Nick Bezhanishvili ; Jim de Groot ; Yde Venema - Coalgebraic Geometric Logic: Basic Theory

lmcs:6205 - Logical Methods in Computer Science, December 8, 2022, Volume 18, Issue 4 - https://doi.org/10.46298/LMCS-18(4:10)2022
Coalgebraic Geometric Logic: Basic TheoryArticle

Authors: Nick Bezhanishvili ORCID; Jim de Groot ORCID; Yde Venema

    Using the theory of coalgebra, we introduce a uniform framework for adding modalities to the language of propositional geometric logic. Models for this logic are based on coalgebras for an endofunctor on some full subcategory of the category of topological spaces and continuous functions. We investigate derivation systems, soundness and completeness for such geometric modal logics, and we specify a method of lifting an endofunctor on Set, accompanied by a collection of predicate liftings, to an endofunctor on the category of topological spaces, again accompanied by a collection of (open) predicate liftings. Furthermore, we compare the notions of modal equivalence, behavioural equivalence and bisimulation on the resulting class of models, and we provide a final object for the corresponding category.


    Volume: Volume 18, Issue 4
    Published on: December 8, 2022
    Accepted on: October 26, 2022
    Submitted on: March 18, 2020
    Keywords: Mathematics - Logic

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