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Graph Characterization of the Universal Theory of Relations

Author Amina Doumane

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Amina Doumane
  • CNRS, ENS Lyon, France

Acknowledgements

I am deeply grateful to Denis Kuperberg and Damien Pous for their great help.

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Amina Doumane. Graph Characterization of the Universal Theory of Relations. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 41:1-41:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.MFCS.2021.41

Abstract

The equational theory of relations can be characterized using graphs and homomorphisms. This result, found independently by Freyd and Scedrov and by Andréka and Bredikhin, shows that the equational theory of relations is decidable. In this paper, we extend this characterization to the whole universal first-order theory of relations. Using our characterization, we show that the positive universal fragment is also decidable.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Discrete mathematics
Keywords
  • Relation algebra
  • Graph homomorphism
  • Equational theories
  • First-order logic

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References

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