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Defining Euler Diagrams: Simple or What?

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Diagrammatic Representation and Inference (Diagrams 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4045))

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Abstract

Many diagrammatic languages are based on closed curves, and various wellformedness conditions are often enforced (such as the curves are simple). We use the term Euler diagram in a very general sense, to mean any .nite collection of closed curves which express information about intersection, containment or disjointness. Euler diagrams have many applications, including the visualization of statistical data [1], displaying the results of database queries [6] and logical reasoning [2, 4, 5]. Three important questions are: for any given piece of information can we draw a diagram representing that information, can we reliably interpret the diagrams and can we reason diagrammatically about that information? The desirable answer to all three questions is yes, but these desires can be con.icting. In this article we investigate the e.ects of enforcing the simplicity condition (as in [1, 2, 6]) or not enforcing it (as in [4, 5]).

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References

  1. Chow, S., Ruskey, F.: Drawing area-proportional Venn and Euler diagrams. In: Liotta, G. (ed.) GD 2003. LNCS, vol. 2912, pp. 466–477. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  2. Hammer, E.: Logic and Visual Information. CSLI Publications, Stanford (1995)

    MATH  Google Scholar 

  3. Howse, J., Stapleton, G., Taylor, J.: Spider diagrams. LMS Journal of Computation and Mathematics 8, 145–194 (2005)

    MATH  MathSciNet  Google Scholar 

  4. Shin, S.-J.: The Logical Status of Diagrams. Cambridge University Press, Cambridge (1994)

    MATH  Google Scholar 

  5. Swoboda, N., Allwein, G.: Heterogeneous reasoning with Euler/Venn diagrams containing named constants and FOL. In: Proceedings of Euler Diagrams 2004. ENTCS, vol. 134. Elsevier Science, Amsterdam (2005)

    Google Scholar 

  6. Verroust, A., Viaud, M.-L.: Ensuring the drawability of Euler diagrams for up to eight sets. In: Blackwell, A.F., Marriott, K., Shimojima, A. (eds.) Diagrams 2004. LNCS (LNAI), vol. 2980, pp. 128–141. Springer, Heidelberg (2004)

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Authors and Affiliations

  1. The Visual Modelling Group, University of Brighton, Brighton, UK

    Andrew Fish & Gem Stapleton

Authors
  1. Andrew Fish
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  2. Gem Stapleton
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Editors and Affiliations

  1. Stanford University,, 94305-4101, Stanford, CA, USA

    Dave Barker-Plummer

  2. Representation and Cognition Group, University of Sussex, Brighton, UK

    Richard Cox

  3. Universidad Politécnica de Madrid, Boadilla del Monte, 28660, Madrid, Spain

    Nik Swoboda

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© 2006 Springer-Verlag Berlin Heidelberg

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Fish, A., Stapleton, G. (2006). Defining Euler Diagrams: Simple or What?. In: Barker-Plummer, D., Cox, R., Swoboda, N. (eds) Diagrammatic Representation and Inference. Diagrams 2006. Lecture Notes in Computer Science(), vol 4045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11783183_14

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  • DOI: https://doi.org/10.1007/11783183_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35623-3

  • Online ISBN: 978-3-540-35624-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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