On the Skeleton of Stonian p-Ortholattices

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.

• Type: Conference
• Year: 2009
• Where: RELMICS
• Authors: Michael Winter, Torsten Hahmann, Michael Gruninger
• Keywords: Boolean Contact Algebras, Lattice Theoretic Version, RELMICS 2009, Stonian P-ortholattices, Theoretical Computer Science