3 Search Results for "Szwast, Wieslaw"

Document
DOI: 10.4230/LIPIcs.CSL.2025.9
On Homogeneous Models of Fluted Languages

Authors: Daumantas Kojelis

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
We study the fluted fragment of first-order logic which is often viewed as a multi-variable non-guarded extension to various systems of description logics lacking role-inverses. In this paper we show that satisfiable fluted sentences (even under reasonable extensions) admit special kinds of "nice" models which we call globally/locally homogeneous. Homogeneous models allow us to simplify methods for analysing fluted logics with counting quantifiers and establish a novel result for the decidability of the (finite) satisfiability problem for the fluted fragment with periodic counting. More specifically, we will show that the (finite) satisfiability problem for the language is Tower-complete. If only two variable are used, computational complexity drops to NExpTime-completeness. We supplement our findings by showing that generalisations of fluted logics, such as the adjacent fragment, have finite and general satisfiability problems which are, respectively, Σ⁰₁- and Π⁰₁-complete. Additionally, satisfiability becomes Σ¹₁-complete if periodic counting quantifiers are permitted.
Cite as

Daumantas Kojelis. On Homogeneous Models of Fluted Languages. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 9:1-9:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kojelis:LIPIcs.CSL.2025.9,
  author =	{Kojelis, Daumantas},
  title =	{{On Homogeneous Models of Fluted Languages}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{9:1--9:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.9},
  URN =		{urn:nbn:de:0030-drops-227669},
  doi =		{10.4230/LIPIcs.CSL.2025.9},
  annote =	{Keywords: Fluted Fragment, Fluted Logic, Fluted Fragment with Periodic Counting, Adjacent Fragment, Adjacent Fragment with Counting, Adjacent Fragment with Periodic Counting, Counting Quantifiers, Periodic Counting Quantifiers, Decidable Fragments of First-Order Logic}
}
Document
DOI: 10.4230/LIPIcs.CSL.2016.39
Quine's Fluted Fragment is Non-Elementary

Authors: Ian Pratt-Hartmann, Wieslaw Szwast, and Lidia Tendera

Published in: LIPIcs, Volume 62, 25th EACSL Annual Conference on Computer Science Logic (CSL 2016)

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.
Cite as

Ian Pratt-Hartmann, Wieslaw Szwast, and Lidia Tendera. Quine's Fluted Fragment is Non-Elementary. In 25th EACSL Annual Conference on Computer Science Logic (CSL 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 62, pp. 39:1-39:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{pratthartmann_et_al:LIPIcs.CSL.2016.39,
  author =	{Pratt-Hartmann, Ian and Szwast, Wieslaw and Tendera, Lidia},
  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 =	{Talbot, Jean-Marc and Regnier, Laurent},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2016.39},
  URN =		{urn:nbn:de:0030-drops-65791},
  doi =		{10.4230/LIPIcs.CSL.2016.39},
  annote =	{Keywords: Quine, fluted fragment, Purdy, non-elementary, satisfiability, decidability}
}
Document
DOI: 10.4230/LIPIcs.STACS.2013.317
FO^2 with one transitive relation is decidable

Authors: Wieslaw Szwast and Lidia Tendera

Published in: LIPIcs, Volume 20, 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)

Abstract
We show that the satisfiability problem for the two-variable first-order logic, FO^2, over transitive structures when only one relation is required to be transitive, is decidable. The result is optimal, as FO^2 over structures with two transitive relations, or with one transitive and one equivalence relation, are known to be undecidable, so in fact, our result completes the classification of FO^2-logics over transitive structures with respect to decidability. We show that the satisfiability problem is in 2-NExpTime. Decidability of the finite satisfiability problem remains open.
Cite as

Wieslaw Szwast and Lidia Tendera. FO^2 with one transitive relation is decidable. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 317-328, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{szwast_et_al:LIPIcs.STACS.2013.317,
  author =	{Szwast, Wieslaw and Tendera, Lidia},
  title =	{{FO^2 with one transitive relation is decidable}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{317--328},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-50-7},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{20},
  editor =	{Portier, Natacha and Wilke, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.317},
  URN =		{urn:nbn:de:0030-drops-39449},
  doi =		{10.4230/LIPIcs.STACS.2013.317},
  annote =	{Keywords: classical decision problem, two-variable first-order logic, decidability, computational complexity}
}
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