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On an Intuitionistic Modal Logic
 Studia Logica
, 2001
"... . 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 IS4our formulation has several important metatheoretic properties. In addition, we study models ..."
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Cited by 19 (4 self)
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. 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 IS4our formulation has several important metatheoretic properties. In addition, we study models of IS4, not in the framework of Kripke 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. 1. Introduction Modal logics are traditionally extensions of classical logic with new operators, or modalities, whose operation is intensional. Modal logics are most commonly justified by the provision of an intuitive semantics based upon `possible worlds', an idea originally due to Kripke. Kripke also provided a possible worlds semantics for intuitionistic logic, and so it is natural to consider intuitionistic logic extended with intensional modalities...
Proof Search in Lax Logic
, 2000
"... This paper describes two new sequent calculi for Lax Logic. One calculus is for proof enumeration for quanti ed Lax Logic, the other calculus is for theorem proving in propositional Lax Logic ..."
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Cited by 4 (0 self)
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This paper describes two new sequent calculi for Lax Logic. One calculus is for proof enumeration for quanti ed Lax Logic, the other calculus is for theorem proving in propositional Lax Logic
Towards a Classical Linear λcalculus
 PROC. OF THE TOKYO CONFERENCE ON LINEAR LOGIC
, 1996
"... This paper considers a typed calculus for classical linear logic. I shall give an explanation of a multipleconclusion formulation for classical logic due to Parigot and compare it to more traditional treatments by Prawitz and others. I shall use Parigot's method to devise a natural deduction formu ..."
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This paper considers a typed calculus for classical linear logic. I shall give an explanation of a multipleconclusion formulation for classical logic due to Parigot and compare it to more traditional treatments by Prawitz and others. I shall use Parigot's method to devise a natural deduction formulation of classical linear logic. I shall also demonstrate a somewhat hidden connexion with the continuationpassing paradigm which gives a new computational interpretation of Parigot's techniques and possibly a new style of continuation programming.