| 弱连通传递框架类的命题逻辑 |
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| 引用本文： | 何文堃,马明辉. 弱连通传递框架类的命题逻辑[J]. 逻辑学研究, 2013, 0(4): 17-29 |
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| 作者姓名： | 何文堃 马明辉 |
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| 作者单位： | 西南大学逻辑与智能研究中心 |
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| 基金项目： | 国家社科基金青年项目“模态可定义性理论研究”（12CZX054） |
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| 摘 要： | 在维瑟（Albert Visser）的基本命题逻辑（BPL）基础上增加公理（p→q）∨（（p→q）→p）得到的逻辑LB相对于弱连通传递框架类是完全的。增加达米特（M.Dummett）公理（p→q）∨（q→p）得到的逻辑LD是不完全的。本文还证明LB具有有穷模型性质,但是不具有两常元性质和析取性质。
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| 关 键 词： | 基本命题逻辑 弱连通性 逻辑性质 |
The Propositional Logic of Weakly Connected Transitive Kripke Frames |
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| Wenkun He Center for the study of Logic and Intelligence,Southwest University Minghui Ma. The Propositional Logic of Weakly Connected Transitive Kripke Frames[J]. Studies in Logic, 2013, 0(4): 17-29 |
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| Authors: | Wenkun He Center for the study of Logic Intelligence Southwest University Minghui Ma |
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| Affiliation: | Center for the study of Logic and Intelligence, Southwest University |
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| Abstract: | The logic LB is obtained from Visser＇s basic propositional logic by adding the axiom （p → q） V （（p → q） → p）. This logic is complete with respect to the class of all weakly connected transitive frames. But the logic LD which is obtained from BPL by adding the Dummett formula （p → q） V （q → p） is not complete. The logic LB has finite model property but no two constant property and no disjunction property. |
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