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Some Results on Modal Axiomatization and Definability for Topological Spaces

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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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Authors and Affiliations

  1. Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, 88003-8001, USA

    Guram Bezhanishvili

  2. A. Razmadze Mathematical Institute, Georgian Academy of Sciences, M. Aleksidze Str. 1, Tbilisi, 0193, Georgia

    Leo Esakia

  3. Department of Computer Science, King's College London, 26-29 Drury Lane, London, WC2B 5RL, UK

    David Gabelaia

Authors
  1. Guram Bezhanishvili
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  2. Leo Esakia
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  3. David Gabelaia
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Correspondence to Guram Bezhanishvili.

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Mathematics Subject Classifications (2000): 03B45, 54G99.

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Bezhanishvili, G., Esakia, L. & Gabelaia, D. Some Results on Modal Axiomatization and Definability for Topological Spaces. Stud Logica 81, 325–355 (2005). https://doi.org/10.1007/s11225-005-4648-6

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  • DOI: https://doi.org/10.1007/s11225-005-4648-6

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