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.
Highlights
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 in Łukasiewicz n-valued propositional logic systems, Go del n-valued propositional logic system and the R0 n-valued propositional logic systems
We provide its algorithm of the membership degree of formulas A is a Γ-conclusion by the constructions of theory root
It is well known that different implication operators and valuation lattices L determine different logic systems
Summary
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. C. Zhang proposed the concept of generalized root of theory [10,11], in propositional logic systems.
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