Consistency Degrees of Theories in Lukasiewicz Fuzzy and n-valued Propositional Logic Systems

By means of theory of truth degrees of formulas, according to deduction theorems and completeness theorems, the new concepts of consistency degrees and polar index for general theories in Lukasewicz fuzzy and n-valued propositional logic systems are introduced. Moreover, sufficient and necessary conditions for a theory Gamma to be consistent, inconsistent and fully divergent are obtained. Finally, Some important properties of truth degree of formula are proposed.