Modelling topological and metrical properties in physical processes
Proceedings of the first international conference on Principles of knowledge representation and reasoning
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
Region connection calculus: its models and composition table
Artificial Intelligence
A representation theorem for Boolean contact algebras
Theoretical Computer Science
Generalized region connection calculus
Artificial Intelligence
Fundamenta Informaticae
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Region Connection Calculus (RCC) is one primary formalism of qualitative spatial reasoning. Standard RCC models are continuous ones where each region is infinitely divisible. This contrasts sharply with the predominant use of finite, discrete models in applications. In a recent paper, Li et al. (2004) initiate a study of countable models that can be constructed step by step from finite models. Of course, some basic problems are left unsolved, for example, how many non-isomorphic countable RCC models are there? This paper investigates these problems and obtains the following results: (i) the exotic RCC model described by Gotts (1996) is isomorphic to the minimal model given by Li and Ying (2004); (ii) there are continuum many non-isomorphic minimal RCC models, where a model is minimal if it can be isomorphically embedded in each RCC model.