Skip to main content

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9060))

  • 947 Accesses

Abstract

The way we use spatial descriptions in many everyday situations is of a qualitative nature. This is often achieved by specifying spatial relations between objects or regions. The advantage of using qualitative descriptions is that we can be less precise and thereby less prone to making an error. For example, it is often easier to decide whether an object is inside another object than to specify exactly where the first object is with respect to the second one. In artificial intelligence, a variety of formalisms have been developed that deal with space on the basis of relations between objects or regions that objects might occupy. One of these formalisms is the RCC theory, which is based on a primitive relation, called connectedness, and uses a set of topological relations, defined on the basis of connectedness, to provide a framework for reasoning about regions. This paper discusses an extension of the RCC theory based on fuzzy logic, which enables us to express preferences among spatial descriptions.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Allen, J.: Maintaining knowledge about temporal intervals. Commun. ACM 26, 832–843 (1983)

    Article  MATH  Google Scholar 

  2. Bloch, I.: Spatial representation of spatial relationship knowledge. In: Proc. KR 2000, pp. 247–258. Breckenridge, Colorado (2000)

    Google Scholar 

  3. Bloch, I.: Fuzzy spatial relationships for image processing and interpretation: A review. Image and Vision Computing 23, 89–110 (2005)

    Article  Google Scholar 

  4. Brewka, G.: Preferred subtheories: An extended logical framework for default reasoning. In: Proc. IJCAI 1989, pp. 1043–1048 (1989)

    Google Scholar 

  5. Cohn, A., Bennett, B., Gooday, J., Gotts, N.: Representing and reasoning with qualitative spatial relations about regions. In: Stock, O. (ed.) Spatial and Temporal Reasoning, pp. 97–134. Kluwer, Dordrecht (1997)

    Chapter  Google Scholar 

  6. Cohn, A., Gotts, N.: The ‘Egg-Yolk’ representation of regions with indeterminate boundaries. In: Burrough, P., Frank, A. (eds.) Geographical Objects with Undetermined Boundaries. GISDATA Series, vol. 2, pp. 171–187. Taylor and Francis, London (1996)

    Google Scholar 

  7. Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, London (1980)

    MATH  Google Scholar 

  8. Egenhofer, M., Al-Taha, K.: Reasoning about gradual changes of topological relationships. In: Frank, A.U., Campari, I., Formentini, U. (eds.) GIS 1992. LNCS, vol. 639, pp. 196–219. Springer, Heidelberg (1992)

    Chapter  Google Scholar 

  9. Freksa, C.: Temporal reasoning based on semi-intervals. Artificial Intelligence 54, 199–227 (1992)

    Article  MathSciNet  Google Scholar 

  10. Freuder, E., Wallace, R.: Partial constraint satisfaction. Artificial Intelligence 58, 21–70 (1992)

    Article  MathSciNet  Google Scholar 

  11. Guesgen, H.: Spatial reasoning based on Allen’s temporal logic. Technical Report TR-89-049, ICSI, Berkeley, California (1989)

    Google Scholar 

  12. Guesgen, H., Hertzberg, J.: Spatial persistence. Applied Intelligence (Special Issue on Spatial and Temporal Reasoning) 6, 11–28 (1996)

    Google Scholar 

  13. Guesgen, H., Hertzberg, J., Philpott, A.: Towards implementing fuzzy Allen relations. In: Proc. ECAI-94 Workshop on Spatial and Temporal Reasoning, Amsterdam, The Netherlands, pp. 49–55 (1994)

    Google Scholar 

  14. Klir, G., Folger, T.: Fuzzy Sets, Uncertainty, and Information. Prentice Hall, Englewood Cliffs (1988)

    Google Scholar 

  15. Lehmann, F., Cohn, A.: The EGG/YOLK reliability hierarchy: Semantic data integration using sorts with prototypes. In: Proc. 3rd International Conference on Information and Knowledge Management (CIKM 1994), pp. 272–279. Gaithersburg, Maryland (1994)

    Google Scholar 

  16. Ligozat, G. (ed.): Qualitative Spatial and Temporal Reasoning. Wiley-ISTE, Hoboken (2011)

    MATH  Google Scholar 

  17. Randell, D., Cui, Z., Cohn, A.: A spatial logic based on regions and connection. In: Proc. KR 1992, pp. 165–176. Cambridge, Massachusetts (1992)

    Google Scholar 

  18. Renz, J.: A spatial odyssey of the interval algebra: 1. directed intervals. In: Proc. IJCAI 2001, pp. 51–56. Seattle, Washington (2001)

    Google Scholar 

  19. Schockaert, S., De Cock, M., Cornelis, C., Kerre, E.: Fuzzy region connection calculus: Representing vague topological information. Journal of Approximate Reasoning 48, 314–331 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  20. Zadeh, L.: Fuzzy sets. Information and Control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Guesgen, H.W. (2015). A Fuzzy Set Approach to Expressing Preferences in Spatial Reasoning. In: Eiter, T., Strass, H., Truszczyński, M., Woltran, S. (eds) Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation. Lecture Notes in Computer Science(), vol 9060. Springer, Cham. https://doi.org/10.1007/978-3-319-14726-0_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-14726-0_12

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-14725-3

  • Online ISBN: 978-3-319-14726-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics