命题逻辑推理问题的代数化求解  

Algebraic Method for Solving Propositional Logic Reasoning Problems

作　　者：黄伟亮[1] 黄勇[2] 丁汀[1] 

机构地区：[1]河南机电职业学院信息工程系,河南郑州450002 [2]广州大学计算机科学与教育软件学院,广东广州510006

出　　处：《河南科技大学学报（自然科学版）》2010年第6期86-89,共4页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(60971093)

摘　　要：数理逻辑对命题逻辑推理问题的处理采用的是公理化的形式演绎推理体系,该方法虽严密、可靠,但它对人的知识水平以及形式化、抽象化能力要求较高。因此,本文用初等代数方式把命题逻辑的演绎推理转化为方程组的计算求解,通过求解方程实现命题逻辑的演绎推理。首先用方程组表示命题逻辑推理中的前提,然后利用数学软件求解,最后把结果转化为要推导的结论,进而实现了命题逻辑推理的代数化求解。实例表明:在计算机技术的支持下,该方法是可靠、有效的。In the fields of mathematical logic,the solution to dealing with propositional logic is to use axiomatic deductive system.The method is rigorous,reliable,but it needs higher abstract ability.Therefore,in the paper,a general algebraic way was used to convert formal propositional logic reasoning into the numerical calculation of algebraic equations.Firstly,the premise of proposition logic reasoning was expressed in algebraic equations.Secondly,the solution was obtained by mathematical software.Finally,the solution was converted to the conclusion of the proposition logic.So algebra of proposition logic was realized through solving the equations.Examples show that the method is reliable and effective in the support of computer technology.

关 键 词：命题逻辑 推理 逻辑联接词 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]