Covering Semantics of Modal Logic S4 and its Completeness

doi:10.3969/j.issn.0372-2112.2012.04.020

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ACTA ELECTRONICA SINICA ›› 2012, Vol. 40 ›› Issue (4) : 745-750. DOI: 10.3969/j.issn.0372-2112.2012.04.020

学术论文

Covering Semantics of Modal Logic S4 and its Completeness

YU Hai¹, ZHAN Wan-rong¹, ZHANG Rui-ling²

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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.

Key words

modal logic / covering semsntics / Kripke semantics / topological semantics / completeness

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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. https://doi.org/10.3969/j.issn.0372-2112.2012.04.020