Abstract
In this article, we investigate the problem of checking consistency in a hybrid formalism, which combines two essential formalisms in qualitative spatial reasoning: topological formalism and cardinal direction formalism. Although much work has been done in developing composition tables for these formalisms, the previous research for integrating heterogeneous formalisms was not sufficient. Instead of using conventional composition tables, we investigate the interactions between topological and cardinal directional relations with the aid of rules that are used efficiently in many research fields such as content-based image retrieval. These rules are shown to be sound, i.e. the deductions are logically correct. Based on these rules, an improved constraint propagation algorithm is introduced to enforce the path consistency. The results of computational complexity of checking consistency for constraint satisfaction problems based on various subsets of this hybrid formalism are presented at the end of this article.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Gerevini, A., Renz, J.: Combining Topological and Size Constraints for Spatial Reasoning. Artificial Intelligence (AIJ) 137(1-2), 1–42 (2002)
Isli, A., Haarslev, V., Moller, R.: Combining cardinal direction relations and relative orientation relations in Qualitative Spatial Reasoning. Fachbereich Informatik, University Hamburg, Technical report FBI-HH-M-304/01 (2001)
Sharma, J.: Integrated spatial reasoning in geographic information systems: combining topology and direction. Ph.D. Thesis, Department of Spatial Information Science and Engineering, University of Maine, Orono, ME (1996)
Allen, J.F.: Maintaining knowledge about temporal intervals. Communications of the ACM 26(11), 832–843 (1983)
Prasad Sistla, A., Yu, C.T., Haddad, R.: Reasoning About Spatial Relations in Picture Retrieval Systems. In: 20th International Conference on Very Large Data Bases, pp. 570–581. Morgan Kaufmann, San Francisco (1994)
Egenhofer, M.: A Formal Definition of Binary Topological Relations. In: Litwin, W., Schek, H.-J. (eds.) FODO 1989. LNCS, vol. 367, pp. 457–472. Springer, Heidelberg (1989)
Randell, D., Cui, Z., Cohn, A.: A spatial logic based on regions and connection. In: Nebel, B., Rich, C., Swartout, W. (eds.) Proc. of the Knowledge Representation and Reasoning, pp. 165–176. Morgan Kaufmann, San Mateo (1992)
Goyal, R., Egenhofer, M.: Cardinal Directions between Extended Spatial Objects. IEEE Transactions on Knowledge and Data Engineering (to be published) (2000)
Skiadopoulos, S., Koubarakis, M.: Composing cardinal direction relations. Artificial Intelligence 152(2), 143–171 (2004)
Randell, D.A., Cohn, A.G., Cui, Z.: Computing Transitivity Tables: A Challenge For Automated Theorem Provers. In: 11th International Conference on Automated Deduction, pp. 786–790. Springer, Berlin (1992)
Cicerone, S., Di Felice, P.: Cardinal directions between spatial objects: the pairwise-consistency problem. Information Sciences 164, 165–188 (2004)
Prasad Sistla, A., Yu, C.T., Haddad, R.: Reasoning About Spatial Relations in Picture Retrieval Systems. International Journal on Very Large Databases (VLDB) 3(4), 570–581 (1994)
Renz, J., Nebel, B.: On the Complexity of Qualitative Spatial Reasoning: A Maximal Tractable Fragment of the Region Connection Calculus. Artificial Intelligence (AIJ) 108(1-2), 69–123 (1999)
Renz, J.: Maximal Tractable Fragments of the Region Connection Calculus: A Complete Analysis. In: 16th International Joint Conference on Artificial Intelligence (IJCAI 1999), Stockholm, Sweden, August 1999, pp. 448–455 (1999)
Skiadopoulos, S., Koubarakis, M.: Qualitative spatial reasoning with cardinal directions. In: 7th International Conference on Principles and Practice of Constraint Programing (CP 2002). LNCS, vol. 2470, pp. 341–355. Springer, Berlin (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sun, H., Li, W. (2005). Spatial Reasoning Based on Rules. In: Mira, J., Álvarez, J.R. (eds) Mechanisms, Symbols, and Models Underlying Cognition. IWINAC 2005. Lecture Notes in Computer Science, vol 3561. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11499220_48
Download citation
DOI: https://doi.org/10.1007/11499220_48
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26298-5
Online ISBN: 978-3-540-31672-5
eBook Packages: Computer ScienceComputer Science (R0)