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DOI: 10.4230/LIPIcs.CSL.2016.39
URN: urn:nbn:de:0030-drops-65791
URL: http://drops.dagstuhl.de/opus/volltexte/2016/6579/
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Pratt-Hartmann, Ian ; Szwast, Wieslaw ; Tendera, Lidia

Quine's Fluted Fragment is Non-Elementary

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LIPIcs-CSL-2016-39.pdf (0.6 MB)


Abstract

We study the fluted fragment, a decidable fragment of first-order logic with an unbounded number of variables, originally identified by W.V. Quine. We show that the satisfiability problem for this fragment has non-elementary complexity, thus refuting an earlier published claim by W.C. Purdy that it is in NExpTime. More precisely, we consider, for all m greater than 1, the intersection of the fluted fragment and the m-variable fragment of first-order logic. We show that this sub-fragment forces (m/2)-tuply exponentially large models, and that its satisfiability problem is (m/2)-NExpTime-hard. We round off by using a corrected version of Purdy's construction to show that the m-variable fluted fragment has the m-tuply exponential model property, and that its satisfiability problem is in m-NExpTime.

BibTeX - Entry

@InProceedings{pratthartmann_et_al:LIPIcs:2016:6579,
  author =	{Ian Pratt-Hartmann and Wieslaw Szwast and Lidia Tendera},
  title =	{{Quine's Fluted Fragment is Non-Elementary}},
  booktitle =	{25th EACSL Annual Conference on Computer Science Logic (CSL 2016)},
  pages =	{39:1--39:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-022-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{62},
  editor =	{Jean-Marc Talbot and Laurent Regnier},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6579},
  URN =		{urn:nbn:de:0030-drops-65791},
  doi =		{10.4230/LIPIcs.CSL.2016.39},
  annote =	{Keywords: Quine, fluted fragment, Purdy, non-elementary, satisfiability, decidability}
}

Keywords: Quine, fluted fragment, Purdy, non-elementary, satisfiability, decidability
Seminar: 25th EACSL Annual Conference on Computer Science Logic (CSL 2016)
Issue Date: 2016
Date of publication: 25.08.2016


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