Abstract: It is known, that person’s thinking is inaccessible to studying by direct physical and psychological methods. In this case it is necessary to have indirect ones. Computers do not understand the psychological description and formalization of thinking mechanisms. Algebra logic analysis of natural language and person’s thinking plays an important role for development of logic mathematics and its applications in artificial intelligence. Only axiomatic method works in this situation. On the basis of axioms’ system we can propose an approach that helps to investigate the structure and properties of objects. The main problem of formal studying of a natural language is shortage of the mathematical apparatus. The axiomatic description of logic mathematics' objects requires preliminary realization of constructive logical tools, which subsequently become a subject of the axiomatic analysis. The paper is devoted the algebra of ideas to axiomatic construction. The carrier of this algebra is naturally interpreted as the set of intelligence ideas (thoughts, concepts and, in general, any subjective conditions of the person). There are devised some methods for application of proposed formal apparatus. Simultaneously with algebra of ideas formal introducing there is considered its intentional interpretation.

Keywords: a predicate, algebra of ideas, artificial intelligence, Cartesian set, algebra of predicates, algebra of single k-dimentional first order predicates.

ACM Classification Keywords: I.2 Artificial intelligence - Natural Language Processing

Link:

ALGEBRA LOGIC APPROACH TO PERSON’S THINKING MECHANISMS FORMALIZATION

Olga Kalinichenko

http://www.foibg.com/ibs_isc/ibs-13/ibs-13-p10.pdf