The Modal Logic of Stone Spaces: Diamond as Derivative

Review of Symbolic Logic 3 (1):26-40 (2010)
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Abstract

We show that if we interpret modal diamond as the derived set operator of a topological space, then the modal logic of Stone spaces isK4and the modal logic of weakly scattered Stone spaces isK4G. As a corollary, we obtain thatK4is also the modal logic of compact Hausdorff spaces andK4Gis the modal logic of weakly scattered compact Hausdorff spaces.

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References found in this work

Modal logic.Alexander Chagrov - 1997 - New York: Oxford University Press. Edited by Michael Zakharyaschev.
Modal Logic.Yde Venema, Alexander Chagrov & Michael Zakharyaschev - 2000 - Philosophical Review 109 (2):286.
Intuitionistic logic and modality via topology.Leo Esakia - 2004 - Annals of Pure and Applied Logic 127 (1-3):155-170.

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