模糊命题模态逻辑的Tableau方法

Tableau approach of fuzzy propositional modal logic

为提高模糊命题模态逻辑(fuzzy propositional modal logic,FPML)的推理能力,本文将经典模态逻辑中的Tableau方法推广到FPML中,提出了基于FPML的Tableau规则并证明了其正确性,给出了模糊断言集合的约简策略;在此基础上给出了FPML中的不一致性和不一致估值的定义。最后给出基于Tableau方法的FPML的一致性检测方法 TFPML和模糊断言集合的不一致估值计算方法 CID,并证明了其正确性。实例分析表明,本文提出的方法是正确有效的。

In order to improve the reasoning ability of fuzzy propositional modal logic（ FPML）,we propose a tableau approach to FPML,including a reduction strategy and tableau rules based on FPML. We also propose a method known as tableau approach of fuzzy propositional modal logic（ TFPML） to check the consistency of FPML,and a computing method known as CID to determine the degree of inconsistency of a fuzzy assertion set. The soundness and completeness of these two methods are proven,and their correctness and effectiveness are illustrated.