格值模态命题逻辑及其完备性  

Lattice-valued modal propositional logic and its completeness

作　　者：王国俊[1] 时慧娴[1] 

机构地区：[1]陕西师范大学数学研究所,西安710062

出　　处：《中国科学：信息科学》2011年第1期66-76,共11页Scientia Sinica(Informationis)

基　　金：国家自然科学基金(批准号:10771129)资助项目

摘　　要：文中以满足第一及第二无限分配律的完备格为工具,建立了格值模态命题逻辑的语义理论,并指出这种语义是经典模态命题逻辑语义理论及[0,1]值模态命题逻辑语义理论的共同推广.给出了QMR0代数的定义,并分别以Boole代数及QMR0代数为背景构建了Boole型格值模态命题逻辑系统B及QMR0型格值模态命题逻辑系统QML*,并证明了系统B及系统QML*的完备性.Based on the concept of the complete lattice satisfying the first and second infinite distributive laws,the present paper introduces the semantics of the lattice-valued modal propositional logic.It is pointed out that this semantics generalizes the semantics of both classical modal propositional logic and[0,1]-valued modal propositional logic.The definition of the QMR0-algebra is proposed,and both the Boole-typed lattice-valued modal propositional logic system B and the QMR0-typed lattice-valued modal propositional logic system QML＊ are constructed by use of Boole-algebras and QMR0-algebras,respectively.The main results of the paper are the completeness theorems of both the system B and QML＊.

关 键 词：格值模态命题逻辑 模态模型 QMR0代数 有效公式 完备性 

分 类 号：O141[理学—数学]