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An expressive completeness theorem for coalgebraic modal mu-calculi
Stockholm University, Faculty of Humanities, Department of Philosophy. University of Amsterdam, The Netherlands.
Number of Authors: 32017 (English)In: Logical Methods in Computer Science, ISSN 1860-5974, E-ISSN 1860-5974, Vol. 13, no 2, article id 14Article in journal (Refereed) Published
Abstract [en]

Generalizing standard monadic second-order logic for Kripke models, we introduce monadic second-order logic interpreted over coalgebras for an arbitrary set functor. We then consider invariance under behavioral equivalence of MSO-formulas. More specifically, we investigate whether the coalgebraic mu-calculus is the bisimulation-invariant fragment of the monadic second-order language for a given functor. Using automata theoretic techniques and building on recent results by the third author, we show that in order to provide such a characterization result it suffices to find what we call an adequate uniform construction for the coalgebraic type functor. As direct applications of this result we obtain a partly new proof of the Janin-Walukiewicz Theorem for the modal mu-calculus, avoiding the use of syntactic normal forms, and bisimulation invariance results for the bag functor (graded modal logic) and all exponential polynomial functors (including the game functor). As a more involved application, involving additional non-trivial ideas, we also derive a characterization theorem for the monotone modal mu-calculus, with respect to a natural monadic second-order language for monotone neighborhood models.

Place, publisher, year, edition, pages
2017. Vol. 13, no 2, article id 14
National Category
Philosophy Language Technology (Computational Linguistics)
Identifiers
URN: urn:nbn:se:su:diva-152686DOI: 10.23638/LMCS-13(2:14)2017ISI: 000419160800016OAI: oai:DiVA.org:su-152686DiVA, id: diva2:1185215
Available from: 2018-02-23 Created: 2018-02-23 Last updated: 2018-02-23Bibliographically approved

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