| 摘要: |
| 中介逻辑是朱梧槚先生提出的一个3-值逻辑.给出了一个命题中介逻辑,其中引入中介连接词~、反对连接词◁以及蕴涵连接词→,并且定义否定连接词.给出了一个Gentzen-型的推导系统,使得该系统关于中介逻辑的3-值语义是可靠的和完备的. |
| 关键词: 中介逻辑 矛盾关系 反对关系 可靠性 完备性 |
| DOI：10.13328/j.cnki.jos.004791 |
| 分类号: |
| 基金项目:国家重点基础研究发展计划(973)(2005CB321901); 软件开发环境国家重点实验室开放课题(SKLSDE-2010KF-06) |
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| Sound and Complete Gentzen Deduction System for Intermediate Propositional Logic |
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ZHU Wu-Jia1, LI Wei2, SUI Yue-Fei3, LUO Jie2
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1.Department of Computer Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;2.State Key Laboratory of Software Development Environment Beijing University of Aeronautics and Astronautics, Beijing 100191, China;3.Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, The Chinese Academy of Sciences, Beijing 100190, China
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| Abstract: |
| The intermediate logic is a three-valued logic proposed by Zhu Wu-Jia. A propositional intermediate logic is proposed in this paper where the intermediate unary connective ~ and the contrary connective ◁ are introduced, and the negative connective ¬ is defined in terms of the unique binary connective →. A Gentzen-typed deduction system is given such that the system is sound and complete with the three-valued semantics of the propositional intermediate logic. |
| Key words: intermediate logic contradictory contrary soundness completeness |
