Article collection "Mathematical Problems of Cybernetics" №7, Moscow, 1998

Authors:Kosovskii N.K., Tishkov A.V.

Sequential Calculus for matching of conflicting conditions distinct degrees of truth

Abstract:

E. Post generalized two-valued propositional logic to finite-valued ones. The article presents a further generalization. It is proposed to consider the heuristic logic of finite-valued predicates as an extension of two-valued logic, adapted to the original descriptions, including in the humanitarian areas of human knowledge. The proposed calculus and its sub-calculuses are convenient to use while analysis of axiomatic systems, if we assign different levels of evidence (truth) to predicates in different fields of knowledge. Similarly, you can use various logical values for the postulates of various sciences, combining several sciences in a single hierarchical system. The predicate calculus of heuristic logic and sequential calculus of heuristic logic are defined. Some properties of the stated sequential calculus, upper bounds of the complexity of testing the tautological nature of a propositional fragment of the considered logic are proved. Semantic validity and completeness are proved. NP-completeness of the satisfiability problem for propositional formulas of the considered theory is proved.

Keywords:

heuristic logic, logic of finite-valued predicates, sequential calculus, NP-completeness