Positive Semantics of Projections in Venn-Euler Diagrams

  • Joseph Yossi Gil
  • John Howse
  • Elena Tulchinsky
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1889)


Venn diagrams and Euler circles have long been used as a means of expressing relationships among sets using visual metaphors such as “disjointness” and “containment” of topological contours. Although the notation is effective in delivering a clear visual modeling of set theoretical relationships, it does not scale well. In this work we study “projection contours”, a new means for presenting sets intersections, which is designed to reduce the clutter in such diagrams. Informally, a projected contour is a contour which describes a set of elements limited to a certain context. The challenge in introducing this notation is in producing precise and consistent semantics for the general case, including a diagram comprising several, possibly interacting, projections, which might even be of the same base set. The semantics investigated here assigns a “positive” meaning to a projection, i.e., based on the list of contours with which it interacts, where contours disjoint to it do not change its semantics. This semantics is produced by a novel Gaussian-like elimination process for solving set equations. In dealing with multiple projections of the same base set, we introduce yet another extension to Venn-Euler diagrams in which the same set can be described by multiple contours.


Venn Diagram Boundary Contour Positive Semantic Euler Diagram Henry VIII 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Joseph Yossi Gil
    • 1
  • John Howse
    • 2
  • Elena Tulchinsky
    • 1
  1. 1.Department of Computer ScienceTechnion-Israel Institute of TechnologyHaifaIsrael
  2. 2.School of Computing and Mathematical SciencesUniversity of BrightonUK

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