MTL代数语义上逻辑公式的概率真度  

Probability Truth Degrees of Formulas in MTL-Algebras Semantics

作　　者：左卫兵[1] 

机构地区：[1]华北水利水电大学数学与信息科学学院,河南郑州450046

出　　处：《电子学报》2015年第2期293-298,共6页Acta Electronica Sinica

基　　金：国家自然科学基金(No.11201145);河南省教育厅自然科学基金(No.13A110719);河南省教育厅人文社会科学研究项目(No.2013-QN-295)

摘　　要：基于L-赋值理论,通过在MTL代数赋值格和全体公式集上分别建立概率测度,利用积分方法提出了MTL代数语义上公式的概率真度.证明了概率真度的MP规则、HS规则及交推理规则;同时引入公式间的概率相似度和伪距离,建立了概率逻辑度量空间.将计量逻辑学中的相关理论推广到基于MTL代数语义的格值逻辑上,使得在格值逻辑上进行程度化推理成为可能.Based on L-evaluation theory and by defining probability measure in MTL-algebra evaluation lattice and set of all formulas respectively,the concept of probability truth degree of formulas in MTL-algebras semantics is introduced by the integral method. The MP rule,HS rule and meet inference rules of probability truth degree are proved. At the meantime,the concept of probability similarity degree and pseudo-distances between formulas are introduced and the probability logic metric space is built. The theory of quantitative logic is expanded to lattice-valued logic based on MTL-algebra semantics,which makes it possible in graded reasoning in lattice-valued logic.

关 键 词：MTL代数 L-赋值 概率真度 概率逻辑度量空间 程度化推理 

分 类 号：O141.1[理学—数学] O189.2[理学—基础数学]