| 格值模态命题逻辑及其完备性 |
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| 引用本文： | 王国俊,时慧娴.格值模态命题逻辑及其完备性[J].中国科学：信息科学,2011(1). |
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| 作者姓名： | 王国俊 时慧娴 |
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| 作者单位： | 陕西师范大学数学研究所; |
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| 基金项目： | 国家自然科学基金(批准号:10771129)资助项目 |
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| 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.
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| 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 |
Lattice-valued modal propositional logic and its completeness |
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| Abstract: | 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 and0,1]-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 propo... |
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| Keywords: | latticed-valued modal propositional logic modal model QMR0-algebra validity completeness |
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