Uniform interpolation in coalgebraic modal logic

Fatemeh Seifan, Lutz Schröder, Dirk Pattinson

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    1 Citation (Scopus)


    A logic has uniform interpolation if its formulas can be projected down to given subsignatures, preserving all logical consequences that do not mention the removed symbols; the weaker property of (Craig) interpolation allows the projected formula - the interpolant - to be different for each logical consequence of the original formula. These properties are of importance, e.g., in the modularization of logical theories. We study interpolation in the context of coalgebraic modal logics, i.e. modal logics axiomatized in rank 1, restricting for clarity to the case with finitely many modalities. Examples of such logics include the modal logics K and KD, neighbourhood logic and its monotone variant, finite-monoid-weighted logics, and coalition logic. We introduce a notion of one-step (uniform) interpolation, which refers only to a restricted logic without nesting of modalities, and show that a coalgebraic modal logic has uniform interpolation if it has one-step interpolation. Moreover, we identify preservation of finite surjective weak pullbacks as a sufficient, and in the monotone case necessary, condition for one-step interpolation. We thus prove or reprove uniform interpolation for most of the examples listed above.

    Original languageEnglish
    Title of host publication7th Conference on Algebra and Coalgebra in Computer Science, CALCO 2017
    EditorsBarbara Konig, Filippo Bonchi
    PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
    ISBN (Electronic)9783959770330
    Publication statusPublished - 1 Nov 2017
    Event7th Conference on Algebra and Coalgebra in Computer Science, CALCO 2017 - Ljubljana, Slovenia
    Duration: 14 Jun 201716 Jun 2017

    Publication series

    NameLeibniz International Proceedings in Informatics, LIPIcs
    ISSN (Print)1868-8969


    Conference7th Conference on Algebra and Coalgebra in Computer Science, CALCO 2017


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