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

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.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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DOI 10.1007/s11225-005-4648-6
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References found in this work BETA

An Essay in Classical Modal Logic.Krister Segerberg - 1971 - Uppsala, Sweden: Uppsala, Filosofiska Föreningen Och Filosofiska Institutionen Vid Uppsala Universitet.
Modal Logic.Alexander Chagrov - 1997 - Oxford, England: Oxford University Press.
The Algebra of Topology.J. C. C. Mckinsey & Alfred Tarski - 1944 - Annals of Mathematics, Second Series 45:141-191.

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Citations of this work BETA

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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