Studia Logica

, Volume 65, Issue 3, pp 383–416 | Cite as

On an Intuitionistic Modal Logic

  • G. M. Bierman
  • V. C. V. de Paiva


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.

intuitionistic logic modal logic proof theory categorical models 


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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • G. M. Bierman
    • 1
  • V. C. V. de Paiva
    • 2
  1. 1.Computer LaboratoryUniversity of CambridgeCambridgeEngland
  2. 2.School of Computer ScienceUniversity of BirminghamEngland

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