Abstract
In many-valued propositional logic systems, Let Z_$\Gamma$_Z be a finite theory, there is a question that if Z_$\Gamma$_Z is a consistency theory in Z_$ n_{1}$_Z-valued logic, is it consistent in Z_$n_{2}$_Z-valued logic? In this paper, we answer this question in following three prominent many-valued propositional logic systems.i.e. \L ukasiewicz many-valued propositional logic systems Z_$L_{n}$_Z, G\"{o}del many-valued propositional logic systems Z_$G_{n}$_Z, and the Z_$R_{0}$_Z-type many-valued propositional logic systems(NM logic) Z_$\mathcal{L}^{*}_{n}$_Z. The result shows that in different logic systems the conclusion is different.