On countable RCC models

Region Connection Calculus (RCC) is the most widely studied formalism of Qualitative Spatial Reasoning. It has been known for some time that each connected regular topological space provides an RCC model. These 'standard' models are inevitable uncountable and regions there cannot be represented finitely. This paper, however, draws researchers' attention to RCC models that can be constructed from finite models hierarchically. Compared with those 'standard' models, these countable models have the nice property that regions where can be constructed in finite steps from basic ones. We first investigate properties of three countable models introduced by Düuntsch, Stell, Li and Ying, resp. In particular, we show that (i) the contact relation algebra of our minimal model is not atomic complete; and (ii) these three models are non-isomorphic. Second, for each n>0, we construct a countable RCC model that is a sub-model of the standard model over the Euclidean unit n-cube; and show that all these countable models are non-isomorphic. Third, we show that every finite model can be isomorphically embedded in any RCC model. This leads to a simple proof for the result that each consistent spatial network has a realization in any RCC model.