On Homogeneous Models of Fluted Languages

Author Daumantas Kojelis



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Author Details

Daumantas Kojelis
  • Department of Computer Science, University of Manchester, UK

Acknowledgements

The author would like to thank Dr. Ian Pratt-Hartmann and Dr. Bartosz Jan Bednarczyk for their valuable feedback.

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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) https://doi.org/10.4230/LIPIcs.CSL.2025.9

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity theory and logic
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

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