Topological Characterization of Consistency of Logic Theories in n-valued Lukasiewicz Logic Luk(n)

She Yanhong; Wang Guojun; He Xiaoli

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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.

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Topological Characterization of Consistency of Logic Theories in n-valued Lukasiewicz Logic Luk(n)

Received Date: 1900-01-01
Rev Recd Date: 1900-01-01
Publish Date: 2010-07-05

Abstract

Abstract

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.
- n-valued propositional logic Luk(n),
- n-valued logic metric space,
- Theory,
- Consistency,
- Interior point,
- Regular sphere