Nesting in Euler Diagrams

This paper outlines the notion of nesting in Euler diagrams, and how nesting affects the interpretation and construction of such diagrams. After setting up the necessary definitions for Euler diagrams at concrete syntax and abstract levels, the notion of nestedness is introduced at the concrete level, then an equivalent notion is given at the abstract level. The natural progression to the diagram semantics is explored. In the final sections, we describe how this work supports tool-building for diagrams, and how effective we might expect this support to be in terms of the proportion of nested diagrams.