Dual-context calculi for modal logic

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  • G. A. Kavvos

We present natural deduction systems and associated modal lambda calculi for the necessity fragments of the normal modal logics K, T, K4, GL and S4. These systems are in the dual-context style: they feature two distinct zones of assumptions, one of which can be thought as modal, and the other as intuitionistic. We show that these calculi have their roots in in sequent calculi. We then investigate their metatheory, equip them with a confluent and strongly normalizing notion of reduction, and show that they coincide with the usual Hilbert systems up to provability. Finally, we investigate a categorical semantics which interprets the modality as a product-preserving functor.

Original languageEnglish
JournalLogical Methods in Computer Science
Volume16
Issue3
Pages (from-to)10:1-10:66
ISSN1860-5974
DOIs
Publication statusPublished - Jan 2020

    Research areas

  • Categorical semantics, Comonads, Curry Howard correspondence, Dual context, Modal logic, Modal type theory, Modality, Natural deduction, Product-preserving functor, Proof theory

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