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Publication type: Article
Author: Lutz Schröder
Title: Expressivity of Coalgebraic Modal Logic: The Limits and Beyond
Volume: 390
Page(s): 230 – 247
Journal: Theoretical Computer Science
Year published: 2008
Abstract: Modal logic has a good claim to being the logic of choice for describing the reactive behaviour of systems modeled as coalgebras. Logics with modal operators obtained from so-called predicate liftings have been shown to be invariant under behavioral equivalence. Expressivity results stating that, conversely, logically indistinguishable states are behaviorally equivalent depend on the existence of separating sets of predicate liftings for the signature functor at hand. Here, we provide a classification result for predicate liftings which leads to an easy criterion for the existence of such separating sets, and we give simple examples of functors that fail to admit expressive normal or monotone modal logics, respectively, or in fact an expressive (unary) modal logic at all. We then move on to polyadic modal logic, where modal operators may take more than one argument formula. We show that every accessible functor admits an expressive polyadic modal logic. Moreover, expressive polyadic modal logics are, unlike unary modal logics, compositional.
Internet: http://dx.doi.org/10.1016/j.tcs.2007.09.023
PDF Version: http://www.informatik.uni-bremen.de/~lschrode/papers/coalgml-ext.pdf
Keywords: coalgebra expressivity modal logic predicate lifting natural relation
Note / Comment: Extends (Schröder 2005)
Status: Reviewed
Last updated: 18. 06. 2008

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