摘要
本文对所有正则蕴涵算子对应的逻辑系统类MTL进行语义研究,指出在MTL中可以建立连续赋值格时的公式积分真度理论,但却不能在这一类逻辑系统的全体公式集上建立由公式间的积分相似度决定的伪度量空间.但凡可以建立如此伪度量空间的逻辑系统,都有个共同的性质,即系统中所有的逻辑运算都是连续的,从而就为在此类逻辑系统中建立统一形式的近似推理提供了可行的框架.
The semantic properties of logic systems MTL induced by regular implication operators were disscussed,the integral truth degree theory of formulas on[0,1] can be founded in MTL.However,the logic pseudo-metric space defined by the integral similarity degree between formulas cannot always be constructed.Moreover,those logic systems which could construct such pseudo-metric spaces have the same properties,i.e.all the logic operators are continuous in terms of pseudo-metric,then a possible framework about approximate reasoning is formed in those logic systems.
出处
《电子学报》
EI
CAS
CSCD
北大核心
2010年第3期497-502,共6页
Acta Electronica Sinica
基金
国家自然科学基金资助项目(No.10771129)
关键词
正则蕴含算子
可测的
积分真度
逻辑伪度量空间
算子的连续性
regular implication operator
measurable
integral truth degree
logic pseudo-metric space
continuity of operator
