Dual-Context Calculi for Modal Logic

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 int...

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Bibliographic Details
Published in:Logical methods in computer science 2020-01, Vol.16, Issue 3
Main Author: G. A. Kavvos
Format: Article
Language:English
Subjects:
computer science - logic in computer science
f.4.1
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Summary: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.
ISSN:1860-5974
DOI:10.23638/LMCS-16(3:10)2020