Defining Euler diagrams: simple or what?

Andrew Fish, Gem Stapleton

Research output: Contribution to conferenceAbstract

Abstract

Euler diagrams are emerging as a powerful tool in a variety of application areas, such as logical reasoning and for representing statistical data. In order to be a reliable means of visualizing information, Euler diagrams must have a firm theoretical underpinning and various formalizations have been given. We illustrate, via pertinent examples, misconceptions and pitfalls that occur as a result of imposing certain well-formedness conditions. In particular, we consider the effect on the interpretation of diagrams, on giving precise definitions and on reasoning systems. First, we highlight some consequences of stipulating that the closed curves must be simple. Secondly, we demonstrate some of the difficulties associated with choosing not to enforce simplicity. We also consider the consequences of defining Euler diagrams inductively and enforcing the connectedness of minimal regions. Choices made when formalizing Euler diagrams can have a profound effect on reasoning systems due to the potential inability to draw a diagram which represents a given collection of set intersections. The issues raised are likely to be interesting to any researcher who is defining diagrams based on closed curves.
Original languageEnglish
Pages109-111
Number of pages3
DOIs
Publication statusPublished - 1 Jan 2006
EventProceedings of the 4th International Conference, Diagrams 2006 - Stanford, CA, USA, 28-30 June, 2006
Duration: 1 Jan 2006 → …

Conference

ConferenceProceedings of the 4th International Conference, Diagrams 2006
Period1/01/06 → …

Bibliographical note

The original publication is available at www.springerlink.com

Keywords

  • Euler diagrams

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