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Named Models in Coalgebraic Hybrid Logic

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Abstract

Hybrid logic extends modal logic with support for reasoning about individual states, designated by so-called nominals. We study hybrid logic in the broad context of coalgebraic semantics, where Kripke frames are replaced with coalgebras for a given functor, thus covering a wide range of reasoning principles including, e.g., probabilistic, graded, default, or coalitional operators. Specifically, we establish generic criteria for a given coalgebraic hybrid logic to admit named canonical models, with ensuing completeness proofs for pure extensions on the one hand, and for an extended hybrid language with local binding on the other. We instantiate our framework with a number of examples. Notably, we prove completeness of graded hybrid logic with local binding.

BibTeX - Entry

@InProceedings{schrder_et_al:LIPIcs:2010:2492,
  author =	{Lutz Schr{\"o}der and Dirk Pattinson},
  title =	{{Named Models in Coalgebraic Hybrid Logic}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{645--656},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Jean-Yves Marion and Thomas Schwentick},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2010/2492},
  URN =		{urn:nbn:de:0030-drops-24920},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2010.2492},
  annote =	{Keywords: Logic in computer science, semantics, deduction, modal logic, coalgebra}
}

Keywords: Logic in computer science, semantics, deduction, modal logic, coalgebra
Seminar: 27th International Symposium on Theoretical Aspects of Computer Science
Issue date: 2010
Date of publication: 2010


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