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.Author's Profile
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2004
DOI
10.1023/a:1005291931660
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Citations of this work
Proof-Theoretic Semantics, a Problem with Negation and Prospects for Modality.Nils Kürbis - 2015 - Journal of Philosophical Logic 44 (6):713-727.
Order-Dual Relational Semantics for Non-distributive Propositional Logics: A General Framework.Chrysafis Hartonas - 2018 - Journal of Philosophical Logic 47 (1):67-94.
What is a Relevant Connective?Shawn Standefer - 2022 - Journal of Philosophical Logic 51 (4):919-950.
Order- dual realational semantics for non-distributive propositional logics.Chrysafis Hartonas - 2017 - Logic Journal of the IGPL 25 (2):145-182.
References found in this work
The formulae-as-types notion of construction.William Alvin Howard - 1980 - In Haskell Curry, Hindley B., Seldin J. Roger & P. Jonathan (eds.), To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus, and Formalism. Academic Press.
