Abstract
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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References
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)
Bauer, M., Johnson-Laird, P.N.: How diagrams can improve reasoning. Psychology Science 4(6), 372–378 (1993)
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)
Chapman, L., Chapman, J.: Atmosphere effect re-examined. Journal of Experimental Psychology 58(3), 220–226 (1959)
Dickstein, L.S.: The effect of figure on syllogistic reasoning. Memory and Cognition 6, 76–83 (1978)
Dickstein, L.S.: The meaning of conversion in syllogistic reasoning. Bulletin of the Psychonomic Society 18(3), 135–138 (1981)
Dobson, M.: Information enforcement and learning with interactive graphical systems. Learning and Instruction 9, 365–390 (1999)
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)
Gergonne, J.D.: Essai de dialectique rationelle. Annuales de Mathematiques pures et appliqukes 7, 189–228 (1817)
Gurr, C.A., Lee, J., Stenning, K.: Theories of diagrammatic reasoning: distinguishing component problems. Minds and Machines 8, 533–557 (1998)
Hammer, E.: Logic and Visual Information. CSLI Publications, Stanford (1995)
Hammer, E., Shin, S.: Euler’s visual logic. History and Philosophy of Logic 19, 1–29 (1998)
Howse, J., Stapleton, G., Taylor, J.: Spider diagrams. LMS Journal of Comrutation and Mathematics 8, 145–194 (2005)
Johnson-Laird, P.N.: Mental Models: Towards a cognitive science of language, inference, and consciousness. Harvard University Press, Cambridge (1983)
Larkin, J., Simon, H.: Why a diagram is (sometimes) worth 10,000 words. Cognitive Science 11, 65–99 (1987)
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)
Mineshima, K., Okada, M., Takemura, R.: A diagrammatic inference system with Euler circles (2009) (submitted to a journal)
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)
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)
Scaife, M., Rogers, Y.: External cognition. International Journal of Human - Computer Studies 45, 185–213 (1996)
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)
Shimojima, A.: On the Efficacy of Representation. PhD thesis, Indiana University (1996b)
Shin, S.-J.: The Logical Status of Diagrams. Cambridge University Press, Cambridge (1994)
Sloman, A.: Interactions between philosophy and ai: the role of intuition and non-logical reasoning in intelligence. Artificial Intelligence 2, 209–225 (1971)
Stapleton, G.: A survey of reasoning systems based on Euler diagrams. In: Euler Diagrams 2004. ENTCS, vol. 134, pp. 127–151. Elsevier, Amsterdam (2005)
Stenning, K.: The cognitive consequences of modality assignment for educational communication: the picture in logic teaching. Learning and Instruction 9, 391–410 (1999)
Stenning, K.: Seeing Reason: Image and Language in Learning to Think. Oxford University Press, Oxford (2002)
Stenning, K., Oberlander, J.: A cognitive theory of graphical and linguistic reasoning. Cognitive Science 19, 97–140 (1995)
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Sato, Y., Mineshima, K., Takemura, R. (2010). The Efficacy of Euler and Venn Diagrams in Deductive Reasoning: Empirical Findings. In: Goel, A.K., Jamnik, M., Narayanan, N.H. (eds) Diagrammatic Representation and Inference. Diagrams 2010. Lecture Notes in Computer Science(), vol 6170. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14600-8_6
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DOI: https://doi.org/10.1007/978-3-642-14600-8_6
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