Strong completeness of coalgebraic modal logics

Lutz Schröder, Dirk Pattinson

In: Susanne Albers , Jean-Yves Marion (Hrsg.). International Symposium on Theoretical Aspects of Computer Science. International Symposium on Theoretical Aspects of Computer Science (STACS-09) February 26-28 Freiburg Germany Seiten 673-684 Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik; Dagstuhl, Germany 2009.


Canonical models are of central importance in modal logic, in particular as they witness strong completeness and hence compactness. While the canonical model construction is well understood for Kripke semantics, non-normal modal logics often present subtle difficulties - up to the point that canonical models may fail to exist, as is the case e.g. in most probabilistic logics. Here, we present a generic canonical model construction in the semantic framework of coalgebraic modal logic, which pinpoints coherence conditions between syntax and semantics of modal logics that guarantee strong completeness. We apply this method to reconstruct canonical model theorems that are either known or folklore, and moreover instantiate our method to obtain new strong completeness results. In particular, we prove strong completeness of graded modal logic with finite multiplicities, and of the modal logic of exact probabilities.


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Deutsches Forschungszentrum für Künstliche Intelligenz
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