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Formal systems for modal operators on locales

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Abstract

In the paper [8], the first author developped a topos- theoretic approach to reference and modality. (See also [5]). This approach leads naturally to modal operators on locales (or ‘spaces without points”). The aim of this paper is to develop the theory of such modal operators in the context of the theory of locales, to axiomatize the propositional modal logics arising in this context and to study completeness and decidability of the resulting systems.

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Authors and Affiliations

  1. Dept. of Mathematics, University of Montreal, Canada

    Gonzalo E. Reyes

  2. Dept. of Mathematics, University of Warsaw, Poland

    Marek W. Zawadowski

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  1. Gonzalo E. Reyes
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  2. Marek W. Zawadowski
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Reyes, G.E., Zawadowski, M.W. Formal systems for modal operators on locales. Stud Logica 52, 595–613 (1993). https://doi.org/10.1007/BF01053262

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  • DOI: https://doi.org/10.1007/BF01053262

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