RCC and the theory of simple regions in R2

The theory of mereology and its topological extensions, called mereotopologies, are point-free approaches that allow to model information while avoiding several puzzling assumptions typical of set-theoretical systems. Although points can be introduced in a mereology or mereotopology, the idea is that one does so only when their existence is clearly motivated. The Region Connection Calculus, RCC, is a mereotopological system that assumes upfront the existence of points: points must be accepted for the system to have the desired semantics. This is awkward from the mereological viewpoint and is considered unsatisfactory from the cognitive and the philosophical perspectives on which mereology rests. We prove that, in dimension two and with the standard semantics, a theory equivalent to RCC can be given without any reference to points at the semantic level also. The theory, based on mereology, uses the topological primitive 'being a simple region' (aka 'being strongly self-connected'). © 2013 Springer International Publishing Switzerland.