谓词逻辑系统MTL■中公式的公理化真度  

Axiomatic truth degrees of formula in MTL■ predicate logic system

作　　者：王波 惠小静[1] 鲁星 WANG Bo;HUI Xiaojing;LU Xing(Mathematics and Computer Science College,Yan′an University,Yan′an 716000,Shaanxi Province,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《浙江大学学报（理学版）》2022年第5期521-526,548,共7页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(11471007,61763045)。

摘　　要：命题逻辑及谓词逻辑计量化是逻辑系统的研究热点之一。在左连续三角模的谓词逻辑系统MTL■中,利用公理化方法提出了MTL■公式的真度,证明了该真度的MP规则、HS规则及交推理规则;同时在谓词逻辑系统MTL■的一阶闭逻辑公式集中引入了相似度和伪距离,证明了关于相似度的一些良好性质,并讨论了逻辑运算关于伪距离的连续性问题。The quantification of propositional logic and predicate logic is a research hotspot. Based on left continuous triangle norm,the concept of truth degree of formulas in MTL■ is introduced by the axiomatic method.The MP rule,HS rule and meet inference rules of this truth degree are proved. Meantime,the concept of similarity degree and pseudodistances of first order closed logic formulas in MTL■ predicate logic system are introduced, some good properties about similarity degree are proved. Furthermore, the continuity problem of logical operators about this pesudo distance is discussed.

关 键 词：谓词逻辑系统MTL■ 公理化真度 相似度 伪距离 

分 类 号：O141.5[理学—数学]