A COMMENT ON RCC: FROM RCC TO RCC<Superscript>++</Superscript>

The Region Connection Calculus (RCC theory) is a well-known spatial representation of topological relations between regions. It claims that the connection relation is primitive in the spatial domain. We argue that the connection relation is indeed primitive to the spatial relations, although in RCC theory there is no room for distance relations. We first analyze some aspects of the RCC theory, e.g. the two axioms in the RCC theory are not strong enough to govern the connection relation, regions in the RCC theory cannot be points, the uniqueness of the operation in the theory is not guaranteed, etc. To solve some of the problems, we propose an extension to the RCC theory by introducing the notion of region category and adding a new axiom which governs the characteristic property of the connection relation. The extended theory is named as RCC⁺⁺. We support the claim that the connection relation is primitive to spatial domain by showing how distance relations, size relations are developed in RCC⁺⁺. At last we revisit a sub-family of un-intended models in RCC theory, argue that RCC⁺⁺ is more suitable than RCC with regards to its original intended model, and discuss the representation limitation of the RCC, as well as RCC⁺⁺.