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Calculus CL as a Formal System

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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

In recent years CL diagrams inspired by Lange’s Cubus Logicus have been used in various contexts of diagrammatic reasoning. However, whether CL diagrams can also be used as a formal system seemed questionable. We present a CL diagram as a formal system, which is a fragment of propositional logic. Syntax and semantics are presented separately and a variant of bitstring semantics is applied to prove soundness and completeness of the system.

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Author information

Authors and Affiliations

  1. Institute of Philosophy, FernUniversität in Hagen, Hagen, Germany

    Jens Lemanski

  2. Institute of Philosophy, Universität Rostock, Rostock, Germany

    Ludger Jansen

  3. Chair for Philosophy, University of Passau, Passau, Germany

    Ludger Jansen

Authors
  1. Jens Lemanski
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  2. Ludger Jansen
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Corresponding author

Correspondence to Jens Lemanski .

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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Lemanski, J., Jansen, L. (2020). Calculus CL as a Formal System. 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_35

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  • DOI: https://doi.org/10.1007/978-3-030-54249-8_35

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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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