A TRACTABLE FORMALISM FOR COMBINING RECTANGULAR CARDINAL RELATIONS WITH METRIC CONSTRAINTS

Angelo Montanari, Isabel Navarrete, Guido Sciavicco, Alberto Tonon

Abstract

Knowledge representation and reasoning in real-world applications often require to integrate multiple aspects of space. In this paper, we focus our attention on the so-called Rectangular Cardinal Direction calculus for qualitative spatial reasoning on cardinal relations between rectangles whose sides are aligned to the axes of the plane. We first show how to extend a tractable fragment of such a calculus with metric constraints preserving tractability. Then, we illustrate how the resulting formalism makes it possible to represent available knowledge on directional relations between rectangles and to derive additional information about them, as well as to deal with metric constraints on the height/width of a rectangle or on the vertical/horizontal distance between rectangles.

References

  1. Allen, J. (1983). Maintaining knowledge about temporal intervals. Communications of the ACM, 26(11):832- 843.
  2. Balbiani, P., Condotta, J., and del Cerro, L. (1998). A model for reasoning about bidimensional temporal relations. In Proceedings of KR-98, pages 124-130.
  3. Balbiani, P., Condotta, J., and del Cerro, L. (2002). Tractability results in the block algebra. Journal of Logic and Computation, 12(5):885-909.
  4. Baykan, C. and Fox, M. (1997). Spatial synthesis by disjunctive constraint satisfaction. Artificial Intelligence for Engineering Design, Analysis and Manufacturing, 11(4):245-262.
  5. Broxvall, M. (2002). A method for metric temporal reasoning. In Proceedings of AAAI-02, pages 513-518.
  6. Cohn, A. and Hazarika, S. (2001). Qualitative spatial representation and reasoning: An overview. Fundamenta Informaticae, 46(1-2):1-29.
  7. Condotta, J. F. (2000). The augmented interval and rectangle networks. In Proceedings of KR-00, pages 571- 579.
  8. Dechter, R., Meiri, I., and Pearl, J. (1991). Temporal constraint networks. Artificial Intelligence, 49(1-3):61- 95.
  9. El-Geresy, B. and Abdelmoty, A. (2001). Qualitative representations in large spatial databases. Proceedings of IDEAS-01, pages 68-75.
  10. Frank, A. (1996). Qualitative spatial reasoning: Cardinal directions as an example. International Journal of Geographical Information Science, 10(3):269-290.
  11. Gatterbauer, W. and Bohunsky, P. (2006). Table extraction using spatial reasoning on the CSS2 visual box model. In Proceedings of AAAI-06, volume 2.
  12. Gerevini, A. and Cristani, M. (1997) On finding a solution in temporal constraint satisfaction problems. In Proceedings of IJCAI-97, pages 1460-1465.
  13. Gerevini, A. and Renz, J. (2002). Combining topological and size information for spatial reasoning. Artificial Intelligence, 137(1-2):1-42.
  14. Goyal, R. (2000). Similarity assessment for cardinal directions between extended spatial objects. PhD thesis, University of Maine, Dept. of Spatial Information Science and Engineering.
  15. Goyal, R. and Egenhofer, M. (2000). Consistent queries over cardinal directions across different levels of detail. In Proceedings of DEXA-00, pages 876-880.
  16. Liu, W., Li, S., and Renz, J. (2009). Combining RCC-8 with qualitative direction calculi: Algorithms and complexity. In Proceedings of IJCAI-09, pages 854-859.
  17. Liu, W., Zhang, X., Li, S., and Ying, M. (2010). Reasoning about cardinal directions between extended objects. Artificial Intelligence, 174:951-983.
  18. Mackworth, A. (1977). Consistency in networks of relations. Artificial Intelligence, 8(1):99-118.
  19. Meiri, I. (1996). Combining qualitative and quantitative constraints in temporal reasoning. Artificial Intelligence, 87(1-2):343-385.
  20. Navarrete, I., Morales, A., Sciavicco, G., and CardenasViedma, M. (2011). Spatial reasoning with rectangular cardinal relations. Technical Report TRDIIC 2/11, Departamento de Ingenieria de la Informacion y las Comunicaciones. Universidad de Murcia. http://sites.google.com/site/aikespatial/RCDC.
  21. Navarrete, I. and Sciavicco, G. (2006). Spatial reasoning with rectangular cardinal direction relations. In Proceedings of the ECAI-06 Workshop on Spatial and Temporal Reasoning, pages 1-10.
  22. Papadias, D. and Theodoridis, Y. (1997). Spatial relations, minimum bounding rectangles, and spatial data structures. International Journal of Geographical Information Science, 11(2):111-138.
  23. Skiadopoulos, S., Giannoukos, C., Sarkas, N., Vassiliadis, P., Sellis, T., and Koubarakis, M. (2005). Computing and managing cardinal direction relations. IEEE Transactions on Knowledge and Data Engineering, 17(12):1610-1623.
  24. Skiadopoulos, S. and Koubarakis, M. (2005). On the consistency of cardinal directions constraints. Artificial Intelligence, 163(1):91-135.
  25. van Beek, P. (1992). Reasoning about qualitative temporal information. Artificial Intelligence, 58(1-3):297-326.
  26. van Beek, P. and Cohen, R. (1990). Exact and approximate reasoning about temporal relations. Computation Intelligence, 6(3):132-147.
  27. Vilain, M. and Kautz, H. (1986). Constraint propagation algorithms for temporal reasoning. In Proceedings of AAAI-86, pages 377-382.
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Paper Citation


in Harvard Style

Montanari A., Navarrete I., Sciavicco G. and Tonon A. (2012). A TRACTABLE FORMALISM FOR COMBINING RECTANGULAR CARDINAL RELATIONS WITH METRIC CONSTRAINTS . In Proceedings of the 4th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART, ISBN 978-989-8425-95-9, pages 154-163. DOI: 10.5220/0003747901540163


in Bibtex Style

@conference{icaart12,
author={Angelo Montanari and Isabel Navarrete and Guido Sciavicco and Alberto Tonon},
title={A TRACTABLE FORMALISM FOR COMBINING RECTANGULAR CARDINAL RELATIONS WITH METRIC CONSTRAINTS},
booktitle={Proceedings of the 4th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},
year={2012},
pages={154-163},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003747901540163},
isbn={978-989-8425-95-9},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 4th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,
TI - A TRACTABLE FORMALISM FOR COMBINING RECTANGULAR CARDINAL RELATIONS WITH METRIC CONSTRAINTS
SN - 978-989-8425-95-9
AU - Montanari A.
AU - Navarrete I.
AU - Sciavicco G.
AU - Tonon A.
PY - 2012
SP - 154
EP - 163
DO - 10.5220/0003747901540163