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  • 标题:Uniform Interpolation in Coalgebraic Modal Logic
  • 本地全文:下载
  • 作者:Fatemeh Seifan ; Lutz Schr{\"o}der ; Dirk Pattinson
  • 期刊名称:LIPIcs : Leibniz International Proceedings in Informatics
  • 电子版ISSN:1868-8969
  • 出版年度:2017
  • 卷号:72
  • 页码:21:1-21:16
  • DOI:10.4230/LIPIcs.CALCO.2017.21
  • 出版社:Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
  • 摘要: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.
  • 关键词:modal logic; coalgebraic logic; uniform interpolation; preservation of weak pullbacks
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