A weakening of alpha graphs: Quasi-boolean algebras

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

6 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 - 10th International Conference, Diagrams 2018, Proceedings
EditorsGem Stapleton, Francesco Bellucci, Amirouche Moktefi, Peter Chapman, Sarah Perez-Kriz
PublisherSpringer Verlag
Pages549-564
Number of pages16
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

Keywords

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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