一种非均匀概率空间下逻辑系统G_3中命题的真度理论  

Truth degree theory of propositions in Godel 3-valued logic system in the space of unevenly distributed probability

作　　者：关晓红[1] 李骏[2] 

机构地区：[1]河南师范大学数学与信息科学学院,河南新乡453007 [2]兰州理工大学理学院,甘肃兰州730050

出　　处：《兰州理工大学学报》2009年第5期135-138,共4页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(10771129);河南省教育厅自然科学研究计划项目(2007110016)

摘　　要：利用势为3的非均匀概率空间的无穷乘积,在Go¨del三值命题逻辑系统中引入公式的真度概念,在三值逻辑14,12,14测度下证明G3中全体公式的真度值之集在[0,1]上是稠密的,并给出公式真度的表达通式,为进一步在三值命题逻辑系统中展开近似推理奠定基础.Using the infinite product of unevenly distributed probability space with potential of 3,the concept of formula truth degree was introduced into the Godel 3-valued propositional logic system.Moreover,it was proved that in the 3-valued（1/4,1/2,1/4）measure the set of truth degree of propositions was dense in ,and a general expression of truth degree was obtained,providing a basis for further developing approximate reasoning of 3-valued propositional logic system.

关 键 词：非均匀概率空间 测度 真度 稠密 

分 类 号：O141.1[理学—数学]