The Efficacy of Euler and Venn Diagrams in Deductive Reasoning: Empirical Findings
This paper discusses the cognitive differences between reasoning with Euler diagrams and reasoning with Venn diagrams. We test subjects’ performances in syllogism solving in case where these two types of diagrams are used. We conduct an analysis on the role played by the conventional devices of each diagram in reasoning processes. Based on this, we hypothesize that of the two types of diagrams, only Euler diagrams could guide subjects without prior knowledge of their inferential strategies for combining diagrams. To test this hypothesis, subjects in our experiment are only provided with instructions on the meanings of diagrams and required to solve reasoning tasks without any instruction on the solving strategies. Our experimental results support the hypothesis and indicate that Euler diagrams can not only contribute to subjects’ correct interpretation of categorical sentences used but also play a crucial role in reasoning processes themselves.
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- Barwise, J., Etchemendy, J.: Visual information and valid reasoning. In: Allwein, G., Barwise, J. (eds.) Logical Reasoning with Diagrams, pp. 3–26. Oxford University Press, Oxford (1991)Google Scholar
- Erickson, J.R.: A set analysis theory of behavior in formal syllogistic reasoning tasks. In: Solso, R. (ed.) Loyola Symposium on Cognition, vol. 2. Erlbaum, Mahwah (1974)Google Scholar
- Gergonne, J.D.: Essai de dialectique rationelle. Annuales de Mathematiques pures et appliqukes 7, 189–228 (1817)Google Scholar
- Johnson-Laird, P.N.: Mental Models: Towards a cognitive science of language, inference, and consciousness. Harvard University Press, Cambridge (1983)Google Scholar
- Mineshima, K., Okada, M., Takemura, R.: A diagrammatic inference system with Euler circles (2009) (submitted to a journal)Google Scholar
- Rizzo, A., Palmonari, M.: The mediating role of artifacts in deductive reasoning. In: Poster Presented at the 27th Annual Conference of the Cognitive Science Society (2005)Google Scholar
- Shimojima, A.: Operational constraints in diagrammatic reasoning. In: Allwein, G., Barwise, J. (eds.) Logical Reasoning with Diagrams, pp. 27–48. Oxford University Press, Oxford (1996a)Google Scholar
- Shimojima, A.: On the Efficacy of Representation. PhD thesis, Indiana University (1996b)Google Scholar
- Stapleton, G.: A survey of reasoning systems based on Euler diagrams. In: Euler Diagrams 2004. ENTCS, vol. 134, pp. 127–151. Elsevier, Amsterdam (2005)Google Scholar