A judgmental reconstruction of modal logic

  • Authors:
  • Frank Pfenning;Rowan Davies

  • Affiliations:
  • Department of Computer Science, Carnegie Mellon University, Pittsburgh PA 15213-3891, USA;Department of Computer Science, Carnegie Mellon University, Pittsburgh PA 15213-3891, USA

  • Venue:
  • Mathematical Structures in Computer Science
  • Year:
  • 2001

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Abstract

We reconsider the foundations of modal logic, following Martin-Löf's methodology of distinguishing judgments from propositions. We give constructive meaning explanations for necessity and possibility, which yields a simple and uniform system of natural deduction for intuitionistic modal logic that does not exhibit anomalies found in other proposals. We also give a new presentation of lax logic and find that the lax modality is already expressible using possibility and necessity. Through a computational interpretation of proofs in modal logic we further obtain a new formulation of Moggi's monadic metalanguage.