Measuring and Reducing Clutter in Euler Diagrams

When modelling with three or more sets Euler diagrams can become crowded or cluttered and their ability to intuitively represent relationships between sets diminishes. Projections are a notation that bring syntactic efficiency to Euler diagrams and the flexibility to represent relationships between sets in a variety of semantically equivalent ways. This paper briefly outlines the first sound and complete system of Euler diagrams to incorporate the notation of projections. It defines a metric for measuring clutter in a diagram and outlines an algorithm that, given a diagram of the system, finds a semantically equivalent diagram(s) with the minimal measure of clutter.