She Yanhong, Wang Guojun, He Xiaoli. Topological Characterization of Consistency of Logic Theories in n-valued Lukasiewicz Logic Luk(n)[J]. Chinese Journal of Electronics, 2010, 19(3): 427-430.
Citation:
She Yanhong, Wang Guojun, He Xiaoli. Topological Characterization of Consistency of Logic Theories in n-valued Lukasiewicz Logic Luk(n)[J]. Chinese Journal of Electronics, 2010, 19(3): 427-430.
She Yanhong, Wang Guojun, He Xiaoli. Topological Characterization of Consistency of Logic Theories in n-valued Lukasiewicz Logic Luk(n)[J]. Chinese Journal of Electronics, 2010, 19(3): 427-430.
Citation:
She Yanhong, Wang Guojun, He Xiaoli. Topological Characterization of Consistency of Logic Theories in n-valued Lukasiewicz Logic Luk(n)[J]. Chinese Journal of Electronics, 2010, 19(3): 427-430.
Let (F(S),p) be the n-valued logic metric space, the present paper characterizes consistency of logic theories in the propositional logic system Luk(n) by means of topological concepts in the n-valued logic metric space. It is proved that a closed theory Gamma is consistent iff it contains no interior points, iff it possesses the truth-forgotten property, iff it contains no non-empty regular sphere.