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^*

^*Corresponding author for this work

Department of Religion and Philosophy

Research output: Chapter in book/report/conference proceeding › Conference contribution › peer-review

10 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
Subtitle of host publication	10th International Conference, Diagrams 2018, Edinburgh, UK, June 18-22, 2018, Proceedings
Editors	Peter Chapman, Gem Stapleton, Amirouche Moktefi, Sarah Perez-Kriz, Francesco Bellucci
Publisher	Springer Cham
Pages	549-564
Number of pages	16
Edition	1st
ISBN (Electronic)	9783319913766
ISBN (Print)	9783319913759
DOIs	https://doi.org/10.1007/978-3-319-91376-6_50
Publication status	Published - 17 May 2018
Event	10th International Conference on the Theory and Application of Diagrams, Diagrams 2018 - Edinburgh, United Kingdom Duration: 18 Jun 2018 → 22 Jun 2018 https://link.springer.com/book/10.1007/978-3-319-91376-6

Publication series

Name	Lecture Notes in Computer Science
Volume	10871
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Name	Lecture Notes in Artificial Intelligence

Name	Diagrams: International Conference on Theory and Application of Diagrams

Conference

Conference	10th International Conference on the Theory and Application of Diagrams, Diagrams 2018
Country/Territory	United Kingdom
City	Edinburgh
Period	18/06/18 → 22/06/18
Internet address	https://link.springer.com/book/10.1007/978-3-319-91376-6

Scopus Subject Areas

Theoretical Computer Science
Computer Science(all)

User-Defined Keywords

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

Access to Document

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

Cite this

Ma, M., & Pietarinen, A. V. (2018). A weakening of alpha graphs: Quasi-boolean algebras. In P. Chapman, G. Stapleton, A. Moktefi, S. Perez-Kriz, & F. Bellucci (Eds.), Diagrammatic Representation and Inference: 10th International Conference, Diagrams 2018, Edinburgh, UK, June 18-22, 2018, Proceedings (1st ed., pp. 549-564). (Lecture Notes in Computer Science; Vol. 10871), (Lecture Notes in Artificial Intelligence), (Diagrams: International Conference on Theory and Application of Diagrams). Springer Cham. 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, Edinburgh, UK, June 18-22, 2018, Proceedings. editor / Peter Chapman ; Gem Stapleton ; Amirouche Moktefi ; Sarah Perez-Kriz ; Francesco Bellucci. 1st. ed. Springer Cham, 2018. pp. 549-564 (Lecture Notes in Computer Science). (Lecture Notes in Artificial Intelligence). (Diagrams: International Conference on Theory and Application of Diagrams).

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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",

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note = "Funding Information: M. Ma—The work supported by the Project Supported by Guangdong Province Higher Vocational Colleges & Schools Pearl River Scholar Funded Scheme (2017). A.-V. Pietarinen—The work supported by the Estonian Research Council Personal Research Grant PUT 1305 (Abduction in the Age of Fundamental Uncertainty) and Nazarbayev University Social Policy Grant 2018–2019. 1 The reference R is to Peirce{\textquoteright}s manuscripts by the Robin number [19]. Publisher Copyright: {\textcopyright} Springer International Publishing AG, part of Springer Nature 2018.; 10th International Conference on the Theory and Application of Diagrams, Diagrams 2018 ; Conference date: 18-06-2018 Through 22-06-2018",

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Ma, M & Pietarinen, AV 2018, A weakening of alpha graphs: Quasi-boolean algebras. in P Chapman, G Stapleton, A Moktefi, S Perez-Kriz & F Bellucci (eds), Diagrammatic Representation and Inference: 10th International Conference, Diagrams 2018, Edinburgh, UK, June 18-22, 2018, Proceedings. 1st edn, Lecture Notes in Computer Science, vol. 10871, Lecture Notes in Artificial Intelligence, Diagrams: International Conference on Theory and Application of Diagrams, Springer Cham, pp. 549-564, 10th International Conference on the Theory and Application of Diagrams, Diagrams 2018 , Edinburgh, United Kingdom, 18/06/18. 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, Edinburgh, UK, June 18-22, 2018, Proceedings. ed. / Peter Chapman; Gem Stapleton; Amirouche Moktefi; Sarah Perez-Kriz; Francesco Bellucci. 1st. ed. Springer Cham, 2018. p. 549-564 (Lecture Notes in Computer Science; Vol. 10871), (Lecture Notes in Artificial Intelligence), (Diagrams: International Conference on Theory and Application of Diagrams).

Research output: Chapter in book/report/conference proceeding › Conference contribution › peer-review

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AU - Ma, Minghui

AU - Pietarinen, Ahti Veikko

N1 - Funding Information: M. Ma—The work supported by the Project Supported by Guangdong Province Higher Vocational Colleges & Schools Pearl River Scholar Funded Scheme (2017). A.-V. Pietarinen—The work supported by the Estonian Research Council Personal Research Grant PUT 1305 (Abduction in the Age of Fundamental Uncertainty) and Nazarbayev University Social Policy Grant 2018–2019. 1 The reference R is to Peirce’s manuscripts by the Robin number [19]. Publisher Copyright: © Springer International Publishing AG, part of Springer Nature 2018.

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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.

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Ma M, Pietarinen AV. A weakening of alpha graphs: Quasi-boolean algebras. In Chapman P, Stapleton G, Moktefi A, Perez-Kriz S, Bellucci F, editors, Diagrammatic Representation and Inference: 10th International Conference, Diagrams 2018, Edinburgh, UK, June 18-22, 2018, Proceedings. 1st ed. Springer Cham. 2018. p. 549-564. (Lecture Notes in Computer Science). (Lecture Notes in Artificial Intelligence). (Diagrams: International Conference on Theory and Application of Diagrams). doi: 10.1007/978-3-319-91376-6_50

A weakening of alpha graphs: Quasi-boolean algebras

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