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Adding Transitivity and Counting to the Fluted Fragment

Authors Ian Pratt-Hartmann, Lidia Tendera

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Author Details

Ian Pratt-Hartmann
  • Department of Computer Science, University of Manchester, UK
  • Institute of Computer Science, University of Opole, Poland
Lidia Tendera
  • Institute of Computer Science, University of Opole, Poland

Funding

This work was supported by the Polish NCN, grant number 2018/31/B/ST6/03662.

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Ian Pratt-Hartmann and Lidia Tendera. Adding Transitivity and Counting to the Fluted Fragment. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 32:1-32:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.CSL.2023.32

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity theory and logic
Keywords
  • fluted logic
  • transitivity
  • counting
  • satisfiability
  • decidability
  • complexity

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