Peirce’s Extended Euler Diagrams and the System Atl Based on Ladd-Franklin’s Exclusion Relations

Fangzhou Xu; Ahti-Veikko Juhani Pietarinen

doi:10.1007/978-3-031-71291-3_25

Peirce’s Extended Euler Diagrams and the System Atl Based on Ladd-Franklin’s Exclusion Relations

Fangzhou Xu, Ahti-Veikko Juhani Pietarinen^*

^*Corresponding author for this work

Academy of Chinese, History, Religion and Philosophy

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

Abstract

We explore Charles Peirce’s innovative extension of Euler diagrams to incorporate negative terms through novel star-shaped curves, representing negation and dualizing the relation of inclusion to express exclusion. The study demonstrates the equivalence of Peirce’s extended Euler diagrams (PED) with the axiomatic system Atl, which is based on Christine Ladd-Franklin’s work on exclusion relations. The PED system is shown to be capable of expressing all fifteen valid syllogisms, thereby streamlining logical reasoning. We also explore the historical development of these diagrams and the implications of considering exclusion as a fundamental relation. By taking exclusion as primary, we connect Peirce’s advancements to Ladd-Franklin’s earlier work, highlighting the simplification of syllogistic reasoning and the historical evolution of Eulerian diagrammatic logic.

Original language	English
Title of host publication	Diagrammatic Representation and Inference
Subtitle of host publication	14th International Conference, Diagrams 2024, Münster, Germany, September 27 – October 1, 2024, Proceedings
Editors	Jens Lemanski, Mikkel Willum Johansen, Emmanuel Manalo, Petrucio Viana, Reetu Bhattacharjee, Richard Burns
Publisher	Springer Cham
Pages	316-324
Number of pages	9
Edition	1st
ISBN (Electronic)	9783031712913
ISBN (Print)	9783031712906
DOIs	https://doi.org/10.1007/978-3-031-71291-3_25
Publication status	Published - 8 Sept 2024
Event	14th International Conference on the Theory and Application of Diagrams, Diagrams 2024 - Münster, Germany Duration: 27 Sept 2024 → 1 Oct 2024 https://diagrams-2024.diagrams-conference.org/ https://link.springer.com/book/10.1007/978-3-031-71291-3

Publication series

Name	Lecture Notes in Computer Science
Volume	14981
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Name	International Conference on Theory and Application of Diagrams

Conference

Conference	14th International Conference on the Theory and Application of Diagrams, Diagrams 2024
Country/Territory	Germany
City	Münster
Period	27/09/24 → 1/10/24
Internet address	https://diagrams-2024.diagrams-conference.org/ https://link.springer.com/book/10.1007/978-3-031-71291-3

Scopus Subject Areas

Theoretical Computer Science
General Computer Science

User-Defined Keywords

Antilogism
Charles Peirce
Christine Ladd-Franklin
Copula of Exclusion
Extended Euler Diagrams

Access to Document

10.1007/978-3-031-71291-3_25

Cite this

Xu, F., & Pietarinen, A.-V. J. (2024). Peirce’s Extended Euler Diagrams and the System Atl Based on Ladd-Franklin’s Exclusion Relations. In J. Lemanski, M. W. Johansen, E. Manalo, P. Viana, R. Bhattacharjee, & R. Burns (Eds.), Diagrammatic Representation and Inference: 14th International Conference, Diagrams 2024, Münster, Germany, September 27 – October 1, 2024, Proceedings (1st ed., pp. 316-324). (Lecture Notes in Computer Science; Vol. 14981), (International Conference on Theory and Application of Diagrams). Springer Cham. https://doi.org/10.1007/978-3-031-71291-3_25

Xu, Fangzhou ; Pietarinen, Ahti-Veikko Juhani. / Peirce’s Extended Euler Diagrams and the System Atl Based on Ladd-Franklin’s Exclusion Relations. Diagrammatic Representation and Inference: 14th International Conference, Diagrams 2024, Münster, Germany, September 27 – October 1, 2024, Proceedings. editor / Jens Lemanski ; Mikkel Willum Johansen ; Emmanuel Manalo ; Petrucio Viana ; Reetu Bhattacharjee ; Richard Burns. 1st. ed. Springer Cham, 2024. pp. 316-324 (Lecture Notes in Computer Science). (International Conference on Theory and Application of Diagrams).

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abstract = "We explore Charles Peirce{\textquoteright}s innovative extension of Euler diagrams to incorporate negative terms through novel star-shaped curves, representing negation and dualizing the relation of inclusion to express exclusion. The study demonstrates the equivalence of Peirce{\textquoteright}s extended Euler diagrams (PED) with the axiomatic system Atl, which is based on Christine Ladd-Franklin{\textquoteright}s work on exclusion relations. The PED system is shown to be capable of expressing all fifteen valid syllogisms, thereby streamlining logical reasoning. We also explore the historical development of these diagrams and the implications of considering exclusion as a fundamental relation. By taking exclusion as primary, we connect Peirce{\textquoteright}s advancements to Ladd-Franklin{\textquoteright}s earlier work, highlighting the simplification of syllogistic reasoning and the historical evolution of Eulerian diagrammatic logic.",

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Xu, F & Pietarinen, A-VJ 2024, Peirce’s Extended Euler Diagrams and the System Atl Based on Ladd-Franklin’s Exclusion Relations. in J Lemanski, MW Johansen, E Manalo, P Viana, R Bhattacharjee & R Burns (eds), Diagrammatic Representation and Inference: 14th International Conference, Diagrams 2024, Münster, Germany, September 27 – October 1, 2024, Proceedings. 1st edn, Lecture Notes in Computer Science, vol. 14981, International Conference on Theory and Application of Diagrams, Springer Cham, pp. 316-324, 14th International Conference on the Theory and Application of Diagrams, Diagrams 2024, Münster, Germany, 27/09/24. https://doi.org/10.1007/978-3-031-71291-3_25

Peirce’s Extended Euler Diagrams and the System Atl Based on Ladd-Franklin’s Exclusion Relations. / Xu, Fangzhou; Pietarinen, Ahti-Veikko Juhani.
Diagrammatic Representation and Inference: 14th International Conference, Diagrams 2024, Münster, Germany, September 27 – October 1, 2024, Proceedings. ed. / Jens Lemanski; Mikkel Willum Johansen; Emmanuel Manalo; Petrucio Viana; Reetu Bhattacharjee; Richard Burns. 1st. ed. Springer Cham, 2024. p. 316-324 (Lecture Notes in Computer Science; Vol. 14981), (International Conference on Theory and Application of Diagrams).

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

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Xu F, Pietarinen AVJ. Peirce’s Extended Euler Diagrams and the System Atl Based on Ladd-Franklin’s Exclusion Relations. In Lemanski J, Johansen MW, Manalo E, Viana P, Bhattacharjee R, Burns R, editors, Diagrammatic Representation and Inference: 14th International Conference, Diagrams 2024, Münster, Germany, September 27 – October 1, 2024, Proceedings. 1st ed. Springer Cham. 2024. p. 316-324. (Lecture Notes in Computer Science). (International Conference on Theory and Application of Diagrams). doi: 10.1007/978-3-031-71291-3_25

Peirce’s Extended Euler Diagrams and the System Atl Based on Ladd-Franklin’s Exclusion Relations

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Scopus Subject Areas

User-Defined Keywords

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