Well-matchedness in Euler Diagrams Mithileysh Sathiyanarayanan and John Howse Visual Modelling Group, University of Brighton, UK {M.Sathiyanarayanan,John.Howse}@brighton.ac.uk Abstract. Euler diagrams are used for visualizing set-based informa- tion. Closed curves represent sets and the relationship between the curves correspond to relationships between sets. A notation is well-matched to meaning when its syntactic relationships are reflected in the seman- tic relationships being represented. Euler diagrams are said to be well- matched to meaning because, for example, curve containment corre- sponds to the subset relationship. In this paper we explore the concept of well-matchedness in Euler diagrams, considering different levels of well-matchedness. We also discuss how the properties, sometimes called well-formedness conditions, of an Euler diagram relate to the levels of well-matchedness. 1 Introduction An Euler diagram is a collection of closed curves in the plane. Curves repre- sent sets and the spatial relationships between the curves represent relationships between the sets. The lefthand diagram in fig. 1 represents the set-theoretic re- lationships C is a subset of A and A is disjoint from B. The righthand diagram in fig. 1 is a Venn diagram and has the same semantics as this Euler diagram. A Venn diagram contains all possible intersections of curves and shading is used to indicate empty sets. For example, the intersection between the curves labelled A and B is shaded indicating that the sets A and B are disjoint. The only part of the curve labelled C that is unshaded is that part within A and outside B indicating that C is a subset of A. Fig. 1. An Euler diagram and an equivalent Venn diagram. 16