License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2021.1
URN: urn:nbn:de:0030-drops-144417
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14441/
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Doumane, Amina

Non-Axiomatizability of the Equational Theories of Positive Relation Algebras (Invited Talk)

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LIPIcs-MFCS-2021-1.pdf (0.3 MB)

Abstract

In the literature, there are two ways to show that the equational theory of relations over a given signature is not finitely axiomatizable. The first-one is based on games and a construction called Rainbow construction. This method is very technical but it shows a strong result: the equational theory cannot be axiomatized by any finite set of first-order formulas. There is another method, based on a graph characterization of the equational theory of relations, which is easier to get and to understand, but proves a weaker result: the equational theory cannot be axiomatized by any finite set of equations.
In this presentation, I will show how to complete the second technique to get the stronger result of non-axiomatizability by first-order formulas.

BibTeX - Entry

@InProceedings{doumane:LIPIcs.MFCS.2021.1,
  author =	{Doumane, Amina},
  title =	{{Non-Axiomatizability of the Equational Theories of Positive Relation Algebras}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14441},
  URN =		{urn:nbn:de:0030-drops-144417},
  doi =		{10.4230/LIPIcs.MFCS.2021.1},
  annote =	{Keywords: Relation algebra, Graph homomorphism, Equational theories, First-order logic}
}

Keywords: Relation algebra, Graph homomorphism, Equational theories, First-order logic
Collection: 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)
Issue Date: 2021
Date of publication: 18.08.2021

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