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Fluted Logic with Counting

Author Ian Pratt-Hartmann



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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

Acknowledgements

The author wishes to thank Prof. L. Tendera for valuable discussions.

Cite AsGet BibTex

Ian Pratt-Hartmann. Fluted Logic with Counting. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 141:1-141:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.ICALP.2021.141

Abstract

The fluted fragment is a fragment of first-order logic in which the order of quantification of variables coincides with the order in which those variables appear as arguments of predicates. It is known that the fluted fragment possesses the finite model property. In this paper, we extend the fluted fragment by the addition of counting quantifiers. We show that the resulting logic retains the finite model property, and that the satisfiability problem for its (m+1)-variable sub-fragment is in m-NExpTime for all positive m. We also consider the satisfiability and finite satisfiability problems for the extension of any of these fragments in which the fluting requirement applies only to sub-formulas having at least three free variables.

Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity theory and logic
Keywords
  • Fluted fragment
  • counting quantifiers
  • satisfiability
  • complexity

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