License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2023.32
URN: urn:nbn:de:0030-drops-174933
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17493/
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Pratt-Hartmann, Ian ; Tendera, Lidia

Adding Transitivity and Counting to the Fluted Fragment

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LIPIcs-CSL-2023-32.pdf (0.8 MB)

Abstract

We study the impact of adding both counting quantifiers and a single transitive relation to the fluted fragment - a fragment of first-order logic originating in the work of W.V.O. Quine. The resulting formalism can be viewed as a multi-variable, non-guarded extension of certain systems of description logic featuring number restrictions and transitive roles, but lacking role-inverses. We establish the finite model property for our logic, and show that the satisfiability problem for its k-variable sub-fragment is in (k+1)-NExpTime. We also derive ExpSpace-hardness of the satisfiability problem for the two-variable, fluted fragment with one transitive relation (but without counting quantifiers), and prove that, when a second transitive relation is allowed, both the satisfiability and the finite satisfiability problems for the two-variable fluted fragment with counting quantifiers become undecidable.

BibTeX - Entry

@InProceedings{pratthartmann_et_al:LIPIcs.CSL.2023.32,
  author =	{Pratt-Hartmann, Ian and Tendera, Lidia},
  title =	{{Adding Transitivity and Counting to the Fluted Fragment}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{32:1--32:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17493},
  URN =		{urn:nbn:de:0030-drops-174933},
  doi =		{10.4230/LIPIcs.CSL.2023.32},
  annote =	{Keywords: fluted logic, transitivity, counting, satisfiability, decidability, complexity}
}

Keywords: fluted logic, transitivity, counting, satisfiability, decidability, complexity
Collection: 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)
Issue Date: 2023
Date of publication: 01.02.2023

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