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Intuitionistic Euler-Venn Diagrams

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Diagrammatic Representation and Inference (Diagrams 2020)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12169))

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Abstract

We present an intuitionistic interpretation of Euler-Venn diagrams with respect to Heyting algebras. In contrast to classical Euler-Venn diagrams, we treat shaded and missing zones differently, to have diagrammatic representations of conjunction, disjunction and intuitionistic implication. Furthermore, we need to add new syntactic elements to express these concepts. We present a cut-free sequent calculus for this language, and prove it to be sound and complete. Furthermore, we show that the rules of cut, weakening and contraction are admissible.

This work was supported by EPSRC Research Programme EP/N007565/1 Science of Sensor Systems Software.

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Authors and Affiliations

  1. University of Liverpool, Liverpool, UK

    Sven Linker

Authors
  1. Sven Linker
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Correspondence to Sven Linker .

Editor information

Editors and Affiliations

  1. Tallinn University of Technology, Tallinn, Estonia

    Ahti-Veikko Pietarinen

  2. Edinburgh Napier University, Edinburgh, UK

    Peter Chapman

  3. University of Groningen, Groningen, The Netherlands

    Leonie Bosveld-de Smet

  4. Université de Lorraine, Nancy, France

    Valeria Giardino

  5. Columbia University, New York, NY, USA

    James Corter

  6. University of Liverpool, Liverpool, UK

    Sven Linker

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Linker, S. (2020). Intuitionistic Euler-Venn Diagrams. In: Pietarinen, AV., Chapman, P., Bosveld-de Smet, L., Giardino, V., Corter, J., Linker, S. (eds) Diagrammatic Representation and Inference. Diagrams 2020. Lecture Notes in Computer Science(), vol 12169. Springer, Cham. https://doi.org/10.1007/978-3-030-54249-8_21

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  • DOI: https://doi.org/10.1007/978-3-030-54249-8_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-54248-1

  • Online ISBN: 978-3-030-54249-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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