基于MV代数语义的格值逻辑的程度化方法  

Graded Method of Lattice-Valued Logic Based on MV-Algebra 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450043

出　　处：《电子学报》2013年第10期2035-2040,共6页Acta Electronica Sinica

基　　金：河南省自然科学基金(No.112300410040);河南省教育厅自然科学基金(No.2011A110012;No.13A110719);河南省高等学校青年骨干教师资助计划(No.2011GGJS-097)

摘　　要：基于MV代数(Many-Valued algebra)语义,通过在MV代数赋值格和全体命题集上分别建立概率测度,利用积分方法提出了一种格值逻辑上命题的概率真度.由此可诱导出命题集上的伪距离,进而在格值逻辑上建立了概率逻辑度量空间并展开程度化推理.本文将计量逻辑学中近似推理方法推广到格值逻辑上,为格值逻辑的程度化提供了一种可行的方法.Based on the notion of MV-algebra semantics,probability measure is set up in MV-algebra evaluation lattice and set of all propositions, and a probability la＇uth degree of propositions in lattice-valued logic is proposed with integral. Thus pseudo- metric in set of all propositions is induced, probability logic metric space is established in lattice-valued logic, and graded reasoning is developed.In summary ,approximate reasoning metlxxi in quantitative logic is expanded to lattice-valued logic,and it is feasible in graded in lattice-valued logic.

关 键 词：MV代数 格值逻辑 概率真度 概率逻辑度量空间 近似推理 

分 类 号：O141.1[理学—数学] O189.2[理学—基础数学]