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)


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
Number of pages17
ISBN (Electronic)9783319913766
ISBN (Print)9783319913759
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

Publication series

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


Conference10th International Conference on the Theory and Application of Diagrams, Diagrams 2018
Country/TerritoryUnited Kingdom
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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