Relations algebras in qualitative spatial reasoning
Fundamenta Informaticae
Boolean connection algebras: a new approach to the Region-Connection Calculus
Artificial Intelligence
A relation — algebraic approach to the region connection calculus
Theoretical Computer Science
A boundary-sensitive approach to qualitative location
Annals of Mathematics and Artificial Intelligence
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Geoinformatica
Topology in Raster and Vector Representation
Geoinformatica
Topological Relations in Hierarchical Partitions
COSIT '99 Proceedings of the International Conference on Spatial Information Theory: Cognitive and Computational Foundations of Geographic Information Science
The Mereotopology of Discrete Space
COSIT '99 Proceedings of the International Conference on Spatial Information Theory: Cognitive and Computational Foundations of Geographic Information Science
Qualitative and Topological Relationships in Spatial Databases
SSD '93 Proceedings of the Third International Symposium on Advances in Spatial Databases
Computational Properties of Qualitative Spatial Reasoning: First Results
KI '95 Proceedings of the 19th Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
Region connection calculus: its models and composition table
Artificial Intelligence
Toward a geometry of common sense: a semantics and a complete axiomatization of mereotopology
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Generalized Region Connection Calculus
Artificial Intelligence
Qualitative spatial reasoning with topological information
Qualitative spatial reasoning with topological information
Extensionality of the RCC8 Composition Table
Fundamenta Informaticae
Qualitative Spatial Representation and Reasoning: An Overview
Fundamenta Informaticae - Qualitative Spatial Reasoning
On minimal models of the Region Connection Calculus
Fundamenta Informaticae
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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 n0, 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.