几个三值命题逻辑系统中命题真度的分布  

Distribution of propositional truth degree in some 3-value propositional logic systems

作　　者：茹永梅[1] 王国俊[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《陕西师范大学学报（自然科学版）》2005年第4期6-10,共5页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金重点资助项目(10331010)

摘　　要：利用势为3的均匀概率空间的无穷乘积在W3、G3、Π3及S3系统中引入了公式的真度概念,得到了命题真度分布的一些性质,同时给出了三值真度推理规则.证明了以上各系统中的全体公式的真度值之集在[0,1]上是稠密的,并给出了其中公式真度的表达通式,即若A∈F(S),则τ(A)=3kn(n=1,2,…,k=0,1,…,3n).此项研究为进一步建立三值命题逻辑的近似推理理论奠定了基础,并且使W3,G3,Π3及S3系统中公式的真度有了统一的理论体系.By means of infinite product of evenly distributed probability spaces, the concept of truth degrees of propositions in 3-valued logic systems W3, G3,П3 and S3 are introduced, and some properties of distribution of propositional truth degree and certain inference rules are obtained. It is proved that the set consisting of all truth degrees of propositions is dense in [0,1 ] and an unified expression of truth degree in the set is obtained, and τ （A） = k/3^n （n = 1,2,%、…, k = 0,1,…, 3 ^n ） for every A in F（S） . These can be used to discuss approximate reasoning theory in W3, G3 ,П3 and S3 in a unified way.

关 键 词：数理逻辑 真度 三值真度推理规则 三值逻辑测度 稠密 

分 类 号：O141.1[理学—数学]