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International Conference on Theory and Application of Diagrams

Diagrams 2016: Diagrammatic Representation and Inference pp 123–138Cite as

Human Reasoning with Proportional Quantifiers and Its Support by Diagrams

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9781))

Abstract

In this paper, we study the cognitive effectiveness of diagrammatic reasoning with proportional quantifiers such as most. We first examine how Euler-style diagrams can represent syllogistic reasoning with proportional quantifiers, building on previous work on diagrams for the so-called plurative syllogism (Rescher and Gallagher, 1965). We then conduct an experiment to compare performances on syllogistic reasoning tasks of two groups: those who use only linguistic material (two sentential premises and one conclusion) and those who are also given Euler diagrams corresponding to the two premises. Our experiment showed that (a) in both groups, the speed and accuracy of syllogistic reasoning tasks with proportional quantifiers like most were worse than those with standard first-order quantifiers such as all and no, and (b) in both standard and non-standard (proportional) syllogisms, speed and accuracy for the group provided with diagrams were significantly better than the group provided only with sentential premises. These results suggest that syllogistic reasoning with proportional quantifiers like most is cognitively complex, yet can be effectively supported by Euler diagrams that represent the proportionality relationships between sets in a suitable way.

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Notes

  1. 1.

    In addition, we can adopt a method using size-scalable diagrams in which object sizes can be changed from a default. Sato et al. [19] reported that the use of size-scalable diagrams in logical reasoning reduced the interfering effect of diagram layout.

  2. 2.

    Note here that the existence of \(C\overline{A}\) region is a counter-example to the argument of the AU1A syllogism. See Takemura [24] for a formal specification of counter-example construction with Euler diagrams.

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Author information

Authors and Affiliations

  1. Interfaculty Initiative in Information Studies, The University of Tokyo, Tokyo, Japan

    Yuri Sato

  2. Center for Simulation Sciences, Ochanomizu University, Tokyo, Japan

    Koji Mineshima

Authors
  1. Yuri Sato
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  2. Koji Mineshima
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Corresponding author

Correspondence to Yuri Sato .

Editor information

Editors and Affiliations

  1. The University of Cambridge , Cambridge, United Kingdom

    Mateja Jamnik

  2. The University of Tokyo , Tokyo, Japan

    Yuri Uesaka

  3. Millersville University , Millersville, Pennsylvania, USA

    Stephanie Elzer Schwartz

Appendices

Appendix 1: The Results of Each Task

Table 2. Accuracy rates and response times (correct answer only) for 39 syllogisms in the Linguistic group (left) and Diagrammatic group (right)
Full size table

Appendix 2: Instructions Used in Experiment

See: http://abelard.flet.keio.ac.jp/person/sato/index/appendix_d16.pdf

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© 2016 Springer International Publishing Switzerland

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Sato, Y., Mineshima, K. (2016). Human Reasoning with Proportional Quantifiers and Its Support by Diagrams. In: Jamnik, M., Uesaka, Y., Elzer Schwartz, S. (eds) Diagrammatic Representation and Inference. Diagrams 2016. Lecture Notes in Computer Science(), vol 9781. Springer, Cham. https://doi.org/10.1007/978-3-319-42333-3_10

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  • DOI: https://doi.org/10.1007/978-3-319-42333-3_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42332-6

  • Online ISBN: 978-3-319-42333-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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