On minimal models of the Region Connection Calculus

Article type: Research Article

Authors: Xia, Lirong | Li, Sanjiang

Affiliations: State Key Laboratory of Intelligent Technology and Systems, Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China. E-mail: [email protected] | State Key Laboratory of Intelligent Technology and Systems, Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China. E-mail: [email protected]

Abstract: 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.

Keywords: Qualitative Spatial Reasoning, Region Connection Calculus, minimal RCC models

Journal: Fundamenta Informaticae, vol. 69, no. 4, pp. 427-446, 2006