逻辑系统G_3中命题的D-条件真度与近似推理  

The D-conditional truth degree of formulas and approximate reasoning in the G_3 propositional logic system

作　　者：崔美华[1] 

机构地区：[1]盐城师范学院数学科学学院,江苏盐城224051

出　　处：《山东大学学报（理学版）》2010年第11期52-58,共7页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(10371106);江苏省高校自然科学基础研究项目(08KJD110008)

摘　　要：基于条件概率的思想,利用赋值集的随机化方法,在三值Gdel命题逻辑系统中引入公式的D-条件真度,证明了D-条件真度的MP规则和HS规则。引入公式间的D-条件相似度和D-条件伪距离,建立了D-条件逻辑度量空间,推导出D-条件伪距离的若干性质,证明了D-逻辑度量空间中二元运算"∨","∧","→"关于D-条件伪距离的连续性。在D-条件逻辑度量空间中提出了三种不同类型的近似推理模式并研究了它们之间的关系。Based on conditional probability, using the randomization method of valuation set, the concept of D-condi- tional truth degree of formulas is introduced in the 3-valued G6del propositional logic system. The MP rule and HS rule of D-conditional truth degrees are proved. The concepts of D-conditional similarity and D-conditional pseudo-distances between formulas are introduced and D-conditional logic metric space is built. Several properties of D-conditional pseu- do-distances are deduced and it is proved that the D-conditional pseudo-distances is continuous on the logical operation of ＂∨＂,＂∧＂,＂→＂in D-conditional logic metric spaces. Three different types of approximate reasoning patterns are discussed in D-conditional logic metric space, and the relationships between them are studied.

关 键 词：逻辑系统G D-条件真度 D-条件伪距离 D-条件逻辑度量空间 近似推理 

分 类 号：O141[理学—数学] O159[理学—基础数学]