一个新的模糊谓词演算形式系统

A new formal deductive system for fuzzy predicate calculus

首先,在模糊逻辑命题演算形式系统L 的基础上,讨论了相应的谓词演算理论,建立了一阶形式系统K ,基于R0代数的基本理论,给出了系统K 的若干语义概念,包括M-解释I,I-赋值,公式的值,真,M-逻辑有效性等,从而形成了模糊谓词演算一种新的语构与语义体系.其次,研究了系统K 的基本性质,指出了系统L 的定理都是系统K 的定理,给出了系统K 与量词有关的一些重要定理,证明了系统L 的重言式在系统K 中的代换实例都是系统K 中关于任何R0链的逻辑有效公式;系统K 的可靠性定理成立,即系统K 中的定理关于任何R0链也是逻辑有效的;系统K 的强可靠性定理也成立,即系统K 在任何理论T下的定理关于任何R0链也是逻辑有效的.最后给出并证明了系统K 的一种新的演绎定理,一阶系统K 及其重要的性质,为模糊推理提供了一种更为合理的逻辑框架.

Based on the formal deductive system LBZ of fuzzy propositional logic,in this paper,a corresponding first-order logic system K of fuzzy predicate logic is built up.By the basic theory of R0 algebras,the semantical concepts of the system K are given out,including M-interpretations I,I-valuations,the values of formulas,truth,M-logically validation and so on.Thus a kind of new syntactical and semantical systems of fuzzy predicate calculus are formed.The fundamental properties of the system K are studied,and it is pointed out that All theorems of the system L are theorems of the system K.Some important theorems about quantifiers are obtained.Moreover,the following results also are proved that all instances of substitution in the system K of tautologies of the system L are logically valid for any R0 chain,the soundness theorem and strong soundness theorem hold in the system K,i.e.,all theorems of (the theory T of )the system K also logically valid for any R0 chain.A new deduction theorem of the system K is stated and proved.The first-order system K and its fundamental properties provide a more ideal logical framework for fuzzy reasoning.