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A judgmental reconstruction of modal logic

Published online by Cambridge University Press:  25 July 2001

FRANK PFENNING
Affiliation:
Department of Computer Science, Carnegie Mellon University, Pittsburgh PA 15213-3891, USA
ROWAN DAVIES
Affiliation:
Department of Computer Science, Carnegie Mellon University, Pittsburgh PA 15213-3891, USA

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.

Type
Research Article
Copyright
2001 Cambridge University Press

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