Journal of Logic, Language and Information

, Volume 24, Issue 4, pp 409–455

How Diagrams Can Support Syllogistic Reasoning: An Experimental Study

Article

DOI: 10.1007/s10849-015-9225-4

Cite this article as:
Sato, Y. & Mineshima, K. J of Log Lang and Inf (2015) 24: 409. doi:10.1007/s10849-015-9225-4

Abstract

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.

Keywords

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

Copyright information

© Springer Science+Business Media Dordrecht 2015

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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