Abstract
In order to put fuzzy reasoning into the framework of logic and lays a solid logical foundation for fuzzy reasoning both syntactically and semantically,this paper transforms FMP(fuzzy modus ponens)into GMP (generalized modus ponens)by formalizing fuzzy reasoning and transplanting it into the classical propositional logic.Base on the concept of truth degrees of formulas,the sustentation degrees between formulas are put forward and a new kind of optimal solving mechanism is established for GMP and CGMP(collective generalized modus ponens).Existence theorems of optimal solutions are proved both for GMP and CGMP,and it is pointed out that there exists a completely similar reasoning mechanism between the classical propositional logic and the fuzzy logic. The graded method presented in this paper makes the algorithmic realization of solution procedure possible and serves as a guideline for the graded reasoning about knowledge.
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