Formal systems for modal operators on locales

Studia Logica 52 (4):595 - 613 (1993)
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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DOI 10.1007/BF01053262
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The Mathematics of Metamathematics.Helena Rasiowa - 1963 - Warszawa, Państwowe Wydawn. Naukowe.
A Topos-Theoretic Approach to Reference and Modality.Gonzalo E. Reyes - 1991 - Notre Dame Journal of Formal Logic 32 (3):359-391.

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