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Erschienen in:
2007 | OriginalPaper | Buchkapitel
Rank-1 Modal Logics Are Coalgebraic
verfasst von : Lutz Schröder, Dirk Pattinson
Erschienen in: STACS 2007
Verlag: Springer Berlin Heidelberg
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Coalgebras provide a unifying semantic framework for a wide variety of modal logics. It has previously been shown that the class of coalgebras for an endofunctor can always be axiomatised in rank 1. Here we establish the converse, i.e. every rank 1 modal logic has a sound and
strongly
complete coalgebraic semantics. As a consequence, recent results on coalgebraic modal logic, in particular generic decision procedures and upper complexity bounds, become applicable to arbitrary rank 1 modal logics, without regard to their semantic status; we thus obtain purely syntactic versions of these results. As an extended example, we apply our framework to recently defined deontic logics.