标准序列逻辑系统S_3中公式的概率真度理论  

The Theory of Probability Truth Degree in Standard Serial Logic System S_3

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：《模糊系统与数学》2009年第6期53-59,共7页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(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三值标准序列逻辑系统中引入了公式的概率真度概念,证明了全体公式的概率真度值之集在[0,1]中没有孤立点;利用概率真度定义了概率相似度和伪距离,进而建立了概率逻辑度量空间,证明了该空间中没有孤立点,为三值命题的近似推理理论提供了一种可能的框架。Based on the infinite product of unevenly distributed probability space, this paper introduced the theory of probability truth degree in 3-valued propositional logic S3. It is proved that the set of probability truth degree of all formulas has no isolated point in [0,1]. The conceptions of probability similarity degree and pseudo-metric on two formulas are defined by means of the concept of probability truth degree of propositions. Moreover, the probability logic metric space is built. It is proved that this space has no isolated point. Then it can provide a possible framework for approximate reasoning theory .

关 键 词：概率测度 概率真度 相似度 伪距离 孤立点 

分 类 号：O141[理学—数学]