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Euler Diagrams for Defeasible Reasoning

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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 investigate Euler diagrammatic systems for defeasible reasoning by extending the usual systems for Euler and Venn diagrams corresponding to standard classical logic. To achieve this, we use the generalized quantifier “most” to formalize defeasible reasoning, as proposed by Schlechta (1995), where defeasible knowledge is represented as “Most A are B” and axioms for “most” are defined. We introduce an Euler diagrammatic system for defeasible reasoning by introducing circle mA that represents “most A” for each circle A. We show that our Euler diagrammatic system is a diagrammatic representation of the symbolic system of the generalized quantifier “most”. Furthermore, we investigate skeptical and credulous strategies in defeasible reasoning with our Euler diagrams.

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Authors and Affiliations

  1. Nihon University, Tokyo, Japan

    Ryo Takemura

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  1. Ryo Takemura
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Correspondence to Ryo Takemura .

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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Takemura, R. (2020). Euler Diagrams for Defeasible Reasoning. 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_23

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  • DOI: https://doi.org/10.1007/978-3-030-54249-8_23

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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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