n值逻辑系统L_n~*中广义重言式的计量化研究  

Quantitative research of generalized tautologies in n-valued propositional logic L_n~*

作　　者：王国俊[1,2] 时慧娴[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 [2]上海市高可信计算重点实验室,华东师范大学,上海200062

出　　处：《陕西师范大学学报（自然科学版）》2009年第2期1-5,12,共6页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10771129)

摘　　要：基于均匀概率空间的无穷乘积,通过考虑使某一公式的赋值不小于(或大于)ζ(ζ∈[0,1])的那些赋值映射之集在总赋值集合中所占的份额,在n值R0-命题逻辑系统L*n中引入公式的ζ-真度及ζ+-真度概念,从而将重言式的概念进行双重程度化;提出了σ-(ζ-重言式)和σ-(ζ+-重言式)理论;研究了ζ-真度(ζ+-真度)与广义重言式及程度化的广义重言式之间的关系,给出了广义真度推理规则.By means of the infinite product of evenly distributed probability spaces,the proportion of the class of valuation which satisfies v(A)≥ζ(or v(A)>ζ,where ζ∈) in the set of all valuations is considered and the concepts of ζ-truth degree and ζ+-truth degree in n-valued R0-propositional logic system Ln  are introduced in order to double-grade the concept of tautology.Also,the theories of σ-(ζ-tautology) and σ-(ζ+-tautology) are defined.Moreover,relationships between ζ-truth degree(ζ+-truth degree) and gene...

关 键 词：广义重言式 ζ-真度 σ-(ζ-重言式) 广义真度推理规则 

分 类 号：O141.1[理学—数学]