Defining Euler Diagrams: Simple or What?

  • Andrew Fish
  • Gem Stapleton
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4045)


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]).


Logical Reasoning Closed Curf Minimal Region Simple Closed Curf Reasoning Rule 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Andrew Fish
    • 1
  • Gem Stapleton
    • 1
  1. 1.The Visual Modelling GroupUniversity of BrightonBrightonUK

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