Consistency of Finite Theory in Three Types of Many-Valued Propositional Logic Systems

In many-valued propositional logic systems, Let Gamma be a finite theory, there is a question that if Gamma is a consistency theory in n₁-valued logic, is it consistent in n₂-valued logic? In this paper, we answer this question in following three prominent many-valued propositional logic systems .i.e. Lukasiewicz many-valued propositional logic systems L_n, Godel many-valued propositional logic systems G_n, and the R₀-type many-valued propositional logic sys- tems(NM logic) L_n*. The result shows that in different logic systems the conclusion is different.