摘要
为了在n值命题逻辑系统中建立一种程度化推理机制,并为其提供一个可能的近似推理框架,利用势为n的均匀概率空间的无穷乘积,在n值G?del命题逻辑系统中引入命题的α-真度概念.证明了一般真度推理规则,给出了判定α-重言式的充分必要条件,并利用命题的α-真度定义了命题间的α-相似度,进而导出命题集上的一种伪距离,使得在n值命题逻辑系统中展开近似推理成为可能.提出的程度化推理方法为近似推理的算法实现奠定了基础,并对知识推理的程度化有所启示.
In order to establish a graded reasoning mechanism and provide a possible framework for approximate reasoning in n-valued propositional logic, this paper introduces the concept of α-truth degrees of propositions in n-valued Godel logical system by using the infinite product of uniformly distributed probability spaces of cardinal n It is proved that the general inference rules with truth degrees hold, and a sufficient and necessary condition to judge α-tautology is obtained. Moreover, an intrinsic pseudo-metric on the set of propositions is defined by means of the similarity degree between propositions, which makes it possible to develop approximate reasoning in n-valued propositional logic. The graded method proposed in this paper lays a foundation for the algorithmic realization of approximate reasoning and serves as a guideline for the graded reasoning about knowledge.
出处
《软件学报》
EI
CSCD
北大核心
2007年第1期33-39,共7页
Journal of Software
基金
国家自然科学基金
陕西师范大学博士创新基金
兰州理工大学优秀青年基金~~
关键词
α-真度
真度
α-相似度
伪距离
α-truth degree
truth degree
α-similarity degree
pseudo-metric
作者简介
李骏（1972-），男，甘肃白银人，博士生，副教授，主要研究领域为非经典数理逻辑，不确定性推理．Corresponding author：Phn： ＋86-29-85314523, E-mail：lijun@stu.snnu.edu.cn
王国俊（1935-），男，教授，博士生导师，CCF高级会员，主要研究领域为不确定性推理，非经典数理逻辑．
