Positive Semantics of Projections in Venn-Euler Diagrams

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 e ective 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 ...

• Type: Conference
• Year: 2000
• Where: DIAGRAMS
• Authors: Joseph Gil, John Howse, Elena Tulchinsky
• Keywords: Artificial Intelligence, Clear Visual Modeling, DIAGRAMS 2000, Set Theoretical Relationships, Topological Contours