Skip to main content
Springer Nature Link
Log in

Euler Diagram Decomposition

  • Conference paper
Diagrammatic Representation and Inference (Diagrams 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5223))

Included in the following conference series:

Abstract

Euler diagrams are a common visual representation of set-theoretic statements, and they have been used for visualising the results of database search queries or as the basis of diagrammatic logical constraint languages for use in software specification. Such applications rely upon the ability to automatically generate diagrams from an abstract description. However, this problem is difficult and is known to be NP-complete under certain wellformedness conditions. Therefore methods to identify when and how one can decompose abstract Euler diagrams into simpler components provide a vital step in improving the efficiency of tools which implement a generation process. One such decomposition, called diagram nesting, has previously been identified and exploited. In this paper, we make substantial progress, defining the notion of a disconnecting contour and identifying the conditions on an abstract Euler diagram that allow us to identify disconnecting contours. If a diagram has a disconnecting contour, we can draw it more easily, by combining the results of drawing smaller diagrams. The drawing problem is just one context which benefits from such diagram decomposition - we can also use the disconnecting contour to provide a more natural semantic interpretation of the Euler diagram.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Chow, S., Ruskey, F.: Drawing area-proportional Venn and Euler diagrams. In: Liotta, G. (ed.) GD 2003. LNCS, vol. 2912, pp. 466–477. Springer, Heidelberg (2004)

    Google Scholar 

  2. Chow, S.C.: Generating and Drawing Area-Proportional Euler and Venn Diagrams. Ph.D thesis, University of Victoria (2007)

    Google Scholar 

  3. DeChiara, R., Erra, U., Scarano, V.: VennFS: A Venn diagram file manager. In: Proceedings of Information Visualisation, pp. 120–126. IEEE Computer Society, Los Alamitos (2003)

    Google Scholar 

  4. DeChiara, R., Erra, U., Scarano, V.: A system for virtual directories using Euler diagrams. In: Proceedings of Euler Diagrams 2004. Electronic Notes in Theoretical Computer Science, vol. 134, pp. 33–53 (2005)

    Google Scholar 

  5. Euler, L.: Letters a une princesse dallemagne sur divers sujets de physique et de philosophie. Letters 2, 102–108 (1775)

    Google Scholar 

  6. Fish, A., Flower, J.: Abstractions of Euler diagrams. In: Proceedings of Euler Diagrams 2004, Brighton, UK. ENTCS, vol. 134, pp. 77–101 (2005)

    Google Scholar 

  7. Fish, A., Flower, J.: Investigating reasoning with constraint diagrams. In: Visual Language and Formal Methods 2004, Rome, Italy. ENTCS, vol. 127, pp. 53–69. Elsevier, Amsterdam (2005)

    Google Scholar 

  8. Flower, J., Fish, A., Howse, J.: Euler diagram generation. Journal of Visual Languages and Computing (2008), http://dx.doi.org/10.1016/j.jvlc.2008.01.004

  9. Flower, J., Howse, J.: Generating Euler diagrams. In: Proceedings of 2nd International Conference on the Theory and Application of Diagrams, Georgia, USA, April 2002, pp. 61–75. Springer, Heidelberg (2002)

    Google Scholar 

  10. Flower, J., Howse, J., Taylor, J.: Nesting in Euler diagrams. In: International Workshop on Graph Transformation and Visual Modeling Techniques, pp. 99–108 (2002)

    Google Scholar 

  11. Flower, J., Howse, J., Taylor, J.: Nesting in Euler diagrams: syntax, semantics and construction. Software and Systems Modelling 3, 55–67 (2004)

    Article  Google Scholar 

  12. Hammer, E., Shin, S.J.: Euler’s visual logic. History and Philosophy of Logic, 1–29 (1998)

    Google Scholar 

  13. Harel, D.: On visual formalisms. In: Glasgow, J., Narayan, N.H., Chandrasekaran, B. (eds.) Diagrammatic Reasoning, pp. 235–271. MIT Press, Cambridge (1998)

    Google Scholar 

  14. Howse, J., Molina, F., Shin, S.-J., Taylor, J.: Type-syntax and token-syntax in diagrammatic systems. In: Proceedings FOIS-2001: 2nd International Conference on Formal Ontology in Information Systems, Maine, USA, pp. 174–185. ACM Press, New York (2001)

    Chapter  Google Scholar 

  15. Howse, J., Stapleton, G., Flower, J., Taylor, J.: Corresponding regions in Euler diagrams. In: Proceedings of 2nd International Conference on the Theory and Application of Diagrams, Georgia, USA, April 2002, pp. 76–90. Springer, Heidelberg (2002)

    Google Scholar 

  16. Howse, J., Stapleton, G., Taylor, J.: Spider diagrams. LMS Journal of Computation and Mathematics 8, 145–194 (2005)

    MATH  MathSciNet  Google Scholar 

  17. Kent, S.: Constraint diagrams: Visualizing invariants in object oriented modelling. In: Proceedings of OOPSLA 1997, October 1997, pp. 327–341. ACM Press, New York (1997)

    Chapter  Google Scholar 

  18. Kestler, H., Muller, A., Gress, T., Buchholz, M.: Generalized Venn diagrams: A new method for visualizing complex genetic set relations. Journal of Bioinformatics 21(8), 1592–1595 (2005)

    Article  Google Scholar 

  19. Ruskey, F.: A survey of Venn diagrams. Electronic Journal of Combinatorics (1997), www.combinatorics.org/Surveys/ds5/VennEJC.html

  20. Shimojima, A.: Inferential and expressive capacities of graphical representations: Survey and some generalizations. In: Blackwell, A.F., Marriott, K., Shimojima, A. (eds.) Diagrams 2004. LNCS (LNAI), vol. 2980, pp. 18–21. Springer, Heidelberg (2004)

    Google Scholar 

  21. Shin, S.-J.: The Logical Status of Diagrams. Cambridge University Press, Cambridge (1994)

    MATH  Google Scholar 

  22. Stapleton, G., Thompson, S., Howse, J., Taylor, J.: The expressiveness of spider diagrams. Journal of Logic and Computation 14(6), 857–880 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  23. Swoboda, N., Allwein, G.: Using DAG transformations to verify Euler/Venn homogeneous and Euler/Venn FOL heterogeneous rules of inference. Journal on Software and System Modeling 3(2), 136–149 (2004)

    Article  Google Scholar 

  24. Venn, J.: On the diagrammatic and mechanical representation of propositions and reasonings. Phil. Mag. (1880)

    Google Scholar 

  25. Verroust, A., Viaud, M.-L.: Ensuring the drawability of Euler diagrams for up to eight sets. In: Blackwell, A.F., Marriott, K., Shimojima, A. (eds.) Diagrams 2004. LNCS (LNAI), vol. 2980, pp. 128–141. Springer, Heidelberg (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Visual Modelling Group, School of Computing, Mathematical and Information Sciences, University of Brighton, Brighton, UK

    Andrew Fish & Jean Flower

Authors
  1. Andrew Fish
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jean Flower
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Gem Stapleton John Howse John Lee

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fish, A., Flower, J. (2008). Euler Diagram Decomposition. In: Stapleton, G., Howse, J., Lee, J. (eds) Diagrammatic Representation and Inference. Diagrams 2008. Lecture Notes in Computer Science(), vol 5223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87730-1_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-87730-1_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87729-5

  • Online ISBN: 978-3-540-87730-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics