The Efficacy of Euler and Venn Diagrams in Deductive Reasoning: Empirical Findings

  • Yuri Sato
  • Koji Mineshima
  • Ryo Takemura
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6170)


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.


Reasoning Process Venn Diagram Deductive Reasoning Reasoning Task Linguistic Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 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
  2. Bauer, M., Johnson-Laird, P.N.: How diagrams can improve reasoning. Psychology Science 4(6), 372–378 (1993)CrossRefGoogle Scholar
  3. Calvillo, P.D., DeLeeuw, K., Revlin, R.: Deduction with Euler Circles: Diagrams That Hurt. In: Barker-Plummer, D., Cox, R., Swoboda, N. (eds.) Diagrams 2006. LNCS (LNAI), vol. 4045, pp. 199–203. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. Chapman, L., Chapman, J.: Atmosphere effect re-examined. Journal of Experimental Psychology 58(3), 220–226 (1959)CrossRefGoogle Scholar
  5. Dickstein, L.S.: The effect of figure on syllogistic reasoning. Memory and Cognition 6, 76–83 (1978)CrossRefGoogle Scholar
  6. Dickstein, L.S.: The meaning of conversion in syllogistic reasoning. Bulletin of the Psychonomic Society 18(3), 135–138 (1981)MathSciNetCrossRefGoogle Scholar
  7. Dobson, M.: Information enforcement and learning with interactive graphical systems. Learning and Instruction 9, 365–390 (1999)CrossRefGoogle Scholar
  8. 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
  9. Gergonne, J.D.: Essai de dialectique rationelle. Annuales de Mathematiques pures et appliqukes 7, 189–228 (1817)Google Scholar
  10. Gurr, C.A., Lee, J., Stenning, K.: Theories of diagrammatic reasoning: distinguishing component problems. Minds and Machines 8, 533–557 (1998)CrossRefGoogle Scholar
  11. Hammer, E.: Logic and Visual Information. CSLI Publications, Stanford (1995)zbMATHGoogle Scholar
  12. Hammer, E., Shin, S.: Euler’s visual logic. History and Philosophy of Logic 19, 1–29 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  13. Howse, J., Stapleton, G., Taylor, J.: Spider diagrams. LMS Journal of Comrutation and Mathematics 8, 145–194 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  14. Johnson-Laird, P.N.: Mental Models: Towards a cognitive science of language, inference, and consciousness. Harvard University Press, Cambridge (1983)Google Scholar
  15. Larkin, J., Simon, H.: Why a diagram is (sometimes) worth 10,000 words. Cognitive Science 11, 65–99 (1987)CrossRefGoogle Scholar
  16. Mineshima, K., Okada, M., Sato, Y., Takemura, R.: Diagrammatic reasoning system with Euler circles: theory and experiment design. In: Stapleton, G., Howse, J., Lee, J. (eds.) Diagrams 2008. LNCS (LNAI), vol. 5223, pp. 188–205. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  17. Mineshima, K., Okada, M., Takemura, R.: A diagrammatic inference system with Euler circles (2009) (submitted to a journal)Google Scholar
  18. Newstead, S., Griggs, R.: Drawing inferences from quantified statements: A study of the square of opposition. Journal of Verbal Learning and Verbal Behavior 22, 535–546 (1983)CrossRefGoogle Scholar
  19. 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
  20. Scaife, M., Rogers, Y.: External cognition. International Journal of Human - Computer Studies 45, 185–213 (1996)CrossRefGoogle Scholar
  21. 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
  22. Shimojima, A.: On the Efficacy of Representation. PhD thesis, Indiana University (1996b)Google Scholar
  23. Shin, S.-J.: The Logical Status of Diagrams. Cambridge University Press, Cambridge (1994)zbMATHGoogle Scholar
  24. Sloman, A.: Interactions between philosophy and ai: the role of intuition and non-logical reasoning in intelligence. Artificial Intelligence 2, 209–225 (1971)CrossRefGoogle Scholar
  25. 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
  26. Stenning, K.: The cognitive consequences of modality assignment for educational communication: the picture in logic teaching. Learning and Instruction 9, 391–410 (1999)CrossRefGoogle Scholar
  27. Stenning, K.: Seeing Reason: Image and Language in Learning to Think. Oxford University Press, Oxford (2002)CrossRefGoogle Scholar
  28. Stenning, K., Oberlander, J.: A cognitive theory of graphical and linguistic reasoning. Cognitive Science 19, 97–140 (1995)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Yuri Sato
    • 1
  • Koji Mineshima
    • 1
  • Ryo Takemura
    • 1
  1. 1.Department of PhilosophyKeio UniversityMinato-kuJapan

Personalised recommendations