She Yanhong, Wang Guojun, He Xiaoli, “Topological Characterization of Consistency of Logic Theories in n-valued Lukasiewicz Logic Luk(n),” Chinese Journal of Electronics, vol. 19, no. 3, pp. 427-430, 2010,
Citation:
She Yanhong, Wang Guojun, He Xiaoli, “Topological Characterization of Consistency of Logic Theories in n-valued Lukasiewicz Logic Luk(n),” Chinese Journal of Electronics, vol. 19, no. 3, pp. 427-430, 2010,
She Yanhong, Wang Guojun, He Xiaoli, “Topological Characterization of Consistency of Logic Theories in n-valued Lukasiewicz Logic Luk(n),” Chinese Journal of Electronics, vol. 19, no. 3, pp. 427-430, 2010,
Citation:
She Yanhong, Wang Guojun, He Xiaoli, “Topological Characterization of Consistency of Logic Theories in n-valued Lukasiewicz Logic Luk(n),” Chinese Journal of Electronics, vol. 19, no. 3, pp. 427-430, 2010,
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.