模糊模态逻辑系统M?uk中的可达广义重言式

J4 ›› 2009, Vol. 44 ›› Issue (8): 80-85.

模糊模态逻辑系统M?uk中的可达广义重言式

陕西师范大学数学与信息科学学院, 陕西西安 710062

收稿日期:2009-03-02 出版日期:2009-08-16 发布日期:2009-11-08
通讯作者: 王国俊(1935-),男,教授,博士生导师,研究方向为非经典数理逻辑,不确定性推理. Email:gjwang@snnu.edu.cn E-mail:gjwang@snnu.edu.cn
作者简介:邹尚田(1981-),男,硕士研究生,研究方向为非经典数理逻辑,不确定性推理.Email:shangtian@snnu.edu.cn
基金资助:
国家自然科学基金资助项目(10771129)

Exact generalized tautologies in fuzzy modal logic system M?uk

College of Mathematics and Information Science, Shaanxi Normal University, Xi' an 710062, Shaanxi, China

Received:2009-03-02 Online:2009-08-16 Published:2009-11-08

摘要/Abstract

摘要：

将赋值格取为单位区间并将二元关系R模糊化,研究了模糊模态逻辑系统M?uk,然后将其赋值格离散化研究了多值模态逻辑系统M?n;证明了在M?n中,对任一可能的赋值α 都存在可达α重言式;在M?uk中对任一有理数α∈［0,1］都存在可达α重言式;指出了在R₀系统中起关键作用的升级算法对M?n系统已不再适用,并分析了其原因。

关键词: ?uk;可达广义重言式;可达广义矛盾式; 类类不空定理')">模糊模态逻辑;模糊模态逻辑系统M?uk;可达广义重言式;可达广义矛盾式; 类类不空定理

Abstract:

The fuzzy modal logic system M?uk is introduced, where the evaluation lattice is taken to be the unite interval and the binary relation R is fuzzif ied, then it is discretized to be the multi-valued fuzzy modal logic system M? n. It is proved that for any possible value α in M?n there exists an exact α-tautology; and in M?uk, for any rational α∈［0,1］, there exists an exac t α-tautology. It is pointed out that the lift-algorithm which plays a key role in R₀systems is not suitable for the system M?n, and the reasons are analyzed.

邹尚田王国俊. 模糊模态逻辑系统M?uk中的可达广义重言式[J]. J4, 2009, 44(8): 80-85.

JU Chang-Tian, WANG Guo-Dun. Exact generalized tautologies in fuzzy modal logic system M?uk[J]. J4, 2009, 44(8): 80-85.

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