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Describing symmetrical structures in logic

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Abstract

We present a simple but general method for the description in logic of discrete geometric structures based on the symmetry group of the structure. As a first step, we write a logic program that defines the structure with a small set of base points and generators for the symmetry group of the structure. We modify this program so that, when it is executed as a program inProlog orClp(ℛ), it enumerates the points of the structure. This method allows compact descriptions of highly symmetrical, yet elaborate structures such as geodesic spheres.

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Author notes

  1. P. A. Strooper

    Present address: Department of Computer Science, University of Queensland, 4072, St. Lucia, Queensland, Australia

Authors and Affiliations

  1. Computer Science Department, University of Victoria, P.O. Box 3055, V8W 3P6, Victoria, BC, Canada

    P. A. Strooper & M. H. van Emden

Authors
  1. P. A. Strooper
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  2. M. H. van Emden
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Strooper, P.A., van Emden, M.H. Describing symmetrical structures in logic. Ann Math Artif Intell 8, 301–314 (1993). https://doi.org/10.1007/BF01530795

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  • DOI: https://doi.org/10.1007/BF01530795

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