Abstract
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.
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