Assertive and existential graphs: A comparison

Ahti Veikko Pietarinen; Daniele Chiffi

doi:10.1007/978-3-319-91376-6_51

Assertive and existential graphs: A comparison

Ahti Veikko Pietarinen^*, Daniele Chiffi

^*Corresponding author for this work

Academy of Chinese, History, Religion and Philosophy

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

11 Citations (Scopus)

Abstract

Peirce’s graphical logic of Existential Graphs (egs) has no specific sign for assertion, although the notion is used virtually everywhere in Peirce’s logical theories. We outline the new system of Assertive Graphs (ags) that makes the embedded notion of assertions in egs explicit, and show how to inferentially transform ags to a classical graphical logic clag, without having to introduce polarities explicitly. We compare the philosophy of notation of ags to egs, where the latter has polarities both in its intuitionistic and classical cases. Our comparison is framed with respect to three different representations of implication, namely as cuts, boxes and scrolls. We also identify three fundamental differences in the meaning of the Sheet of Assertion and compare those with Peirce’s own proposed interpretation.

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	565-581
Number of pages	17
Edition	1st
ISBN (Electronic)	9783319913766
ISBN (Print)	9783319913759
DOIs	https://doi.org/10.1007/978-3-319-91376-6_51
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

User-Defined Keywords

Assertion
Assertive graphs
Existential graphs
Implication
Intuitionistic graphs
Polarity
Sheet of assertion

Access to Document

10.1007/978-3-319-91376-6_51

Cite this

Pietarinen, A. V., & Chiffi, D. (2018). Assertive and existential graphs: A comparison. 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. 565-581). (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_51

Pietarinen, Ahti Veikko ; Chiffi, Daniele. / Assertive and existential graphs : A comparison. 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. 565-581 (Lecture Notes in Computer Science). (Lecture Notes in Artificial Intelligence). (Diagrams: International Conference on Theory and Application of Diagrams).

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title = "Assertive and existential graphs: A comparison",

abstract = "Peirce{\textquoteright}s graphical logic of Existential Graphs (egs) has no specific sign for assertion, although the notion is used virtually everywhere in Peirce{\textquoteright}s logical theories. We outline the new system of Assertive Graphs (ags) that makes the embedded notion of assertions in egs explicit, and show how to inferentially transform ags to a classical graphical logic clag, without having to introduce polarities explicitly. We compare the philosophy of notation of ags to egs, where the latter has polarities both in its intuitionistic and classical cases. Our comparison is framed with respect to three different representations of implication, namely as cuts, boxes and scrolls. We also identify three fundamental differences in the meaning of the Sheet of Assertion and compare those with Peirce{\textquoteright}s own proposed interpretation.",

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note = "Funding Information: A.-V. Pietarinen—The work supported by the Estonian Research Council Personal Research Grant PUT 1305 (Abduction in the Age of Fundamental Uncertainty, PI Pietarinen), and Nazarbayev University Social Policy Grant 2018–2019. D. Chiffi—The work supported by the Estonian Research Council Personal Research Grant PUT 1305 (Abduction in the Age of Fundamental Uncertainty, PI Pietarinen). 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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Pietarinen, AV & Chiffi, D 2018, Assertive and existential graphs: A comparison. 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. 565-581, 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_51

Assertive and existential graphs: A comparison. / Pietarinen, Ahti Veikko; Chiffi, Daniele.
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. 565-581 (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 proceeding › peer-review

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N1 - Funding Information: A.-V. Pietarinen—The work supported by the Estonian Research Council Personal Research Grant PUT 1305 (Abduction in the Age of Fundamental Uncertainty, PI Pietarinen), and Nazarbayev University Social Policy Grant 2018–2019. D. Chiffi—The work supported by the Estonian Research Council Personal Research Grant PUT 1305 (Abduction in the Age of Fundamental Uncertainty, PI Pietarinen). Publisher Copyright: © Springer International Publishing AG, part of Springer Nature 2018.

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N2 - Peirce’s graphical logic of Existential Graphs (egs) has no specific sign for assertion, although the notion is used virtually everywhere in Peirce’s logical theories. We outline the new system of Assertive Graphs (ags) that makes the embedded notion of assertions in egs explicit, and show how to inferentially transform ags to a classical graphical logic clag, without having to introduce polarities explicitly. We compare the philosophy of notation of ags to egs, where the latter has polarities both in its intuitionistic and classical cases. Our comparison is framed with respect to three different representations of implication, namely as cuts, boxes and scrolls. We also identify three fundamental differences in the meaning of the Sheet of Assertion and compare those with Peirce’s own proposed interpretation.

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Pietarinen AV, Chiffi D. Assertive and existential graphs: A comparison. 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. 565-581. (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_51

Assertive and existential graphs: A comparison

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