Abstract
Shimojima and Katagiri have demonstrated that diagrams reduce “inferential load” during reasoning by scaffolding visual-spatial aspects of memory. In response, we wondered why, if this is true, that proofs are usually text based? The purpose of this paper is to explore ergonomic affordances of text that may encourage its use in the communication of proofs by building on prior work in attention. We claim that textual notations may focus a reasoner’s “spotlight” of attention through serialized sequential chunks, whereas many diagrams may “diffuse” attention and that a diagrammatic notation system that serialized information in chunks amenable to focused attention could leverage the power of textual notations. We present such an example through a case study focused on generalized constraint diagrams, a visual logic with attributes that may support focused attention and extract ergonomic principles that may transcend each notation system.
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References
Ballard, D.H., Hayhoe, M.M., Pook, P.K., Rao, R.P.N.: Deictic codes for the embodiment of cognition. Behavioral and Brain Sciences 20, 723–767 (1995)
Barwise, J., Etchemendy, J.: Visual information and valid reasoning. In: Logical Reasoning with Diagrams, pp. 3–25. Oxford University Press, Inc., Oxford (1996)
Coppin, P., Hockema, S.: A cognitive exploration of the “non-visual” nature of geometric proofs. In: Cox, P., Fish, A., Howse, J. (eds.) Visual Languages and Logic, pp. 81–95 (September 2009)
Gil, J., Howse, J., Kent, S.: Towards a formalization of constraint diagrams. In: Proc. IEEE Symposia on Human-Centric Computing (HCC 2001), Stresa, Italy, pp. 72–79. IEEE Computer Society Press, Los Alamitos (2001)
Larkin, J.H., Simon, H.A.: Why a diagram is (sometimes) worth ten thousand words. Cognitive Science 11(1), 65–100 (1987)
Lemon, O., de Rijke, M., Shimojima, A.: Editorial: Efficacy of diagrammatic reasoning. Journal of Logic, Language and Information 8(3), 265–271 (1999)
Mumma, J.: Ensuring generality in euclid’s diagrammatic arguments. In: Diagrammatic Representation and Inference, pp. 222–235 (2008)
Mumma, J.: Proofs, pictures, and euclid. In: Synthese (2009)
Scholl, B.J.: Objects and attention: The state of the art. Cognition 80(1-2), 1–46 (2001)
Shimojima, A., Katagiri, Y.: An Eye-Tracking study of exploitations of spatial constraints in diagrammatic reasoning. In: Diagrammatic Representation and Inference, pp. 74–88 (2008)
Spivey, M.J., Geng, J.J.: Oculomotor mechanisms activated by imagery and memory: eye movements to absent objects. Psychological Research 65(4), 235–241 (2001)
Stapleton, G., Delaney, A.: Evaluating and generalizing constraint diagrams. Journal of Visual Languages and Computing 19(4), 499–521 (2008)
Tennant, N.: The withering away of formal semantics? Mind & Language 1(4), 302–318 (1986)
Treisman, A.M., Gelade, G.: A feature-integration theory of attention. Cognitive Psychology 12(1), 97–136 (1980)
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Coppin, P., Burton, J., Hockema, S. (2010). An Attention Based Theory to Explore Affordances of Textual and Diagrammatic Proofs. 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_27
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DOI: https://doi.org/10.1007/978-3-642-14600-8_27
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