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.ICALP.2019.116
URN: urn:nbn:de:0030-drops-106923
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10692/
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Fortin, Marie

FO = FO^3 for Linear Orders with Monotone Binary Relations

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LIPIcs-ICALP-2019-116.pdf (0.5 MB)

Abstract

We show that over the class of linear orders with additional binary relations satisfying some monotonicity conditions, monadic first-order logic has the three-variable property. This generalizes (and gives a new proof of) several known results, including the fact that monadic first-order logic has the three-variable property over linear orders, as well as over (R,<,+1), and answers some open questions mentioned in a paper from Antonopoulos, Hunter, Raza and Worrell [FoSSaCS 2015]. Our proof is based on a translation of monadic first-order logic formulas into formulas of a star-free variant of Propositional Dynamic Logic, which are in turn easily expressible in monadic first-order logic with three variables.

BibTeX - Entry

@InProceedings{fortin:LIPIcs:2019:10692,
  author =	{Marie Fortin},
  title =	{{FO = FO^3 for Linear Orders with Monotone Binary Relations}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{116:1--116:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Christel Baier and Ioannis Chatzigiannakis and Paola Flocchini and Stefano Leonardi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10692},
  URN =		{urn:nbn:de:0030-drops-106923},
  doi =		{10.4230/LIPIcs.ICALP.2019.116},
  annote =	{Keywords: first-order logic, three-variable property, propositional dynamic logic}
}

Keywords: first-order logic, three-variable property, propositional dynamic logic
Collection: 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)
Issue Date: 2019
Date of publication: 04.07.2019

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