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Publication type: Article in Proceedings
Author: Lutz Schröder, Dirk Pattinson
Editor: Wolfgang Thomas, Pascal Weil
Title: Rank-1 Modal Logics are Coalgebraic
Book / Collection title: International Symposium on Theoretical Aspects of Computer Science (STACS 07)
Volume: 4393
Page(s): 573 – 585
Series: Lecture Notes in Computer Science
Year published: 2007
Publisher: Springer
Abstract: 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.

Internet: http://dx.doi.org/10.1007/978-3-540-70918-3_49
PDF Version: http://www.informatik.uni-bremen.de/~lschrode/papers/rank1coalg.pdf
Keywords: semantics deduction decidability complexity modal logic coalgebra
Note / Comment: Extended version available
Status: Reviewed
Last updated: 20. 02. 2009

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