命题逻辑系统R_0L_(3n+1)中公式的Γ-真度及性质  

TheΓ-Truth Degrees of Formulas in Propositional Logic System R_0L_(3n+1) with Properties

作　　者：吴洪博[1] 周建仁[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710062

出　　处：《计算机学报》2015年第8期1672-1679,共8页Chinese Journal of Computers

基　　金：国家自然科学基金项目(11171196);中央高校基本科研业务费专项资金项目(GK201501001)资助~~

摘　　要：计量逻辑理论是王国俊教授于21世纪初期建立的一种新型逻辑理论,真度理论在计量逻辑理论中发挥着关键的作用.该文将真度概念加以推广,在(3n+1)-值模糊命题逻辑系统R0L中引入了公式相对于含有限个命题变元的理论的Γ-真度;讨论了与析取连接词、合取连接词、蕴含连接词、否定连接词等基本逻辑连接词相关的Γ-真度性质;讨论了与分离规则MP,三段论规则HS等推理规则相关的Γ-真度性质.该文的工作为将计量逻辑的思想融入(3n+1)-值模糊命题逻辑系统R0L并建立基于给定理论的近似推理基本框架和相关的逻辑度量空间奠定了基础.The theory of quantitative logic is a new theory of logic established by Wang Guojun in the early part of 21 st century,and theory of truth degrees of formulas plays a key role in the theory of quantitative logic.In this paper,the concept of truth degree of a formula is generalized toΓ-truth degree of a formula relative to the theoryΓwhich contains finite propositional variables in（3n＋1）-valued propositional logic system R0L;the basic properties ofΓ-truth degrees relative to connectives of disjunction,conjunction,implication,negation are investigated;the basic properties ofΓ-truth degrees relative to inference rules of Modus ponens,Hypothetical syllogism are discussed.The work presented in this paper is a basis for introducing the idea of quantitative logic to（3n＋1）-valued propositional logic system R0L and establishing framework of approximate reasoning based on a given theory and relevant logic metric spaces.

关 键 词：模糊逻辑 计量逻辑 命题逻辑系统R0L Γ-真度 连接词 MP规则 HS规则 

分 类 号：O141.1[理学—数学]