On minimal models of the Region Connection Calculus

• Autorzy: Xia L. , Li S.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

qualitative spatial reasoning (QSR); Region Connection Calculus; minimal RCC models

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2006
• Tom: Vol. 69, nr 4
• Strony: 427--446
• Opis fizyczny: bibliogr. 9 poz.

Twórcy

autor

Xia L.

autor

Li S.

• Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China,

Bibliografia

• [1] Düntsch, I., Wang, H., McCloskey, S.: A relation-algebraic approach to the Region Connection Calculus, Theoretical Computer Science, 255, 2001, 63-83.
• [2] Düntsch, I., Winter, M.: A Representation Theorem for Boolean Contact Algebras, Theoretical Computer Science (B), 2005, To appear.
• [3] Gotts, N.: An axiomatic approach to spatial information systems, Research Report 96.25, School of Computer Studies, University of Leeds, 1996.
• [4] Li, S., Ying, M.: Region Connection Calculus: Its models and composition table, Artificial Intelligence, 145(1-2), 2003, 121-146.
• [5] Li, S., Ying, M.: Generalized Region Connection Calculus, Artificial Intelligence, 160(1-2), 2004, 1-34.
• [6] Li, S., Ying, M., Li, Y.: On countable RCC models, Fundamenta Informaticae, 65(4), 2005, 329-351.
• [7] Randell, D., Cohn, A.: Modelling topological and metrical properties of physical processes, First International Conference on the Principles of Knowledge Representation and Reasoning (R. Brachman, H. Levesque, R. Reiter, Eds.), Morgan Kaufmann, Los Altos, 1989.
• [8] Randell, D., Cui, Z., Cohn, A.: A spatial logic based on regions and connection, Proceedings of the 3rd International Conference on Knowledge Representation and Reasoning (B. Nebel, W. Swartout, C. Rich, Eds.), Morgan Kaufmann, Los Allos, 1992.
• [9] Stell, J.: Boolean connection algebras: A new approach to the Region-Connection Calculus, Artificial Intelligence, 122, 2000, 111-136.