一类具有3种否定的模糊模态命题逻辑

摘要

In the fuzzy knowledge processing,it is a basic theory for distinguishing,expressing,reasoning and calculating for different negative knowledge.The fuzzy propositional logic formal system FLCOM with contradictory negation,opposition negation and medium negation is a theory which can fully describe the different negation with its relation and law in fuzzy knowledge.In this paper,a fuzzy modal propositional logic system MKCOM with three kinds of negation was proposed based on FLCOM and the medium modal propositional logic MK,as well as the expansion system MTCOM,MS4COM and MS5COM of MKCOM.Then the interpretation of semantics and syntax about MKCOM was discussed,and the reliability and completeness theorems of MKCOM were proved.%对不同否定知识的认知、区分、表达、推理及计算是模糊知识研究处理的一个基础.具有矛盾否定、对立否定和中介否定的模糊命题逻辑形式系统FLCOM是一种能够完整描述模糊知识中的不同否定及其关系与规律的理论.基于FLCOM和中介模态命题逻辑MK,提出一类具有3种否定的模糊模态命题逻辑VKCOM及其扩充系统MTCOM,MS4 COM和MS5COM;讨论了MKCOM的语义和语法解释,并证明了MKCOM的可靠性定理和完备性定理.