| 模态逻辑S4的覆盖语义及其完备性 |
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| 引用本文： | 于海,詹婉荣,张瑞玲.模态逻辑S4的覆盖语义及其完备性[J].电子学报,2012,40(4):745-750. |
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| 作者姓名： | 于海 詹婉荣 张瑞玲 |
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| 作者单位： | 1. 洛阳师范学院数学科学学院,河南洛阳,471022
2. 洛阳师范学院信息技术学院,河南洛阳,471022 |
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| 基金项目： | 国家自然科学基金，河南省基础与前沿研究计划 |
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| 摘 要： | 基于第六种覆盖粗糙集模型提出了模态逻辑S4的覆盖语义,利用覆盖模型与Kripke模型之间的关系,证明了覆盖语义的可靠性和完备性定理.进一步讨论了覆盖语义与Alexandrov拓扑语义之间的关系.证明了覆盖语义与Alexandrov拓扑语义是和谐一致的.
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| 关 键 词： | 模态逻辑 覆盖语义 Kripke语义 拓扑语义 完备性 |
| 收稿时间： | 2011-05-04 |
Covering Semantics of Modal Logic S4 and its Completeness |
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| YU Hai
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ZHAN Wan-rong
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ZHANG Rui-ling.Covering Semantics of Modal Logic S4 and its Completeness[J].Acta Electronica Sinica,2012,40(4):745-750. |
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| Authors: | YU Hai ZHAN Wan-rong ZHANG Rui-ling |
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| Affiliation: | 1.Academy of Mathematics and Science,Luoyang Normal College,Luoyang,Henan 471022,China;2.Academy of Information Technology,Luoyang Normal College,Luoyang,Henan 471022,China) |
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| Abstract: | Based on the sixth type of covering-based rough set model,covering semantics of modal logic S4 is proposed.The reliability and completeness theorems with respect to covering semantics are proved by means of the relationships between covering model and Kripke model.Moreover,the relationships between covering semantics and Alexandrov topological semantics are also discussed.It is proved that covering semantics and Alexandrov topological semantics are harmonious and consistent. |
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| Keywords: | modal logic covering semsntics Kripke semantics topological semantics completeness |
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