经典命题逻辑中的近似推理与强近似推理  

Approximate and Strong Entailments in Classical Propositional Logic System

作　　者：罗清君[1,2] 王国俊[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]西安财经学院统计学院,陕西西安710100

出　　处：《模糊系统与数学》2012年第4期20-24,共5页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(10771129;11171200);陕西教育厅自然科学基金资助项目(09JK439)

摘　　要：基于命题逻辑公式之间相似度的概念,在经典命题逻辑系统中提出了两种近似推理模式,得到了它们的一些基本性质。讨论了这两种推理模式与经典推理模式之间的关系。此外,当理论Γ有限时,本文分别给出Γ在α程度上近似推出公式A和理论Σ的充要条件。最后,我们给出公式A与有限理论Γ的结论集D(Γ)之间距离的计算公式。In this paper,based on the concept of similarity degree between propositional logic formulas,two kinds of entailments in classical propositional logic system are proposed and some basic properties of these entailments are studied. The relationships between these entailments and classical approximate reasoning models are discussed.Moreover,we obtain the sufficient and necessary conditions that the theory Γ can conclude the formula A or the theory Σ with the degree α.In the end,the method of computing the distance between a formula and the conclusion set of a finite theory is obtained.

关 键 词：命题逻辑 近似推理 强近似推理 

分 类 号：O141[理学—数学]