带有不同否定的模糊命题逻辑的形式演绎系统

摘要

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.%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。