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On countable RCC models

Li S., Ying M., Li Y.

Fundamenta Informaticae

2005

Vol. 65, nr 4

329--351

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 Düntsch, 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.

Extensionality of the RCC8 Composition Table

Li S., Ying M.

Fundamenta Informaticae

2003

Vol. 55, nr 3,4

363-385

This paper is mainly concerned with the RCC8 composition table entailed by the Region Connection Calculus (RCC), a well-known formalism for Qualitative Spatial Reasoning. This table has been independently generated by Egenhofer in the context of Geographic Information Systems. It has been known for some time that the table is not extensional for each RCC model. This paper however shows that the Egenhofer model is indeed an extensional one for the RCC8 composition table. Moreover this model is the maximal extensional one for the RCC8 composition table in a sense.