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一类Lukasiewicz n+1值逻辑系统中VDF问题的求解理论
Solution to the VDF Problem in the Kind of (n+1)-Valued Lukasiewicz Logic System

罗清君;王国俊;
LUO Qingjun,WANG Guojun

西安财经学院统计学院,陕西师范大学数学研究所 西安,陕西,710062,西安交通大学基础科学研究中心,陕西师范大学数学研究所,西安,陕西,710062,,西安,陕西,710061 310027,西安,陕西,710049
(School of Statistics, Xi'an Institute of Finance and Economics, Xi'an, Shaanxi, 710061, P. R. China; Research Center for Science, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, P. R. China;Institute of Mathematics, Shaanxi Normal Uniersity, Xi'an, Sh

收稿日期: 2007-04-25
出版日期: 2007-04-25

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摘要 为在经典逻辑学中建立Fuzzy分离规则的推理模式,由赋值决定公式问题(简称VDF问题)已经提出,并已在二值命题逻辑L和p+1(p为素数)值Lukasiewicz命题逻辑中得到了解决,但是对一般的n+1(n>3且n不是素数)值Lukasiewicz命题逻辑系统Ln+1,VDF问题相当复杂且尚未解决.本文尝试在一类特殊的n+1值Lukasiewicz命题逻辑系统Ln+1,即Ln+1的赋值域Wn+1的所有子代数在包含序下构成一个链中建立VDF问题的求解理论,并完满地解决了这类n+1值Lukasiewicz命题逻辑系统Ln+1中的VDF问题.
关键词 FMP规则Lukasiewicz逻辑系统赋值决定公式    
Abstract:The valuationally decided formula question(briefly, VDF question)has been proposed and solved in classical 2-valued prepositional logic and Lukasiewicz (p+1)-valued propostional logic, which are non-fuzzy versions of fuzzy modus ponens in classical logic. The VDF question is complicated and unsolved in (n+1)-valued Lukasiewicz logic system for n>3, where n is not prime. This paper intents to bulid theory for solution to the VDF question in (n+1)-valued Lukasiewicz logic system, where it's subalgebras compose a chain, and solves the VDF question in this kind of (n+1)-valued Lukasiewicz logic system.
Key words Lukasiewicz logic system    valuationally decided formula question
[1] 宋玉靖. Lukasiewicz p+1值逻辑系统中VDF问题的解决[J]. 数学进展, 2004, 33(5): 607-614.
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