命题逻辑中概率真度的相似度及伪距离  

SIMILARITY DEGREE AND PSEUDO-DISTANCE OF THE PROBABILITY TRUTH DEGREE FOR FORMULAE IN THE PROPOSITIONAL LOGIC SYSTEM

作　　者：于西昌[1] 胡凯[2,3] 张兴芳[3] 

机构地区：[1]聊城职业技术学院,山东252000 [2]北京师范大学数学科学学院,北京100875 [3]聊城大学数学科学学院,山东252059

出　　处：《系统科学与数学》2009年第12期1559-1570,共12页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(60875034);山东省自然科学基金(Y2003A01)资助课题

摘　　要：通过引入赋值密度函数、边缘密度函数等概念,给出了连续值命题逻辑系统中公式概率真度的定义,研究了概率真度的推理规则并证明了全体公式的概率真度之集在[0,1]中的稠密性,在此基础上给出了3种相似度,讨论了其性质及关系,并由此定义了3种伪距离,确定了三者之间的比例关系,为推理程度的数值化提供了依据。By introducing the concepts of valuation density function and edge density function, a definition of probability truth degree for formula in the continuous value propositional logic is proposed,studies some inference rules of probability truth degree and proves the density of probability truth degree in. On this groundwork, three similarities are given which discusses the properties of the relationship. By introducing similarity degree, the definition of pseudo-distance is proposed, and determines the relationship between them. Thus the basis for the inference degree＇s numerical is proved.

关 键 词：赋值密度函数 概率真度 推理规则 相似度 伪距离 

分 类 号：O141.1[理学—数学] TP18[理学—基础数学]