a result of the comparator identification method application, we obtain a mathematical description of the studied subjective states of a subject, as well as the form of the function underlying the transformation of physical objects into subjective images generated by them. Conclusions. The results of this paper provide a mathematical substantiation of the possibility of using the comparator identification method in human intelligence modeling.