Defining Euler Diagrams: Simple or What?

摘要

Many diagrammatic languages are based on closed curves, and various wellformedness conditions are often enforced (such as the curves are simple). We use the term Euler diagram in a very general sense, to mean any .nite collection of closed curves which express information about intersection, containment or disjointness. Euler diagrams have many applications, including the visualization of statistical data [1], displaying the results of database queries [6] and logical reasoning [2, 4, 5]. Three important questions are: for any given piece of information can we draw a diagram representing that information, can we reliably interpret the diagrams and can we reason diagrammatically about that information? The desirable answer to all three questions is yes, but these desires can be con.icting. In this article we investigate the e.ects of enforcing the simplicity condition (as in [1, 2, 6]) or not enforcing it (as in [4, 5]).