Publication
Rank-1 Modal Logics are Coalgebraic
Lutz Schröder; Dirk Pattinson
In: Wolfgang Thomas; Pascal Weil (Hrsg.). Theoretical Aspects of Computer Science (STACS 07). International Symposium on Theoretical Aspects of Computer Science (STACS-07), February 22-24, Aachen, Germany, Pages 573-585, Lecture Notes in Computer Science (LNCS), Vol. 4393, ISBN 978-3-540-70917-6, Springer, 2007.
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.