От сентенциальной логики к логике символьных выражений.

Abstract

The classical sentential logic which enrichment with help of truthfulness and falsehood operators is proposed in this paper. It is possible to express both semantical and non-semantical laws of contradiction and excluded middle in this logic. We adopted three groups of axioms in this logic: I) axioms of the classical logic for formulas that are prefixed by truthfulness and falsehood operators; 2) axioms that express truth conditions for implication and 3) axiom that expresses the bivalence principle. This logic is generalized by extending of definition domain of truth and falsity predicates to any symbolic expressions universe of logic language. All axioms except bivalence principle is generalized to this universe too. So we get the symbolic expressions logic.