# Defining Euler Diagrams: Simple or What?

• Andrew Fish
• Gem Stapleton
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4045)

## Abstract

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]).

## Keywords

Logical Reasoning Closed Curf Minimal Region Simple Closed Curf Reasoning Rule
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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