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The Positivication of Coalgebraic Logics Dahlqvist, Fredrik Kurz, Alexander Coalgebraic logic coalgebras enriched category theory boolean algebra distributive lattice positive modal logic monotone modal logic We present positive coalgebraic logic in full generality, and show how to obtain a positive coalgebraic logic from a boolean one. On the model side this involves canonically computing a endofunctor T': Pos->Pos from an endofunctor T: Set->Set, in a procedure previously defined by the second author et alii called posetification. On the syntax side, it involves canonically computing a syntax-building functor L': DL->DL from a syntax-building functor L: BA->BA, in a dual procedure which we call positivication. These operations are interesting in their own right and we explicitly compute posetifications and positivications in the case of several modal logics. We show how the semantics of a boolean coalgebraic logic can be canonically lifted to define a semantics for its positive fragment, and that weak completeness transfers from the boolean case to the positive case. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Fredrik Dahlqvist and Alexander Kurz 2017 Is Part Of LIPIcs, Volume 72, 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CALCO.2017.9 urn:nbn:de:0030-drops-80425 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2017.9 eng https://creativecommons.org/licenses/by/3.0/legalcode