带有不同否定的模糊命题逻辑的形式演绎系统  

Formal Deductive System of Fuzzy Propositional Logic with Different Negations

作　　者：张胜礼[1,2] 

机构地区：[1]陕西师范大学计算机科学学院西安710119 [2]兴义民族师范学院信息技术学院,贵州兴义562400

出　　处：《计算机科学与探索》2014年第4期494-505,共12页Journal of Frontiers of Computer Science and Technology

基　　金：贵州省科学技术基金项目Grant No.2324[2012]Contract J~~

摘　　要：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。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.

关 键 词：模糊逻辑 矛盾否定 对立否定 中介否定 中介模糊公式 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]