Strong Completeness of Coalgebraic Modal Logics

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Strong Completeness of Coalgebraic Modal Logics
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. In modal logic, completeness proofs come in two flavours: weak...
Lutz Schröder, Dirk Pattinson
Added 20 May 2010
Updated 20 May 2010
Type Conference
Year 2009
Authors Lutz Schröder, Dirk Pattinson
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