带有不同否定的模糊命题逻辑的形式演绎系统

对于模糊知识及其否定关系，潘正华指出应该明确地分为矛盾否定关系、对立否定关系和中介否定关系，并建立了一种具有矛盾否定、对立否定和中介否定的模糊集FScom（fuzzy sets with contradictory negation， opposite negation and medium negation），随后建立了一种改进的模糊集IFScom（improved FScom）。为给模糊集FScom及其改进IFScom提供一种逻辑工具，提出了一种带有矛盾否定、对立否定和中介否定的模糊命题逻辑演算系统FPcom，并在给定无穷值语义赋值模型以及可满足性定义下，证明了FPcom具有可靠性和完备性。FPcom在一定意义上可视为对中介命题演算系统的改进。

Formal Deductive System of Fuzzy Propositional Logic with Different Negations

For different kinds of negative relations in fuzzy knowledge, Pan Zhenghua pointed out that the negations in fuzzy knowledge should be composed of three distinct classes：contradictory negation, opposite negation and medium negation, and proposed the fuzzy sets with contradictory negation, opposite negation and medium negation denoted as FScom. Subsequently, the author presented a kind of improved fuzzy set IFScom （improved fuzzy sets with contra-dictory negation, opposite negation and medium negation）. Firstly, this paper proposes a novel type of fuzzy proposi-tional logic which corresponds to FScom and IFScom. Then, it gives the infinite-valued semantic model and satisfi-ability of FPcom, and proves the soundness theorem and the completeness theorem of FPcom. In some sense, FPcom may be considered as an improved medium propositional calculus system.