Journal of Philosophical Logic

, Volume 28, Issue 1, pp 47-60

First online:

Interpretations of intuitionist logic in non-normal modal logics

  • Colin OakesAffiliated withDepartment of Philosophy, Marquette University

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Historically, it was the interpretations of intuitionist logic in the modal logic S4 that inspired the standard Kripke semantics for intuitionist logic. The inspiration of this paper is the interpretation of intuitionist logic in the non-normal modal logic S3: an S3 model structure can be 'looked at' as an intuitionist model structure and the semantics for S3 can be 'cashed in' to obtain a non-normal semantics for intuitionist propositional logic. This non-normal semantics is then extended to intuitionist quantificational logic.

logic intuitionist logic modal logic semantics model(s)