Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Bezhanishvili, Nick; de Groot, Jim; Venema, Yde https://www.dagstuhl.de/lipics License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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URN: urn:nbn:de:0030-drops-114354
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Coalgebraic Geometric Logic

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Abstract

Using the theory of coalgebra, we introduce a uniform framework for adding modalities to the language of propositional geometric logic. Models for this logic are based on coalgebras for an endofunctor T on some full subcategory of the category Top of topological spaces and continuous functions. We compare the notions of modal equivalence, behavioural equivalence and bisimulation on the resulting class of models, and we provide a final object for the corresponding category. Furthermore, we specify a method of lifting an endofunctor on Set, accompanied by a collection of predicate liftings, to an endofunctor on the category of topological spaces.

BibTeX - Entry

@InProceedings{bezhanishvili_et_al:LIPIcs:2019:11435,
  author =	{Nick Bezhanishvili and Jim de Groot and Yde Venema},
  title =	{{Coalgebraic Geometric Logic}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-120-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{139},
  editor =	{Markus Roggenbach and Ana Sokolova},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11435},
  URN =		{urn:nbn:de:0030-drops-114354},
  doi =		{10.4230/LIPIcs.CALCO.2019.7},
  annote =	{Keywords: Coalgebra, Geometric Logic, Modal Logic, Topology}
}

Keywords: Coalgebra, Geometric Logic, Modal Logic, Topology
Seminar: 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)
Issue date: 2019
Date of publication: 25.11.2019


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