命题逻辑系统 R03n ＋1中公式的Γ-真度及性质

摘要

The theory of quantitative logic is a new theory of logic established by Wang Guojun in the early part of 21st 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 to Γ-truth degree of a formula relative to the theory Γwhich contains finite propositional variables in (3n+1)-valued propositional logic system R0;the basic properties of Γ-truth degrees relative to connectives of disjunction,conjunction,implication,negation are investigated;the basic properties of Γ-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 R0 and establishing framework of approximate reasoning based on a given theory and relevant logic metric spaces.%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 R0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 R0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。