Venn Diagrams with “Most”: A Natural Logic Approach

Xinwen Liu; Ahti Veikko Pietarinen

doi:10.1007/978-3-030-86062-2_27

Venn Diagrams with “Most”: A Natural Logic Approach

Xinwen Liu, Ahti Veikko Pietarinen^*

^*Corresponding author for this work

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

Abstract

This note exposes a little-known fact originally proposed by Nicholas Rescher in 1965, that the generalized second-order quantifier “Most” and the rules governing its behavior can be incorporated into Euler-Venn diagrams with an iconic notion of an arrow and its head and vane extensions and contractions. The objective is then to analyse this work further and to link it with the related but independently developed recent work in the area of natural logic.

Original language	English
Title of host publication	Diagrammatic Representation and Inference
Subtitle of host publication	12th International Conference, Diagrams 2021, Virtual, September 28–30, 2021, Proceedings
Editors	Amrita Basu, Gem Stapleton, Sven Linker, Catherine Legg, Emmanuel Manalo, Petrucio Viana
Publisher	Springer Cham
Pages	264-268
Number of pages	5
ISBN (Electronic)	9783030860622
ISBN (Print)	9783030860615
DOIs	https://doi.org/10.1007/978-3-030-86062-2_27
Publication status	Published - 3 Sept 2021
Event	12th International Conference on the Theory and Application of Diagrams, Diagrams 2021 - Virtual, Online Duration: 28 Sept 2021 → 30 Sept 2021 https://link.springer.com/book/10.1007/978-3-030-86062-2

Publication series

Name	Lecture Notes in Computer Science
Volume	12909
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	12th International Conference on the Theory and Application of Diagrams, Diagrams 2021
City	Virtual, Online
Period	28/09/21 → 30/09/21
Internet address	https://link.springer.com/book/10.1007/978-3-030-86062-2

Scopus Subject Areas

Theoretical Computer Science
Computer Science(all)

User-Defined Keywords

Arrow
Most
Natural logic
Rescher quantifier
Venn diagrams

Access to Document

10.1007/978-3-030-86062-2_27

Cite this

Liu, X., & Pietarinen, A. V. (2021). Venn Diagrams with “Most”: A Natural Logic Approach. In A. Basu, G. Stapleton, S. Linker, C. Legg, E. Manalo, & P. Viana (Eds.), Diagrammatic Representation and Inference: 12th International Conference, Diagrams 2021, Virtual, September 28–30, 2021, Proceedings (pp. 264-268). (Lecture Notes in Computer Science; Vol. 12909), (Lecture Notes in Artificial Intelligence), (Diagrams: International Conference on Theory and Application of Diagrams). Springer Cham. https://doi.org/10.1007/978-3-030-86062-2_27

Liu, Xinwen ; Pietarinen, Ahti Veikko. / Venn Diagrams with “Most” : A Natural Logic Approach. Diagrammatic Representation and Inference: 12th International Conference, Diagrams 2021, Virtual, September 28–30, 2021, Proceedings. editor / Amrita Basu ; Gem Stapleton ; Sven Linker ; Catherine Legg ; Emmanuel Manalo ; Petrucio Viana. Springer Cham, 2021. pp. 264-268 (Lecture Notes in Computer Science). (Lecture Notes in Artificial Intelligence). (Diagrams: International Conference on Theory and Application of Diagrams).

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title = "Venn Diagrams with “Most”: A Natural Logic Approach",

abstract = "This note exposes a little-known fact originally proposed by Nicholas Rescher in 1965, that the generalized second-order quantifier “Most” and the rules governing its behavior can be incorporated into Euler-Venn diagrams with an iconic notion of an arrow and its head and vane extensions and contractions. The objective is then to analyse this work further and to link it with the related but independently developed recent work in the area of natural logic.",

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author = "Xinwen Liu and Pietarinen, {Ahti Veikko}",

note = "Funding Information: Basic Research Program (HSE University); National Social Science Fund China 20&ZD046 Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.; 12th International Conference on the Theory and Application of Diagrams, Diagrams 2021 ; Conference date: 28-09-2021 Through 30-09-2021",

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doi = "10.1007/978-3-030-86062-2_27",

language = "English",

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editor = "Amrita Basu and Gem Stapleton and Sven Linker and Catherine Legg and Emmanuel Manalo and Petrucio Viana",

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Liu, X & Pietarinen, AV 2021, Venn Diagrams with “Most”: A Natural Logic Approach. in A Basu, G Stapleton, S Linker, C Legg, E Manalo & P Viana (eds), Diagrammatic Representation and Inference: 12th International Conference, Diagrams 2021, Virtual, September 28–30, 2021, Proceedings. Lecture Notes in Computer Science, vol. 12909, Lecture Notes in Artificial Intelligence, Diagrams: International Conference on Theory and Application of Diagrams, Springer Cham, pp. 264-268, 12th International Conference on the Theory and Application of Diagrams, Diagrams 2021, Virtual, Online, 28/09/21. https://doi.org/10.1007/978-3-030-86062-2_27

Venn Diagrams with “Most”: A Natural Logic Approach. / Liu, Xinwen; Pietarinen, Ahti Veikko.
Diagrammatic Representation and Inference: 12th International Conference, Diagrams 2021, Virtual, September 28–30, 2021, Proceedings. ed. / Amrita Basu; Gem Stapleton; Sven Linker; Catherine Legg; Emmanuel Manalo; Petrucio Viana. Springer Cham, 2021. p. 264-268 (Lecture Notes in Computer Science; Vol. 12909), (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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AB - This note exposes a little-known fact originally proposed by Nicholas Rescher in 1965, that the generalized second-order quantifier “Most” and the rules governing its behavior can be incorporated into Euler-Venn diagrams with an iconic notion of an arrow and its head and vane extensions and contractions. The objective is then to analyse this work further and to link it with the related but independently developed recent work in the area of natural logic.

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Liu X, Pietarinen AV. Venn Diagrams with “Most”: A Natural Logic Approach. In Basu A, Stapleton G, Linker S, Legg C, Manalo E, Viana P, editors, Diagrammatic Representation and Inference: 12th International Conference, Diagrams 2021, Virtual, September 28–30, 2021, Proceedings. Springer Cham. 2021. p. 264-268. (Lecture Notes in Computer Science). (Lecture Notes in Artificial Intelligence). (Diagrams: International Conference on Theory and Application of Diagrams). doi: 10.1007/978-3-030-86062-2_27

Venn Diagrams with “Most”: A Natural Logic Approach

Abstract

Publication series

Conference

Scopus Subject Areas

User-Defined Keywords

Access to Document

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