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Publication type: Article in Proceedings
Author: Lutz Schröder, Dirk Pattinson
Editor: Susanne Albers, Jean-Yves Marion
Title: Strong completeness of coalgebraic modal logics
Book / Collection title: 26th International Symposium on Theoretical Aspects of Computer Science (STACS 2009)
Page(s): 673 – 684
Series: Leibniz International Proceedings in Informatics
Year published: 2009
Publisher: Schloss Dagstuhl - Leibniz-Center of Informatics, Dagstuhl, Germany
Abstract: 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.
Internet: http://drops.dagstuhl.de/opus/volltexte/2009/1855
Status: Reviewed
Last updated: 24. 11. 2009

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