Bi-Heyting algebras, toposes and modalities

Journal of Philosophical Logic 25 (1):25 - 43 (1996)
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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    David DeVidi & Graham Solomon (1997). In Intuitionistic Modal Logic. Australasian Journal of Philosophy 75 (2):201 – 213.
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