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International Conference on Relational and Algebraic Methods in Computer Science

RAMiCS 2023: Relational and Algebraic Methods in Computer Science pp 140–157Cite as

Representable and Diagonally Representable Weakening Relation Algebras

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Part of the Lecture Notes in Computer Science book series (LNCS,volume 13896)

Abstract

A binary relation defined on a poset is a weakening relation if the partial order acts as a both-sided compositional identity. This is motivated by the weakening rule in sequent calculi and closely related to models of relevance logic. For a fixed poset the collection of weakening relations is a subreduct of the full relation algebra on the underlying set of the poset. We present a two-player game for the class of representable weakening relation algebras akin to that for the class of representable relation algebras. This enables us to define classes of abstract weakening relation algebras that approximate the quasivariety of representable weakening relation algebras. We give explicit finite axiomatisations for some of these classes. We define the class of diagonally representable weakening relation algebras and prove that it is a discriminator variety. We also provide explicit representations for several small weakening relation algebras.

Keywords

  • Weakening relation algebra
  • Relevance frames
  • Sugihara monoids
  • Representation games

This work was supported by the Engineering and Physical Sciences Research Council EP/S021566/1.

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Authors and Affiliations

  1. Chapman University, Orange, USA

    Peter Jipsen

  2. UCL (University College London), London, UK

    Jaš Šemrl

Authors
  1. Peter Jipsen
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  2. Jaš Šemrl
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Correspondence to Jaš Šemrl .

Editor information

Editors and Affiliations

  1. Deutsches Zentrum für Luft- und Raumfahrt, Augsburg, Germany

    Roland Glück

  2. Aix-Marseille University, Marseille, France

    Luigi Santocanale

  3. Brock University, St Catharines, ON, Canada

    Michael Winter

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Jipsen, P., Šemrl, J. (2023). Representable and Diagonally Representable Weakening Relation Algebras. In: Glück, R., Santocanale, L., Winter, M. (eds) Relational and Algebraic Methods in Computer Science. RAMiCS 2023. Lecture Notes in Computer Science, vol 13896. Springer, Cham. https://doi.org/10.1007/978-3-031-28083-2_9

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  • DOI: https://doi.org/10.1007/978-3-031-28083-2_9

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