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

By means of t heor y of t r uth deg rees of for mu las, according to deduction t heorems and completeness theorems, t he new conceptsof consistency deg re es and p olar index for gener al theor i es in Łukasew icz f uzzy and n-valued propositional log i c s ystems areint ro duce d. More over, su fficient and necessar y conditions for a theor y Γ to be consistent, inconsistent, and f ully divergent areobtained. Finally, some impor t ant proper t ies of t r uth deg rees of for mu las are prop osed.