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Towards a diagrammatic classification

Published online by Cambridge University Press:  24 July 2013

Valeria Giardino
Valeria Giardino*
Affiliation:
Institut Jean Nicod (CNSR-EHESS-ENS), Pavillon Jardin, Ecole Normale Supèrieure, 29, rue d'Ulm, 75005 Paris, France; e-mail: Valeria.Giardino@ens.fr
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Abstract

In this article I present and discuss some criteria to provide a diagrammatic classification. Such a classification is of use for exploring in detail the domain of diagrammatic reasoning. Diagrams can be classified in terms of the use we make of them—static or dynamic—and of the correspondence between their space and the space of the data they are intended to represent. The investigation is not guided by the opposition visual vs. non-visual, but by the idea that there is a continuous interaction between diagrams and language. Diagrammatic reasoning is characterized by a duality, since it refers both to an object, the diagram, having its spatial characteristics, and to a subject, the user, who interprets them. A particular place in the classification is occupied by constructional diagrams, which exhibit for the user instructions for the application of some procedures.

Type
Articles
Information
The Knowledge Engineering Review , Volume 28 , Special Issue 3: Visualization, Visual Representation and Reasoning , September 2013 , pp. 237 - 248
Copyright
Copyright © Cambridge University Press 2013 

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References

Barwise, J., Etchemendy, J. 1996. Visual information and valid reasoning. In Logical Reasoning with Diagrams, Allwein, G. & Barwise, J. (eds). Oxford University Press, 3–25.Google Scholar
Booker, P. J. 1963. A History of Engineering Drawing. Chatto and Windus.Google Scholar
Derrida, J. [1967] 1974. Of Grammatology. The Johns Hopkins University Press.Google Scholar
Ferguson, E. S. 1992. Engineering and the Minds Eye. MIT Press.Google Scholar
Fischbein, E. 1987. Intuition in Science and Mathematics. Kluwer.Google Scholar
Grosholz, E. R. 2007. Representation and Productive Ambiguity in Mathematics and the Sciences. Oxford University Press.CrossRefGoogle Scholar
Lakoff, G., Nuñez, R. 2001. Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being. Basic Books.Google Scholar
Larkin, J. H., Simon, H. A. 1995. Why a diagram is (sometimes) worth ten thousand words. In Diagrammatic Reasoning: Cognitive and Computational Perspectives, Chandrasekaran, B., Glasgow, J. & Hari Narayan, N. (eds). AAAI Press; The MIT Press, 69–109.Google Scholar
Maynard, P. 2005. Drawing Distinctions: The Variety of Graphic Expression. Cornell University Press.CrossRefGoogle Scholar
Nelsen, R. 1997. Proofs Without Words: Exercises in Visual Thinking, Classroom Resource Materials, The Mathematical Association of America.Google Scholar
Nelsen, R. 2001. Proofs Without Words II: More Exercises in Visual Thinking, Classroom Resource Materials, The Mathematical Association of America.Google Scholar
Peirce, C. S. 1885. On the algebra of logic: a contribution to the philosophy of notation. In The Writings of Charles S. Peirce (1980–2000), Vol. 5, Christian Kloesel et al. (eds). Indiana University Press, 162–189.Google Scholar
Peirce, C. S. 1906. Prolegomena to an apology for pragmaticism. The Monist 16(4), 492–546.CrossRefGoogle Scholar
Pinker, S. 1990. A theory of graph comprehension. In Artificial Intelligence and the Future of Testing, Feedle, R. (ed.). Hillsdale, NJ: Erlbaum, 73–126.Google Scholar
Polya, G. 1945. How to Solve It: A New Aspect of Mathematical Method. Princeton University Press.CrossRefGoogle Scholar
Sheffer, H. M. 1926. Review of A. N. Whitehead and B. Russell, Principia Mathematica, in ‘Isis’ 8, 226–231.Google Scholar
Shimojima, A. 2001. The graphic-linguistic distinction. Artificial Intelligence Review 15, 5–27.Google Scholar
Shin, S.-J. 2004. Heterogeneous reasoning and its logic. Bulletin of Symbolic Logic 10(1), 86–106.CrossRefGoogle Scholar
Stenning, K., Lemon, O. 2001. Aligning logical and psychological perspectives on diagrammatic reasoning. Artificial Intelligence Review 15, 29–62.CrossRefGoogle Scholar
Stenning, K., Inder, R., Neilson, I. 1995. Applying semantic concepts to analysing medias and modalities. In Diagrammatic Reasoning: Cognitive and Computational Perspectives, Chandrasekaran, B., Glasgow, J. & Hari Narayan, N. (eds). AAAI Press; The MIT Press, 303–338.Google Scholar
Tennant, D. 1984. The withering away of formal semantics? Mind and Language 1, 302–318.CrossRefGoogle Scholar
Tufte, E. [1983] 2001. The Visual Display of Quantitative Information, 2nd edition. Graphics Press.Google Scholar
Willats, J. 1997. Art and Representation: New Principles in the Analysis of Pictures. Princeton University Press.Google Scholar
Wittgenstein, L. [1953] 2001. Philosophical Investigations. Blackwell Publishing.Google Scholar
Wollheim, R. 2003. In difense of seeing-in. In Looking into Pictures. An Interdisciplinary Approach to Pictorial Space, Hecht, H., Schwartz, R. & Atherton, M. (eds). The MIT Press, 3–15.CrossRefGoogle Scholar