Abstract
People make mistakes. Whether because lines are misdrawn, data are mistabulated, or because coffee is spilled on documents, diagrammatic representations may not be entirely correct. Yet experience tells that such diagrams are not entirely useless.
In this paper, we describe a semantic theory of representation, which naturally explains the utility of erroneous diagrams. In particular, the theory captures the possibility of obtaining true pieces of information from erroneous representations in a reliable manner.
We identify two dimensions along which there are choices in how to read a representation. In one dimension, we may read only part of the representation, avoiding the erroneous information. We call this partial reading. In the other, we focus on abstract properties of the representation, ignoring errors in the precision of the information represented. We call this abstract reading. Along either or both dimensions, true information can be obtained from erroneous diagrams.
The theory is based on Barwise and Seligman’s channel theory, and captures these different modes of readings in terms of multiple representation systems in which a diagram carries information about its target. On this theory, one and the same diagram can be accurate in one system and inaccurate in others, and the reader switches systems when they read the diagram in different modes.
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Notes
- 1.
We thank an anonymous reviewer for drawing attention to the issue of apparent ubiquity of inexact diagrams.
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Shimojima, A., Barker-Plummer, D. (2020). Channel-Theoretic Account of the Semantic Potentials of False Diagrams. 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_10
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