A weakening of alpha graphs: Quasi-boolean algebras

Minghui Ma, Ahti Veikko Pietarinen*

*Corresponding author for this work

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

11 Citations (Scopus)

Abstract

Peirce introduced the Alpha part of the logic of Existential Graphs (egs) as a diagrammatic syntax and graphical system corresponding to classical propositional logic. The logic of quasi-Boolean algebras (De Morgan algebras) is a weakening of classical propositional logic. We develop a graphical system of weak Alpha graphs for quasi-Boolean algebras, and show its soundness and completeness with respect to this algebra. Weak logical graphs arise with only minor modifications to the transformation rules of the original theory of egs. Implications of these modifications to the meaning of the sheet of assertion are then also examined.

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
Pages549-564
Number of pages16
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

  • Existential graphs
  • Quasi-Boolean algebra
  • Sheet of assertion
  • Weak Alpha graphs

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