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Random Models and Guarded Logic

Author Oskar Fiuk

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LIPIcs.STACS.2026.37.pdf
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ACM Subject Classification
  • Theory of computation → Finite Model Theory
Keywords
  • guarded fragment
  • finite model property
  • probabilistic method

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Abstract

Building on ideas of Gurevich and Shelah for the Gödel Class, we present a new probabilistic proof of the finite model property for the Guarded Fragment of First-Order Logic. Our proof is conceptually simple and yields the optimal doubly-exponential upper bound on the size of minimal models. We precisely analyse the obtained bound, up to constant factors in the exponents, and construct sentences that enforce models of tightly matching size. The probabilistic approach adapts naturally to the Triguarded Fragment, an extension of the Guarded Fragment that also subsumes the Two-Variable Fragment. Finally, we derandomise the probabilistic proof by providing an explicit model construction which replaces randomness with deterministic hash functions.

Cite As Get BibTex

Oskar Fiuk. Random Models and Guarded Logic. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 37:1-37:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.STACS.2026.37

Author Details

Oskar Fiuk
  • Institute of Computer Science, University of Wrocław, Poland

Funding

Polish National Science Center, grant No. 2021/41/B/ST6/00996.

Acknowledgements

I am deeply grateful to Prof. Emanuel Kieroński for his guidance and supervision throughout this work. I also thank the third reviewer of ICALP 2025 for providing detailed and valuable feedback on an earlier version of this paper.

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