License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CALCO.2017.9
URN: urn:nbn:de:0030-drops-80425
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8042/
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Dahlqvist, Fredrik ; Kurz, Alexander

The Positivication of Coalgebraic Logics

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LIPIcs-CALCO-2017-9.pdf (0.6 MB)

Abstract

We present positive coalgebraic logic in full generality, and show how to obtain a positive coalgebraic logic from a boolean one. On the model side this involves canonically computing a endofunctor T': Pos->Pos from an endofunctor T: Set->Set, in a procedure previously defined by the second author et alii called posetification. On the syntax side, it involves canonically computing a syntax-building functor L': DL->DL from a syntax-building functor L: BA->BA, in a dual procedure which we call positivication. These operations are interesting in their own right and we explicitly compute posetifications and positivications in the case of several modal logics. We show how the semantics of a boolean coalgebraic logic can be canonically lifted to define a semantics for its positive fragment, and that weak completeness transfers from the boolean case to the positive case.

BibTeX - Entry

@InProceedings{dahlqvist_et_al:LIPIcs:2017:8042,
  author =	{Fredrik Dahlqvist and Alexander Kurz},
  title =	{{The Positivication of Coalgebraic Logics}},
  booktitle =	{7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)},
  pages =	{9:1--9:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-033-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{72},
  editor =	{Filippo Bonchi and Barbara K{\"o}nig},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8042},
  URN =		{urn:nbn:de:0030-drops-80425},
  doi =		{10.4230/LIPIcs.CALCO.2017.9},
  annote =	{Keywords: Coalgebraic logic, coalgebras, enriched category theory, boolean algebra, distributive lattice, positive modal logic, monotone modal logic}
}

Keywords: Coalgebraic logic, coalgebras, enriched category theory, boolean algebra, distributive lattice, positive modal logic, monotone modal logic
Collection: 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)
Issue Date: 2017
Date of publication: 17.11.2017

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