命题逻辑公式的真度及其近似推理.pdf

聊城大学硕士学位论文摘要近年来,王国俊教授提出了一种关于模糊命题逻辑的新理论一模糊命题逻辑公式的真度理论,: 、扩张、收缩等概念,给出了已有的命题逻辑公式真度的一种新的等价性定义,从而使此概念更加严密化和简单化. :在不同逻辑系统中我们通过对两类公式的真度进行了大小比较与分析,其结果在一定程度上反映了不同逻辑系统公式的真度分布情况,揭示了蕴涵算子对公式真度的影响,从而,使我们对蕴涵算子的进一步研究奠定了一定的基础. ,Luk,G6d及Ⅱ中一个典型公式pl—p2的真度;然后比较了公式p1一岛在这四个逻辑系统中真度的大小;最后,研究了每个逻辑系统中公式A一岛的真度随”变化的情况. (爿,B)与自然的距离p(a,研的概念推广到模糊命题逻辑系统r、G砌和n中,并讨论了它们之间的关系. 讨论的结果表明:在Lukasiewicz命题模糊逻辑系统中,它们之间的关系为:善(4,B)= 1-p(以B),而在G6d、l'. 理关键词:命题逻辑系统:命题变元集;真度:真度分布;相似度;距离;近似推聊城大学硕士学位论文 Abstract In recent years,Wang Guojun,a professor,proposes thenew theory oftruth degree on fuzzy propositions logic aframework forfuzzy it not perfect ,I have studied thetheory on thebasisofthatin thepaper: equivalent definition ofthetruthdegree oftheformula inpropositional logic system isgiventhrough introducing theconcepts ofevaluation,dilating and contracting ofpropositional variable sets,SO thatit can bemore strict and simple. distribution ofthe truth degrees ofpropositional logic formulas indifferent propositional Iooc systems缸studied:the truth degrees of two kinds offormulas pared indifferent Io’glcsystems,SO that the distribution ofdifferentIogiesystems’ truth degrees can bereflected to acertainextent,and theimplication operators’effects on truth degree can berevealed,thus,establishing thebase for the further research of theimplication operators. ,the formula pl—P2’s truth degrees are calculated respectively infour 疗一valued propositional logicsystems r,Luk,GSdandII;then,they pared; finally,the changing ofA一见’S truth degrees along with isstudied inthe four logicsystems. concepts ofthe integrated resemblance degrees善(彳,丑)and the distance p(A,曰)between A and B in Lukasiewicz's logic system are extended tothe fuzzy propositionallogic systemsL",GSdandⅡ,andtherelationsbetween