Projections in Venn-Euler diagrams

Abstract

Venn diagrams and Euler circles have long been used to express constraints on sets and their relationships with other sets. However, these notations can get very cluttered when we consider many closed curves or contours. In order to reduce this clutter, and to focus attention within the diagram appropriately, the notion of a projected contour, or projection, is introduced. Informally, a projected contour is a contour that describes a set of elements limited to a certain context. Through a series of examples, we develop a formal semantics of projections and discuss the issues involved in introducing these.