Abstract
In this paper we are concerned with logical and cognitive aspects of reasoning with Euler circles. We give a proof-theoretical analysis of diagrammatic reasoning with Euler circles involving unification and deletion rules. Diagrammatic syllogistic reasoning is characterized as a particular class of the general diagrammatic proofs. Given this proof-theoretical analysis, we present some conjectures on cognitive aspects of reasoning with Euler diagrams. Then we propose a design of experiment for a cognitive psychological study.
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References
Ando, J., Shikishima, C., Hiraishi, K., Sugimoto, Y., Takemura, R., Okada, M.: At the crossroads of logic, psychology, and behavioral genetics. In: Okada, M., et al. (eds.) Reasoning and Cognition, pp. 19–36. Keio University Press (2006)
Braine, M., O’Brien, D.: Mental logic. Lawrence Erlbaum Associates, Mahwah (1998)
Blackett, D.: Elementary Topology. Academic Press, London (1983)
Calvillo, P.D., DeLeeuw, K., Revlin, R.: Deduction with Euler Circles. In: Baker-Plummer, D., et al. (eds.) Diagrams 2006. LNCS (LNAI), vol. 4045, pp. 199–203. Springer, Heidelberg (2006)
Chater, N., Oakford, M.: The probability heuristics model of syllogistic reasoning. Cognitive Psychology 38, 191–258 (1999)
Dickstein, L.S.: The effect of figure on syllogistic reasoning. Memory and Cognition 6, 76–83 (1978)
Euler, L.: Lettres à une Princesse d’Allemagne sur Divers Sujets de Physique et de Philosophie. De l’Académie des Sciences, Saint-Pétersbourg (1768)
Evans, J., Newstead, S.E., Byrne, R.: Human Reasoning. Lawrence Erlbaum Associates, Mahwah (1993)
Hammer, E.: Logic and Visual Information. CSLI Publications (1995)
Hammer, E., Shin, S.: Euler’s visual logic. History and Philosophy of Logic 19, 1–29 (1998)
Meyer, B.: Diagrammatic evaluation of visual mathematical notations. In: Anderson, M., Meyer, B., Olivier, P. (eds.) Diagrammatic Representation and Reasoning, pp. 261–277. Springer, Heidelberg (2001)
Peirce, C.S.: Collected Papers IV. Harvard University Press (1897/1933)
Rips, L.J.: The Psychology of Proof. MIT Press, Cambridge (1994)
Rizzo, A., Palmonari, M.: The mediating role of artifacts in deductive reasoning. In: Poster in the 27th Annual Conference of the Cognitive Science Society (2005)
Sato, Y., Takemura, R., Mineshima, K., Shikishima, C., Sugimoto, Y., Ando, J., Okada, M.: Some remarks on deductive syllogistic reasoning studies. In: Okada, M., Takemura, R., Ando, J. (eds.) Reports on Interdisciplinary Logic Inference Studies, pp. 3–32. Keio University Press (2008)
Shin, S.-J.: The Logical Status of Diagrams. Cambridge University Press, Cambridge (1994)
Stapleton, G.: A survey of reasoning systems based on Euler diagrams. In: Euler Diagrams 2004. ENTCS, vol. 134, pp. 127–151. Elsevier, Amsterdam (2005)
Stapleton, G., Rodgers, P., Howse, J., Taylor, J.: Properties of Euler diagrams. In: Stapleton, G., Rodgers, P., Howse, J. (eds.) Proc. Layout of Software Engineering Diagrams. ECEASST, vol. 7, pp. 2–16 (2007)
Stenning, K.: Seeing Reason. Oxford University Press, Oxford (2002)
Stenning, K., Oberlander, J.: A cognitive theory of graphical and linguistic reasoning. Cognitive Science 19, 97–140 (1995)
Stenning, K., van Lambalgen, M.: Human Reasoning and Cognitive Science. MIT Press, Cambridge (2007)
Swoboda, N., Allwein, G.: Using DAG transformations to verify Euler/Venn homogeneous and Euler/Venn FOL heterogeneous rules of inference. Journal on Software and System Modeling 3(2), 136–149 (2004)
Swoboda, N., Allwein, G.: Heterogeneous reasoning with Euler/Venn diagrams containing named constants and FOL. ENTCS, vol. 134, pp. 153–187. Elsevier, Amsterdam (2005)
Venn, J.: Symbolic Logic. Macmillan, Basingstoke (1881)
Zhang, J., Norman, D.A.: Representations in distributed cognitive tasks. Cognitive Science 18(1), 87–122 (1994)
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Mineshima, K., Okada, M., Sato, Y., Takemura, R. (2008). Diagrammatic Reasoning System with Euler Circles: Theory and Experiment Design. In: Stapleton, G., Howse, J., Lee, J. (eds) Diagrammatic Representation and Inference. Diagrams 2008. Lecture Notes in Computer Science(), vol 5223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87730-1_19
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DOI: https://doi.org/10.1007/978-3-540-87730-1_19
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