Corresponding regions in Euler diagrams

John Howse, Gem Stapleton, Jean Flower, John Taylor

Research output: Chapter in Book/Conference proceeding with ISSN or ISBNConference contribution with ISSN or ISBNResearchpeer-review

Abstract

Euler diagrams use topological properties to represent set-theoretical concepts and thus are `intuitive' to some people. When reasoning with Euler diagrams, it is essential to have a notion of correspondence among the regions in different diagrams. At the semantic level, two regions correspond when they represent the same set. However, we wish to construct a purely syntactic definition of corresponding regions, so that reasoning can take place entirely at the diagrammatic level. This task is interesting in Euler diagrams because some regions of one diagram may be missing from another. We construct the correspondence relation from `zones' or minimal regions, introducing the concept of `zonal regions' for the case in which labels may differ between diagrams. We show that the relation is an equivalence relation and that it is a generalization of the counterpart relations introduced by Shin and Hammer.
Original languageEnglish
Title of host publicationDiagrammatic Representation and Inference, Second International Conference, Diagrams 2002
Place of PublicationBerlin Heidelberg
PublisherSpringer-Verlag
Pages146-160
Number of pages15
Volume2317
ISBN (Print)9783540435617
DOIs
Publication statusPublished - 1 Jan 2002
EventDiagrammatic Representation and Inference, Second International Conference, Diagrams 2002 - Callaway Gardens, GA, USA, April 18-20, 2002
Duration: 1 Jan 2002 → …

Publication series

NameLecture Notes in Computer Science

Conference

ConferenceDiagrammatic Representation and Inference, Second International Conference, Diagrams 2002
Period1/01/02 → …

Fingerprint

Euler
Diagram
Correspondence
Reasoning
Equivalence relation
Topological Properties
Intuitive
Concepts

Keywords

  • Visual languages
  • Euler diagrams

Cite this

Howse, J., Stapleton, G., Flower, J., & Taylor, J. (2002). Corresponding regions in Euler diagrams. In Diagrammatic Representation and Inference, Second International Conference, Diagrams 2002 (Vol. 2317, pp. 146-160). (Lecture Notes in Computer Science). Berlin Heidelberg: Springer-Verlag. https://doi.org/10.1007/3-540-46037-3_7
Howse, John ; Stapleton, Gem ; Flower, Jean ; Taylor, John. / Corresponding regions in Euler diagrams. Diagrammatic Representation and Inference, Second International Conference, Diagrams 2002. Vol. 2317 Berlin Heidelberg : Springer-Verlag, 2002. pp. 146-160 (Lecture Notes in Computer Science).
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Howse, J, Stapleton, G, Flower, J & Taylor, J 2002, Corresponding regions in Euler diagrams. in Diagrammatic Representation and Inference, Second International Conference, Diagrams 2002. vol. 2317, Lecture Notes in Computer Science, Springer-Verlag, Berlin Heidelberg, pp. 146-160, Diagrammatic Representation and Inference, Second International Conference, Diagrams 2002, 1/01/02. https://doi.org/10.1007/3-540-46037-3_7

Corresponding regions in Euler diagrams. / Howse, John; Stapleton, Gem; Flower, Jean; Taylor, John.

Diagrammatic Representation and Inference, Second International Conference, Diagrams 2002. Vol. 2317 Berlin Heidelberg : Springer-Verlag, 2002. p. 146-160 (Lecture Notes in Computer Science).

Research output: Chapter in Book/Conference proceeding with ISSN or ISBNConference contribution with ISSN or ISBNResearchpeer-review

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N2 - Euler diagrams use topological properties to represent set-theoretical concepts and thus are `intuitive' to some people. When reasoning with Euler diagrams, it is essential to have a notion of correspondence among the regions in different diagrams. At the semantic level, two regions correspond when they represent the same set. However, we wish to construct a purely syntactic definition of corresponding regions, so that reasoning can take place entirely at the diagrammatic level. This task is interesting in Euler diagrams because some regions of one diagram may be missing from another. We construct the correspondence relation from `zones' or minimal regions, introducing the concept of `zonal regions' for the case in which labels may differ between diagrams. We show that the relation is an equivalence relation and that it is a generalization of the counterpart relations introduced by Shin and Hammer.

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Howse J, Stapleton G, Flower J, Taylor J. Corresponding regions in Euler diagrams. In Diagrammatic Representation and Inference, Second International Conference, Diagrams 2002. Vol. 2317. Berlin Heidelberg: Springer-Verlag. 2002. p. 146-160. (Lecture Notes in Computer Science). https://doi.org/10.1007/3-540-46037-3_7