Covering Semantics of Modal Logic S4 and its Completeness

YU Hai; ZHAN Wan-rong; ZHANG Rui-ling

doi:10.3969/j.issn.0372-2112.2012.04.020

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Covering Semantics of Modal Logic S4 and its Completeness

更新时间：2025-07-16

- Covering Semantics of Modal Logic S4 and its Completeness
- Acta Electronica Sinica Vol. 40, Issue 4, Pages: 745-750(2012)
- 作者机构：
  
  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
  3. 洛阳师范学院数学科学学院河南洛阳,471022
  4. 洛阳师范学院信息技术学院河南洛阳,471022
- 作者简介：
- 基金信息：
- DOI：10.3969/j.issn.0372-2112.2012.04.020
  CLC： O142TP301
- Published：2012
- 稿件说明：
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YU Hai, ZHAN Wan-rong, ZHANG Rui-ling. Covering Semantics of Modal Logic S4 and its Completeness[J]. Acta Electronica Sinica, 2012, 40(4): 745-750.
DOI：

YU Hai, ZHAN Wan-rong, ZHANG Rui-ling. Covering Semantics of Modal Logic S4 and its Completeness[J]. Acta Electronica Sinica, 2012, 40(4): 745-750. DOI： 10.3969/j.issn.0372-2112.2012.04.020.

摘要

基于第六种覆盖粗糙集模型提出了模态逻辑

4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.

Abstract

Based on the sixth type of covering-based rough set model

covering semantics of modal logic

4 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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