The Theory of Membership Degree of Γ-Conclusion in Several n-Valued Logic Systems

Jiancheng Zhang

Department of Mathematics, Quanzhou Normal University, Quanzhou, China.

DOI: 10.4236/ajor.2012.22017                

Abstract

Based on the analysis of the properties of Γ-conclusion by means of deduction theorems, completeness theorems and the theory of truth degree of formulas, the present papers introduces the concept of the membership degree of formulas A is a consequence of Γ (or Γ-conclusion) in Lukasiewicz n-valued propositional logic systems, Godel n-valued propositional logic system and the R₀ n-valued propositional logic systems. The condition and related calculations of formulas A being Γ-conclusion were discussed by extent method. At the same time, some properties of membership degree of formulas A is a Γ-conclusion were given. We provide its algorithm of the membership degree of formulas A is a Γ-conclusion by the constructions of theory root.

Keywords

N-Valued Propositional Logic; Γ-Conclusion; Theory; Root; Membership Degree

Conflicts of Interest

The authors declare no conflicts of interest.

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