n值S-MTL逻辑系统中命题的Borel概率真度理论  

Theory of probabilistic truth degree of propositions in n-valued S-MTL logic system

作　　者：李骏[1] 郑刚[1] 

机构地区：[1]兰州理工大学理学院,兰州730050

出　　处：《计算机工程与应用》2014年第2期39-43,共5页Computer Engineering and Applications

基　　金：国家自然科学基金(No.10771129);兰州理工大学博士基金资助项目

摘　　要：在n值S-MTL逻辑系统的统一框架下,通过视全体赋值之集为通常乘积拓扑空间,给出了命题的Borel概率真度定义。通过构造公式所诱导的阶梯函数给出了公式真度的积分表达式,进而利用命题的Borel概率真度在该逻辑系统中引入公式间的相似度及其伪距离,使得在n值S-MTL逻辑系统的统一框架下搭建起融随机性和整体性于一体的近似推理模型成为可能。The present paper introduces the notion of probabilistic truth degree of formulas in the unified framework of n-valued S-MTL logic by means of Borel probability measures on the space of all valuations endowed with the usual product topology. The integral expression of truth degree of formulas is given, similarity degree and pseudo metric between formulas are introduced based on the probabilistic truth degree of formulas, this makes it possible to construct a kind of model behaved both randomly and globally for approximate reasoning in the unified framework of n-valued S-MTL logic.

关 键 词：计量逻辑学 Borel概率测度 伪距离 近似推理 

分 类 号：O141.1[理学—数学]