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On the Skeleton of Stonian p-Ortholattices

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Relations and Kleene Algebra in Computer Science (RelMiCS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5827))

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Abstract

Boolean Contact Algebras (BCA) establish the algebraic counterpart of the mereotopolopy induced by the Region Connection Calculus (RCC). Similarly, Stonian p-ortholattices serve as a lattice theoretic version of the ontology RT − of Asher and Vieu. In this paper we study the relationship between BCAs and Stonian p-ortholattices. We show that the skeleton of every Stonian p-ortholattice is a BCA, and, conversely, that every BCA is isomorphic to the skeleton of a Stonian p-ortholattice. Furthermore, we prove the equivalence between algebraic conditions on Stonian p-ortholattices and the axioms C5, C6, and C7 for BCAs.

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Authors and Affiliations

  1. Department of Computer Science, Brock University, St. Catharines, ON, Canada

    Michael Winter

  2. Department of Computer Science, University of Toronto,  

    Torsten Hahmann

  3. Department of Mechanical and Industrial Engineering, Department of Computer Science, University of Toronto,  

    Michael Gruninger

Authors
  1. Michael Winter
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  2. Torsten Hahmann
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  3. Michael Gruninger
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Editors and Affiliations

  1. Institut für Informatik, Christian-Albrechts-Universität zu Kiel, Olshausenstraße 40, 24098, Kiel, Germany

    Rudolf Berghammer

  2. College of Engineering, Qatar University, P.O. Box 2713, CSE 209, Doha, Qatar,  

    Ali Mohamed Jaoua

  3. Institut für Informatik, Universität Augsburg, Universitätsstr. 6a, 86135, Augsburg, Germany

    Bernhard Möller

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Winter, M., Hahmann, T., Gruninger, M. (2009). On the Skeleton of Stonian p-Ortholattices. In: Berghammer, R., Jaoua, A.M., Möller, B. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2009. Lecture Notes in Computer Science, vol 5827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04639-1_24

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  • DOI: https://doi.org/10.1007/978-3-642-04639-1_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04638-4

  • Online ISBN: 978-3-642-04639-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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