Abstract
Towards the study of covering based rough set semantics for modal logic [39], we present a modal system corresponding to the covering systems P3,C1, and CGr. We also study the modal systems for boundary operators based on generalized approximation spaces as well as covering systems. Our study also leads to covering semantics for some contingency logics and provide its connection with rough set theory. Further, an alternative modal system based on the contingency modal operator is provided corresponding to the covering system P4.
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