Skip to main content
SpringerLink
Log in

Consistency Checking for Qualitative Spatial Reasoning with Cardinal Directions

  • Conference paper
  • First Online:
Principles and Practice of Constraint Programming - CP 2002 (CP 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2470))

Abstract

We present a formal model for qualitative spatial reasoning with cardinal directions and study the problem of checking the consistency of a set of cardinal direction constraints. We present the first algorithm for this problem, prove its correctness and analyze its computational complexity. Utilizing the above algorithm we prove that the consistency checking of a set of basic cardinal direction constraints can be performed in time while the consistency checking of an unrestricted set of cardinal direction constraints is NP-complete. Finally, we briefly discuss some extensions to the basic model.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Berretti, A. Del Bimbo, and E. Vicario. Modeling Spatial Relationships between Color Sets. In Proceeding of IEEE Workshop on Content-based Access of Image and Video Libraries (CVPR-2000), June 2000.

    Google Scholar 

  2. W. G. Chinn and N. E. Steenrod. First Concepts of Topology. The Mathematical Association of America, 1966.

    Google Scholar 

  3. E. Clementini, P. Di Fellice, and G. Califano. Composite Regions in Topological Queries. Information Systems, 7:759–594, 1995.

    Google Scholar 

  4. E. Clementini, P. Di Fellice, and D. Hernandez. Qualitative Representation of Positional Information. Artificial Intelligence, 95:317–356, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  5. J. P. Delgrande, A. Gupta, and T. Van Allen. Point Based Approaches to Qualitative Temporal Reasoning. In Proceedings of the AAAI-99, pages 739–744, 1999.

    Google Scholar 

  6. B. Faltings. Qualitative Spatial Reasoning Using Algebraic Topology. In Proceedings of COSIT-95, volume 988 of LNCS, 1995.

    Google Scholar 

  7. A.U. Frank. Qualitative Spatial Reasoning about Distances and Directions in Geographic Space. Journal of Visual Languages and Computing, 3:343–371, 1992.

    Article  Google Scholar 

  8. C. Freksa. Using Orientation Information for Qualitative Spatial Reasoning. In Proceedings of COSIT-92, volume 639 of LNCS, pages 162–178, 1992.

    Google Scholar 

  9. R. Goyal and M. J. Egenhofer. Cardinal Directions Between Extended Spatial Objects. IEEE Transactions on Data and Knowledge Engineering, (in press), 2000. Available at http://www.spatial.maine.edu/~max/RJ36.html.

  10. R. Goyal and M. J. Egenhofer. Consistent Queries over Cardinal Directions across Different Levels of Detail. In Proceedings of the 11th International Workshop on Database and Expert Systems Applications, 2000.

    Google Scholar 

  11. G. Ligozat. Reasoning about Cardinal Directions. Journal of Visual Languages and Computing, 9:23–44, 1998.

    Article  Google Scholar 

  12. S. Lipschutz. Set Theory and Related Topics. McGraw Hill, 1998.

    Google Scholar 

  13. A. Mukerjee and G. Joe. A Qualitative Model for Space. In Proceedings of AAAI-90, pages 721–727, 1990.

    Google Scholar 

  14. D. Papadias. Relation-Based Representation of Spatial Knowledge. PhD thesis, Dept. of Electrical and Computer Engineering, National Technical University of Athens, 1994.

    Google Scholar 

  15. D. Papadias, N. Arkoumanis, and N. Karacapilidis. On The Retrieval of Similar Configurations. In Proceedings of 8th International Symposium on Spatial Data Handling (SDH), 1998.

    Google Scholar 

  16. C. H. Papadimitriou, D. Suciu, and V. Vianu. Topological Queries in Spatial Databases. Journal of Computer and System Sciences, 58(1):29–53, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  17. D. A. Randell, Z. Cui, and A. Cohn. A Spatial Logic Based on Regions and Connection. In Proceedings of KR’ 92. Morgan Kaufmann, October 1992.

    Google Scholar 

  18. J. Renz and B. Nebel. On the Complexity of Qualitative Spatial Reasoning: A Maximal Tractable Fragment of the Region Connection Calculus. Artificial Intelligence, 1–2:95–149, 1999.

    MathSciNet  Google Scholar 

  19. A. P. Sistla, C. Yu, and R. Haddad. Reasoning About Spatial Relationships in Picture Retrieval Systems. In Proceedings of VLDB-94, pages 570–581, 1994.

    Google Scholar 

  20. S. Skiadopoulos and M. Koubarakis. Composing Cardinal Directions Relations. In Proceedings of the 7th International Symposium on Spatial and Temporal Databases (SSTD-01), volume 2121 of LNCS, pages 299–317, July 2001.

    Chapter  Google Scholar 

  21. S. Skiadopoulos and M. Koubarakis. Qualitative Spatial Reasoning with Cardinal Directions: Semantics, Algorithms and Computational Complexity. Manuscript in preparation, 2002.

    Google Scholar 

  22. P. van Beek. Reasoning About Qualitative Temporal Information. Artificial Intelligence, 58:297–326, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  23. M. Vilain, H. Kautz, and P. van Beek. Constraint Propagation Algorithms for Temporal Reasoning: A Revised Report. In Readings in Qualitative Reasoning about Physical Systems, pages 373–381. Morgan Kaufmann, 1989.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Electrical and Computer Engineering, National Technical University of Athens, Zographou, 157 73, Athens, Greece

    Spiros Skiadopoulos

  2. Dept. of Electronic and Computer Engineering, Technical University of Crete, Chania, 73100, Crete, Greece

    Manolis Koubarakis

Authors
  1. Spiros Skiadopoulos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Manolis Koubarakis
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Brown University, Box 1910, Providence, RI, 02912, USA

    Pascal Van Hentenryck

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Skiadopoulos, S., Koubarakis, M. (2002). Consistency Checking for Qualitative Spatial Reasoning with Cardinal Directions. In: Van Hentenryck, P. (eds) Principles and Practice of Constraint Programming - CP 2002. CP 2002. Lecture Notes in Computer Science, vol 2470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46135-3_23

Download citation

  • DOI: https://doi.org/10.1007/3-540-46135-3_23

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44120-5

  • Online ISBN: 978-3-540-46135-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation