Definition of Strong Equality of Tautologies and Universal System for Various Propositional Logics

Abstract

Earlier we have introduced a definition of strong equality of classical tautologies, according to which two tautologies are equal iff they have the same hardness. The strong equality implies well known equality, but not vice versa. The strong equality is based on the notion of determinitive conjunct, using of which some new deduction system for classical propositional logic were defined. Here the notions of strong equality of tautologies for various logics are suggested and the idea of construction of universal deduction system for various propositional logics is given.