Consistency Degrees of Theories in Łukasiewicz Fuzzy and n-Valued Propositional Logic Systems - Jiancheng Zhang (Applied Computational Intelligence and Soft Computing)
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 Łukasewicz fuzzy and n-valued propositional logic systems are introduced. Moreover, sufficient and necessary conditions for a theory Γ to be consistent, inconsistent, and fully divergent are obtained. Finally, some important properties of truth degrees of formulas are proposed.