A weakening of alpha graphs: Quasi-boolean algebras

Minghui Ma; Ahti Veikko Pietarinen

doi:10.1007/978-3-319-91376-6_50

A weakening of alpha graphs: Quasi-boolean algebras

Minghui Ma, Ahti Veikko Pietarinen

Nazarbayev University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

5 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 language	English
Title of host publication	Diagrammatic Representation and Inference - 10th International Conference, Diagrams 2018, Proceedings
Editors	Gem Stapleton, Francesco Bellucci, Amirouche Moktefi, Peter Chapman, Sarah Perez-Kriz
Publisher	Springer Verlag
Pages	549-564
Number of pages	16
ISBN (Print)	9783319913759
DOIs	https://doi.org/10.1007/978-3-319-91376-6_50
Publication status	Published - Jan 1 2018
Event	10th International Conference on the Theory and Application of Diagrams, Diagrams 2018 - Edinburgh, United Kingdom Duration: Jun 18 2018 → Jun 22 2018

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10871 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	10th International Conference on the Theory and Application of Diagrams, Diagrams 2018
Country	United Kingdom
City	Edinburgh
Period	6/18/18 → 6/22/18

Keywords

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

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-319-91376-6_50

Fingerprint Dive into the research topics of 'A weakening of alpha graphs: Quasi-boolean algebras'. Together they form a unique fingerprint.

Cite this

Ma, M., & Pietarinen, A. V. (2018). A weakening of alpha graphs: Quasi-boolean algebras. In G. Stapleton, F. Bellucci, A. Moktefi, P. Chapman, & S. Perez-Kriz (Eds.), Diagrammatic Representation and Inference - 10th International Conference, Diagrams 2018, Proceedings (pp. 549-564). (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_50

A weakening of alpha graphs : Quasi-boolean algebras. / Ma, Minghui; Pietarinen, Ahti Veikko.

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. 549-564 (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 proceeding › Conference contribution

Ma, M & Pietarinen, AV 2018, A weakening of alpha graphs: Quasi-boolean algebras. 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. 549-564, 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_50

Ma M, Pietarinen AV. A weakening of alpha graphs: Quasi-boolean algebras. 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. 549-564. (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_50

Ma, Minghui ; Pietarinen, Ahti Veikko. / A weakening of alpha graphs : Quasi-boolean algebras. 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. 549-564 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{d0a0cabf0ebb4d43a19ca7adbb0c30f9,

title = "A weakening of alpha graphs: Quasi-boolean algebras",

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.",

keywords = "Existential graphs, Quasi-Boolean algebra, Sheet of assertion, Weak Alpha graphs",

author = "Minghui Ma and Pietarinen, {Ahti Veikko}",

year = "2018",

month = jan,

day = "1",

doi = "10.1007/978-3-319-91376-6_50",

language = "English",

isbn = "9783319913759",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "549--564",

editor = "Gem Stapleton and Francesco Bellucci and Amirouche Moktefi and Peter Chapman and Sarah Perez-Kriz",

booktitle = "Diagrammatic Representation and Inference - 10th International Conference, Diagrams 2018, Proceedings",

address = "Germany",

note = "10th International Conference on the Theory and Application of Diagrams, Diagrams 2018 ; Conference date: 18-06-2018 Through 22-06-2018",

}

TY - GEN

T1 - A weakening of alpha graphs

T2 - 10th International Conference on the Theory and Application of Diagrams, Diagrams 2018

AU - Ma, Minghui

AU - Pietarinen, Ahti Veikko

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Existential graphs

KW - Quasi-Boolean algebra

KW - Sheet of assertion

KW - Weak Alpha graphs

UR - http://www.scopus.com/inward/record.url?scp=85048600404&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85048600404&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-91376-6_50

DO - 10.1007/978-3-319-91376-6_50

M3 - Conference contribution

AN - SCOPUS:85048600404

SN - 9783319913759

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 549

EP - 564

BT - Diagrammatic Representation and Inference - 10th International Conference, Diagrams 2018, Proceedings

A2 - Stapleton, Gem

A2 - Bellucci, Francesco

A2 - Moktefi, Amirouche

A2 - Chapman, Peter

A2 - Perez-Kriz, Sarah

PB - Springer Verlag

Y2 - 18 June 2018 through 22 June 2018

ER -