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The Mathematics of Boundaries: A Beginning

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Diagrammatic Representation and Inference (Diagrams 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4045))

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Abstract

The intuitive properties of configurations of planar non-overlapping closed curves (boundaries) are presented as a pure boundary mathematics. The mathematics, which is not incorporated in any existing formalism, is constructed from first principles, that is, from empty space. When formulated as patternequations, boundary algebras map to elementary logic and to integer arithmetic.

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References

  1. Bricken, W., Gullichsen, E.: Introduction to Boundary Logic. Future Computing Systems 2(4), 1–77 (1989)

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Author information

Authors and Affiliations

  1. Boundary Institute, 18488 Prospect Road, Suite 14, Saratoga, CA, 95070, USA

    William Bricken

Authors
  1. William Bricken
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Editors and Affiliations

  1. Stanford University,, 94305-4101, Stanford, CA, USA

    Dave Barker-Plummer

  2. Representation and Cognition Group, University of Sussex, Brighton, UK

    Richard Cox

  3. Universidad Politécnica de Madrid, Boadilla del Monte, 28660, Madrid, Spain

    Nik Swoboda

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© 2006 Springer-Verlag Berlin Heidelberg

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Bricken, W. (2006). The Mathematics of Boundaries: A Beginning. In: Barker-Plummer, D., Cox, R., Swoboda, N. (eds) Diagrammatic Representation and Inference. Diagrams 2006. Lecture Notes in Computer Science(), vol 4045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11783183_8

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  • DOI: https://doi.org/10.1007/11783183_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35623-3

  • Online ISBN: 978-3-540-35624-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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