Corresponding regions in Euler diagrams

Howse, John, Stapleton, Gem, Flower, Jean and Taylor, John (2002) Corresponding regions in Euler diagrams In: Diagrammatic Representation and Inference, Second International Conference, Diagrams 2002, Callaway Gardens, GA, USA, April 18-20, 2002.

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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.

Item Type: Contribution to conference proceedings in the public domain ( Full Paper)
Uncontrolled Keywords: Visual languages; Euler diagrams
Subjects: G000 Computing and Mathematical Sciences
DOI (a stable link to the resource): 10.1007/3-540-46037-3_7
Faculties: Faculty of Science and Engineering > School of Computing, Engineering and Mathematics > Visual Modelling
Depositing User: Converis
Date Deposited: 26 Nov 2007
Last Modified: 20 Apr 2015 15:46

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