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Relating Kleene Algebras with Pseudo Uninorms

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Dynamic Logic. New Trends and Applications (DaLí 2022)

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Abstract

This paper explores a strict relation between two core notions of the semantics of programs and of fuzzy logics: Kleene Algebras and (pseudo) uninorms. It shows that every Kleene algebra induces a pseudo uninorm, and that some pseudo uninorms induce Kleene algebras. This connection establishes a new perspective on the theory of Kleene algebras and provides a way to build (new) Kleene algebras. The latter aspect is potentially useful as a source of formalism to capture and model programs acting with fuzzy behaviours and domains.

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Notes

  1. 1.

    The reader can also find in the literature \(\downarrow e\) and \(\uparrow e\), respectively.

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Author information

Authors and Affiliations

  1. Department of Informatics and Applied Mathematics, Federal University of Rio Grande do Norte, Natal, Brazil

    Benjamin Bedregal & Regivan Santiago

  2. CIDMA, Department of Mathematics, Aveiro University, Aveiro, Portugal

    Alexandre Madeira & Manuel Martins

Authors
  1. Benjamin Bedregal
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  2. Regivan Santiago
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  3. Alexandre Madeira
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  4. Manuel Martins
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Corresponding author

Correspondence to Alexandre Madeira .

Editor information

Editors and Affiliations

  1. Universidad Nacional de Córdoba, Córdoba, Argentina

    Carlos Areces

  2. Universidade de Lisboa, Lisbon, Portugal

    Diana Costa

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Bedregal, B., Santiago, R., Madeira, A., Martins, M. (2023). Relating Kleene Algebras with Pseudo Uninorms. In: Areces, C., Costa, D. (eds) Dynamic Logic. New Trends and Applications. DaLí 2022. Lecture Notes in Computer Science, vol 13780. Springer, Cham. https://doi.org/10.1007/978-3-031-26622-5_3

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  • DOI: https://doi.org/10.1007/978-3-031-26622-5_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-26621-8

  • Online ISBN: 978-3-031-26622-5

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