Stonian p-ortholattices: A new approach to the mereotopology RT0

摘要

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.