Journal of Logic, Language and Information

, Volume 24, Issue 4, pp 409–455 | Cite as

How Diagrams Can Support Syllogistic Reasoning: An Experimental Study

  • Yuri Sato
  • Koji Mineshima


This paper explores the question of what makes diagrammatic representations effective for human logical reasoning, focusing on how Euler diagrams support syllogistic reasoning. It is widely held that diagrammatic representations aid intuitive understanding of logical reasoning. In the psychological literature, however, it is still controversial whether and how Euler diagrams can aid untrained people to successfully conduct logical reasoning such as set-theoretic and syllogistic reasoning. To challenge the negative view, we build on the findings of modern diagrammatic logic and introduce an Euler-style diagrammatic representation system that is designed to avoid problems inherent to a traditional version of Euler diagrams. It is hypothesized that Euler diagrams are effective not only in interpreting sentential premises but also in reasoning about semantic structures implicit in given sentences. To test the hypothesis, we compared Euler diagrams with other types of diagrams having different syntactic or semantic properties. Experiment compared the difference in performance between syllogistic reasoning with Euler diagrams and Venn diagrams. Additional analysis examined the case of a linear variant of Euler diagrams, in which set-relationships are represented by one-dimensional lines. The experimental results provide evidence supporting our hypothesis. It is argued that the efficacy of diagrams in supporting syllogistic reasoning crucially depends on the way they represent the relational information contained in categorical sentences.


Efficacy of diagrams Human reasoning Logic and cognition Human experimentation Quantification Categorical syllogism External representation 



Parts of this study were presented at the 6th Diagrams Conference (August, 2010) in Portland and the 7th Diagrams Conference (July, 2012) in Canterbury. This study was partially supported by Grant-in-Aid for JSPS Fellows (21\(\cdot \)7357; 25\(\cdot \)2291) to the first author. The authors would like to thank Mitsuhiro Okada, Atsushi Shimojima, Ryo Takemura, and Keith Stenning for the valuable advice and Philip Johnson-Laird and Malcolm Bauer for permission to use unpublished results.


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Authors and Affiliations

  1. 1.Department of General Systems Studies, Graduate School of Arts and SciencesThe University of TokyoTokyoJapan
  2. 2.Center for Simulation SciencesOchanomizu UniversityTokyoJapan

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