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This paper gives an algebraic representation of the subtheories RT^-, RT"E"C^-, and RT of Asher and Vieu's first-order ontology of mereotopology RT"0. 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 RT"E"C^- 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.