Bi-Heyting algebras, toposes and modalities

Journal of Philosophical Logic 25 (1):25 - 43 (1996)
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Abstract

The aim of this paper is to introduce a new approach to the modal operators of necessity and possibility. This approach is based on the existence of two negations in certain lattices that we call bi-Heyting algebras. Modal operators are obtained by iterating certain combinations of these negations and going to the limit. Examples of these operators are given by means of graphs

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Citations of this work

On an Intuitionistic Logic for Pragmatics.Gianluigi Bellin, Massimiliano Carrara & Daniele Chiffi - 2018 - Journal of Logic and Computation 50 (28):935–966..
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Category theory.Jean-Pierre Marquis - 2008 - Stanford Encyclopedia of Philosophy.

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References found in this work

A topos-theoretic approach to reference and modality.Gonzalo E. Reyes - 1991 - Notre Dame Journal of Formal Logic 32 (3):359-391.
Doctrines in categorical logic.Anders Kock & Gonzalo E. Reyes - 1977 - In Jon Barwise (ed.), Handbook of mathematical logic. New York: North-Holland. pp. 90.

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