On an intuitionistic modal logic

Studia Logica 65 (3):383-416 (2000)
Abstract
In this paper we consider an intuitionistic variant of the modal logic S4 (which we call IS4). The novelty of this paper is that we place particular importance on the natural deduction formulation of IS4— our formulation has several important metatheoretic properties. In addition, we study models of IS4— not in the framework of Kirpke semantics, but in the more general framework of category theory. This allows not only a more abstract definition of a whole class of models but also a means of modelling proofs as well as provability.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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Reprint years 2004
DOI 10.1023/A:1005291931660
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Proof Theory for Modal Logic.Sara Negri - 2011 - Philosophy Compass 6 (8):523-538.
A Proof-Theoretic Investigation of a Logic of Positions.Stefano Baratella & Andrea Masini - 2003 - Annals of Pure and Applied Logic 123 (1-3):135-162.
A New S4 Classical Modal Logic in Natural Deduction.Maria Da Paz N. Medeiros - 2006 - Journal of Symbolic Logic 71 (3):799 - 809.

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