Lukasiewicz三值逻辑中命题的真度值之集在［0,1］上的分布

J4 ›› 2009, Vol. 44 ›› Issue (10): 54-59.

Lukasiewicz三值逻辑中命题的真度值之集在［0,1］上的分布

马丽娜王国俊

陕西师范大学数学与信息科学学院, 陕西西安 710062; 陕西师范大学数学研究所, 陕西西安 710062)

收稿日期:2009-01-17 出版日期:2009-10-16 发布日期:2009-12-07
作者简介:马丽娜(1980)，女，博士研究生，讲师，研究方向为不确定性推理.Email:malina@snnu.edu.cn
基金资助:
国家自然科学基金资助项目(10771129)

Theory of truth degrees in Lukasiewicz three valued propositional logic

MA Li-Na, WANG Guo-Dun

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

Received:2009-01-17 Online:2009-10-16 Published:2009-12-07

摘要/Abstract

摘要：

利用势为三的非均匀概率空间的无穷乘积,在Lukasiewicz三值命题逻辑系统L-3中引入命题的真度概念,给出了真度推理规则,证明了在三值逻辑(a/5,b/5,c/5)测度下全体公式的真度值之集在［0,1］上是稠密的,并给出了公式真度的表达通式,为进一步建立三值命题逻辑系统的近似推理奠定了基础。

关键词: 非均匀概率空间;真度;稠密

Abstract:

Based on the infinite product of unevenly distributed probability space, the theory of truth degrees in Lukasiewicz three valued propositional logicis introduced and inference rules with truth degrees are given. Moreover, it is proved that the set of truth degrees of propositions in the three valued (a/5,b/5,c/5)logic measure isdense in ［0,1］,and expressions of truth degrees are obtained. This paves the way for further study on approximate reasoning.

Key words: uneven probability space; truth degree; dense

中图分类号:

O141.1

马丽娜王国俊. Lukasiewicz三值逻辑中命题的真度值之集在［0,1］上的分布[J]. J4, 2009, 44(10): 54-59.

MA Li-Na, WANG Guo-Dun. Theory of truth degrees in Lukasiewicz three valued propositional logic[J]. J4, 2009, 44(10): 54-59.

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