Abstract
Choosing effective representations for a problem and for the person solving it has benefits, including the ability or inability to solve it. We previously devised a novel framework consisting of a language to describe representations and computational methods to analyse them in terms of their formal and cognitive properties. In this paper we demonstrate the application of this framework to a variety of notations including natural languages, formal languages, and diagrams. We show how our framework, and the analysis of representations that it enables, gives us insight into how and why we can select representations which are appropriate for both the task and the user.
This work was supported by the EPSRC grants EP/R030650/1, EP/R030642/1, EP/T019034/1 and EP/T019603/1. We thank Gem Stapleton for her useful comments.
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Notes
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- 2.
These calculations rely on parameters whose values we gave provisionally based on the literature, but which need to be tuned based on empirical data.
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The costs, broken down per cognitive property, can be found in appendix.
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Raggi, D., Stockdill, A., Jamnik, M., Garcia Garcia, G., Sutherland, H.E.A., Cheng, P.CH. (2020). Dissecting Representations. In: Pietarinen, AV., Chapman, P., Bosveld-de Smet, L., Giardino, V., Corter, J., Linker, S. (eds) Diagrammatic Representation and Inference. Diagrams 2020. Lecture Notes in Computer Science(), vol 12169. Springer, Cham. https://doi.org/10.1007/978-3-030-54249-8_11
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