On the Skeleton of Stonian p-Ortholattices

Authors:
Michael Winter;Torsten Hahmann;Michael Gruninger
Affiliations:
Department of Computer Science, Brock University, St. Catharines, Canada;Department of Computer Science, University of Toronto,;Department of Mechanical and Industrial Engineering, Department of Computer Science, University of Toronto,
Venue:
RelMiCS '09/AKA '09 Proceedings of the 11th International Conference on Relational Methods in Computer Science and 6th International Conference on Applications of Kleene Algebra: Relations and Kleene Algebra in Computer Science
Year:
2009

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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.