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Publication type: Article in Proceedings
Author: Lutz Schröder
Editor: Vladimiro Sassone
Title: Expressivity of Coalgebraic Modal Logic: The Limits and Beyond
Book / Collection title: Foundations of Software Science And Computation Structures
Volume: 3441
Page(s): 440 – 454
Series: Lecture Notes in Computer Science
Year published: 2005
Publisher: Springer, Berlin
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://www.springerlink.com/openurl.asp?genre=article&issn=0302-9743&volume=3441&spage=440
PDF Version: http://www.informatik.uni-bremen.de/~lschrode/papers/coalgml.pdf
PostScript Version: http://www.informatik.uni-bremen.de/~lschrode/papers/coalgml.ps
Keywords: coalgebra expressivity modal logic predicate lifting natural relation
Status: Reviewed
Last updated: 03. 04. 2006

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