Stonian p-ortholattices: A new approach to the mereotopology RT0
This paper gives an algebraic representation of the subtheories RT-, RTEC-, and RT of Asher and Vieu's first-order ontology of mereotopology RT0. It corrects and extends previous work on the representation of these mereotopologies. We develop the theory of p-ortholattices - lattices that are both orthocomplemented and pseudocomplemented - and show that together with the Stone identity (x . y)* = x* + y* or equivalent definitions the natural, class of Stonian p-ortholattices can be defined. The main contribution of the paper consists of a representation theorem for RT- as Stonian p-ortholattices. Moreover, it is shown that the class of models of RTEC- is, isomorphic to the non-distributive Stonian p-ortholattices and a characterization of RT is given by a set of four algebras of which one need to be a subalgebra of the present lattice model. As corollary we obtain that Axiom (A11) - existence of two externally connected regions - is in fact a theorem of the remaining axioms of RT. (C) 2009 Elsevier B.V. All rights reserved.
stonian p-ortholattice mereotopology qualitative spatial reasoning (qsr) region-based space non-distributive pseudocomplemented lattice