Assertive and existential graphs: A comparison

Ahti Veikko Pietarinen*, Daniele Chiffi

*Corresponding author for this work

    Research output: Chapter in book/report/conference proceedingConference proceedingpeer-review

    11 Citations (Scopus)

    Abstract

    Peirce’s graphical logic of Existential Graphs (egs) has no specific sign for assertion, although the notion is used virtually everywhere in Peirce’s logical theories. We outline the new system of Assertive Graphs (ags) that makes the embedded notion of assertions in egs explicit, and show how to inferentially transform ags to a classical graphical logic clag, without having to introduce polarities explicitly. We compare the philosophy of notation of ags to egs, where the latter has polarities both in its intuitionistic and classical cases. Our comparison is framed with respect to three different representations of implication, namely as cuts, boxes and scrolls. We also identify three fundamental differences in the meaning of the Sheet of Assertion and compare those with Peirce’s own proposed interpretation.

    Original languageEnglish
    Title of host publicationDiagrammatic Representation and Inference
    Subtitle of host publication10th International Conference, Diagrams 2018, Edinburgh, UK, June 18-22, 2018, Proceedings
    EditorsPeter Chapman, Gem Stapleton, Amirouche Moktefi, Sarah Perez-Kriz, Francesco Bellucci
    PublisherSpringer Cham
    Pages565-581
    Number of pages17
    Edition1st
    ISBN (Electronic)9783319913766
    ISBN (Print)9783319913759
    DOIs
    Publication statusPublished - 17 May 2018
    Event10th International Conference on the Theory and Application of Diagrams, Diagrams 2018 - Edinburgh, United Kingdom
    Duration: 18 Jun 201822 Jun 2018
    https://link.springer.com/book/10.1007/978-3-319-91376-6

    Publication series

    NameLecture Notes in Computer Science
    Volume10871
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349
    NameLecture Notes in Artificial Intelligence
    NameDiagrams: International Conference on Theory and Application of Diagrams

    Conference

    Conference10th International Conference on the Theory and Application of Diagrams, Diagrams 2018
    Country/TerritoryUnited Kingdom
    CityEdinburgh
    Period18/06/1822/06/18
    Internet address

    Scopus Subject Areas

    • Theoretical Computer Science
    • Computer Science(all)

    User-Defined Keywords

    • Assertion
    • Assertive graphs
    • Existential graphs
    • Implication
    • Intuitionistic graphs
    • Polarity
    • Sheet of assertion

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