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A Generic Approach to Diagrammatic Representation: The Case of Single Feature Indicator Systems

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Diagrammatic Representation and Inference (Diagrams 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9781))

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Abstract

In this paper we take a generic approach to developing a theory of representation systems. Our approach involves giving an abstract formal characterization of a class of representation systems, and proving formal results based on this characterization.

We illustrate this approach by defining and investigating two closely related classes of representations that we call Single Feature Indicator Systems (SFIS), with and without neutrality. Many common representations including tables, such as timetables and work schedules; connectivity graphs, including route maps and circuit diagrams; and statistical charts such as bar graphs, either are SFIS or contain one as a component.

By describing SFIS abstractly, we are able to prove some properties of all of these representation systems by virtue of the fact that the properties can be proved on the basis of the abstract definition only. In particular we show that certain abstract inference rules are sound, and that each instance admits concrete inference rules obtained by instantiating the abstract counterparts.

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Notes

  1. 1.

    We sometime call this the core theory, hence the subscript “c”.

References

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Author information

Authors and Affiliations

  1. Faculty of Culture and Information Science, Doshisha University, 1-3 Tatara-Miyakodani, Kyotanabe, 610-0394, Japan

    Atsushi Shimojima

  2. CSLI/Stanford University, Cordura Hall, 210 Panama Street, Stanford, CA, 94305, USA

    Dave Barker-Plummer

Authors
  1. Atsushi Shimojima
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  2. Dave Barker-Plummer
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Corresponding author

Correspondence to Atsushi Shimojima .

Editor information

Editors and Affiliations

  1. The University of Cambridge , Cambridge, United Kingdom

    Mateja Jamnik

  2. The University of Tokyo , Tokyo, Japan

    Yuri Uesaka

  3. Millersville University , Millersville, Pennsylvania, USA

    Stephanie Elzer Schwartz

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© 2016 Springer International Publishing Switzerland

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Shimojima, A., Barker-Plummer, D. (2016). A Generic Approach to Diagrammatic Representation: The Case of Single Feature Indicator Systems. In: Jamnik, M., Uesaka, Y., Elzer Schwartz, S. (eds) Diagrammatic Representation and Inference. Diagrams 2016. Lecture Notes in Computer Science(), vol 9781. Springer, Cham. https://doi.org/10.1007/978-3-319-42333-3_7

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  • DOI: https://doi.org/10.1007/978-3-319-42333-3_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42332-6

  • Online ISBN: 978-3-319-42333-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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