Some Results on Modal Axiomatization and Definability for Topological Spaces

Studia Logica 81 (3):325-355 (2005)
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Abstract

We consider two topological interpretations of the modal diamond—as the closure operator (C-semantics) and as the derived set operator (d-semantics). We call the logics arising from these interpretations C-logics and d-logics, respectively. We axiomatize a number of subclasses of the class of nodec spaces with respect to both semantics, and characterize exactly which of these classes are modally definable. It is demonstrated that the d-semantics is more expressive than the C-semantics. In particular, we show that the d-logics of the six classes of spaces considered in the paper are pairwise distinct, while the C-logics of some of them coincide.

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Citations of this work

Topological completeness of the provability logic GLP.Lev Beklemishev & David Gabelaia - 2013 - Annals of Pure and Applied Logic 164 (12):1201-1223.
Positive provability logic for uniform reflection principles.Lev Beklemishev - 2014 - Annals of Pure and Applied Logic 165 (1):82-105.

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References found in this work

An essay in classical modal logic.Krister Segerberg - 1971 - Uppsala,: Filosofiska föreningen och Filosofiska institutionen vid Uppsala universitet.
Modal logic.Alexander Chagrov - 1997 - New York: Oxford University Press. Edited by Michael Zakharyaschev.
The Algebra of Topology.J. C. C. Mckinsey & Alfred Tarski - 1944 - Annals of Mathematics, Second Series 45:141-191.
Five critical modal systems.L. Esakia & V. Meskhi - 1977 - Theoria 43 (1):52-60.

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