Beta Assertive Graphs

Francesco Bellucci, Daniele Chiffi, Ahti Veikko Pietarinen*

*Corresponding author for this work

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


Assertive graphs (AGs) modify Peirce’s Alpha part of Existential Graphs (EGs) and are used to reason about assertions without any ad hoc sign of assertion. This paper presents an extension of propositional AGs to Beta by lines. Absence of polarities necessitate Beta-AGs to resort to two kinds of lines: standard lines (a certain method of asserting), and barbed lines (a general method of asserting). A new set of rules of transformations for Beta-AGs is presented that derive theorems of quantificational intuitionistic logic. Beta-AGs offer a new system to analyse assertions through quantificational diagrams.

Original languageEnglish
Title of host publicationDiagrammatic Representation and Inference
Subtitle of host publication11th International Conference, Diagrams 2020, Tallinn, Estonia, August 24–28, 2020, Proceedings
EditorsAhti-Veikko Pietarinen, Peter Chapman, Leonie Bosveld-de Smet, Valeria Giardino, James Corter, Sven Linker
PublisherSpringer Cham
Number of pages5
ISBN (Electronic)9783030542498
ISBN (Print)9783030542481
Publication statusPublished - 29 Jul 2020
Event11th International Conference on the Theory and Application of Diagrams, Diagrams 2020 - Tallinn, Estonia
Duration: 24 Aug 202028 Aug 2020

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


Conference11th International Conference on the Theory and Application of Diagrams, Diagrams 2020
Internet address

Scopus Subject Areas

  • Theoretical Computer Science
  • Computer Science(all)

User-Defined Keywords

  • Existential/Assertive graphs
  • Intuitionistic logic
  • Quantifier


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