| 一类命题逻辑的一般弱框架择类语义 |
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| 引用本文： | 冯棉.一类命题逻辑的一般弱框架择类语义[J].中山大学学报论丛,2011,4(2). |
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| 作者姓名： | 冯棉 |
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| 作者单位： | 华东师范大学哲学系 |
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| 基金项目： | 教育部人文社会科学重点研究基地重大项目《结构推理及其应用研究》 |
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| 摘 要： | 命题逻辑的一般弱框架择类语义是相干邻域语义的变形,其特点是：采用择类运算来刻画逻辑常项;语义运算与逻辑联结词之间有清晰的对应关系,可以从整体上处理一类逻辑,具有普适性。本文将这种语义用于一类B、C、K、W命题逻辑,包括相干逻辑R及其线性片段、直觉主义逻辑及其BCK片段等,并借助典范框架和典范赋值,证明了这些逻辑系统的可靠性和完全性。
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| 关 键 词： | 结构规则 相干逻辑 线性片段 直觉主义逻辑 BCK片段 一般弱框架择类语义 |
Class-selection Semantics on General Weak Frames for a Class of Propositional Logics |
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| Abstract: | Class-selection semantics on general weak frames of prepositional logics is a transformation of relevant neighborhood semantics.Characteristically,it employs class-selection operations to describe logical constants,and the resulting clear corresponding relations between semantic operations and logical connectives can properly deal with a class of logics as a whole,with general applicability.This paper applies such semantics to a class of propositional logics with B,C,K or W,including relevant logic R and its linear fragment,intuitionistic propositional logic and its BCK fragment,etc.It also proves the soundness and completeness of these logical systems by canonical frame and canonical valuation. |
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