Assertive and existential graphs

A comparison

Ahti Veikko Pietarinen, Daniele Chiffi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 - 10th International Conference, Diagrams 2018, Proceedings
EditorsGem Stapleton, Francesco Bellucci, Amirouche Moktefi, Peter Chapman, Sarah Perez-Kriz
PublisherSpringer Verlag
Pages565-581
Number of pages17
ISBN (Print)9783319913759
DOIs
Publication statusPublished - Jan 1 2018
Event10th International Conference on the Theory and Application of Diagrams, Diagrams 2018 - Edinburgh, United Kingdom
Duration: Jun 18 2018Jun 22 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10871 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference10th International Conference on the Theory and Application of Diagrams, Diagrams 2018
CountryUnited Kingdom
CityEdinburgh
Period6/18/186/22/18

Fingerprint

Graph in graph theory
Assertion
Polarity
Logic
Notation
Transform
Graphics

Keywords

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Pietarinen, A. V., & Chiffi, D. (2018). Assertive and existential graphs: A comparison. In G. Stapleton, F. Bellucci, A. Moktefi, P. Chapman, & S. Perez-Kriz (Eds.), Diagrammatic Representation and Inference - 10th International Conference, Diagrams 2018, Proceedings (pp. 565-581). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10871 LNAI). Springer Verlag. https://doi.org/10.1007/978-3-319-91376-6_51

Assertive and existential graphs : A comparison. / Pietarinen, Ahti Veikko; Chiffi, Daniele.

Diagrammatic Representation and Inference - 10th International Conference, Diagrams 2018, Proceedings. ed. / Gem Stapleton; Francesco Bellucci; Amirouche Moktefi; Peter Chapman; Sarah Perez-Kriz. Springer Verlag, 2018. p. 565-581 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10871 LNAI).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Pietarinen, AV & Chiffi, D 2018, Assertive and existential graphs: A comparison. in G Stapleton, F Bellucci, A Moktefi, P Chapman & S Perez-Kriz (eds), Diagrammatic Representation and Inference - 10th International Conference, Diagrams 2018, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10871 LNAI, Springer Verlag, pp. 565-581, 10th International Conference on the Theory and Application of Diagrams, Diagrams 2018 , Edinburgh, United Kingdom, 6/18/18. https://doi.org/10.1007/978-3-319-91376-6_51
Pietarinen AV, Chiffi D. Assertive and existential graphs: A comparison. In Stapleton G, Bellucci F, Moktefi A, Chapman P, Perez-Kriz S, editors, Diagrammatic Representation and Inference - 10th International Conference, Diagrams 2018, Proceedings. Springer Verlag. 2018. p. 565-581. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-91376-6_51
Pietarinen, Ahti Veikko ; Chiffi, Daniele. / Assertive and existential graphs : A comparison. Diagrammatic Representation and Inference - 10th International Conference, Diagrams 2018, Proceedings. editor / Gem Stapleton ; Francesco Bellucci ; Amirouche Moktefi ; Peter Chapman ; Sarah Perez-Kriz. Springer Verlag, 2018. pp. 565-581 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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