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.CSL.2021.18
URN: urn:nbn:de:0030-drops-134520
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13452/
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Dawar, Anuj ; Sankaran, Abhisekh

Extension Preservation in the Finite and Prefix Classes of First Order Logic

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Abstract

It is well known that the classic Łoś-Tarski preservation theorem fails in the finite: there are first-order definable classes of finite structures closed under extensions which are not definable (in the finite) in the existential fragment of first-order logic. We strengthen this by constructing for every n, first-order definable classes of finite structures closed under extensions which are not definable with n quantifier alternations. The classes we construct are definable in the extension of Datalog with negation and indeed in the existential fragment of transitive-closure logic. This answers negatively an open question posed by Rosen and Weinstein.

BibTeX - Entry

@InProceedings{dawar_et_al:LIPIcs:2021:13452,
  author =	{Anuj Dawar and Abhisekh Sankaran},
  title =	{{Extension Preservation in the Finite and Prefix Classes of First Order Logic}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{18:1--18:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-175-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{183},
  editor =	{Christel Baier and Jean Goubault-Larrecq},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13452},
  URN =		{urn:nbn:de:0030-drops-134520},
  doi =		{10.4230/LIPIcs.CSL.2021.18},
  annote =	{Keywords: finite model theory, preservation theorems, extension closed, composition, Datalog, Ehrenfeucht-Fraisse games}
}

Keywords: finite model theory, preservation theorems, extension closed, composition, Datalog, Ehrenfeucht-Fraisse games
Collection: 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)
Issue Date: 2021
Date of publication: 13.01.2021

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