Abstractions of Euler diagrams

Euler diagrams are a graphical means to represent information. Providing an abstraction captures the pertinent information precisely, ignoring irrelevant details (where relevancy is dependent upon the application domain). We present two new abstractions and show that these are equivalent to a standard existing (zone-based) representation. Examples illustrate the potential usefulness of different abstractions in various areas, such as: identifying properties like nestedness or drawability, expressing the semantics in a more readable manner, and in the layout of diagrams.