Jim de Groot ; Dirk Pattinson - Modal meet-implication logic

lmcs:7026 - Logical Methods in Computer Science, July 14, 2022, Volume 18, Issue 3 - https://doi.org/10.46298/lmcs-18(3:1)2022
Modal meet-implication logic

Authors: Jim de Groot ; Dirk Pattinson

    We extend the meet-implication fragment of propositional intuitionistic logic with a meet-preserving modality. We give semantics based on semilattices and a duality result with a suitable notion of descriptive frame. As a consequence we obtain completeness and identify a common (modal) fragment of a large class of modal intuitionistic logics. We recognise this logic as a dialgebraic logic, and as a consequence obtain expressivity-somewhere-else. Within the dialgebraic framework, we then investigate the extension of the meet-implication fragment of propositional intuitionistic logic with a monotone modality and prove completeness and expressivity-somewhere-else for it.


    Volume: Volume 18, Issue 3
    Published on: July 14, 2022
    Accepted on: April 7, 2022
    Submitted on: December 29, 2020
    Keywords: Mathematics - Logic,Computer Science - Logic in Computer Science

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