Advertisement

Computational structure in three-valued nearness relations

  • Matt Duckham
  • Michael Worboys
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2205)

Abstract

The development of cognitively plausible models of human spatial reasoning may ultimately result in computational systems that are better equipped to meet human needs. This paper explores how human subjects perceive the qualitative spatial relation nearness within an environmental space. Based on experimental data, a three-valued nearness relation is analysed in two stages. First, the results are analysed with special reference to the existence of subsets of candidate landmark places, from which nearness relations between other places may be partially inferred. Second, the desirable properties of such landmark sets are considered and some of their formal properties are presented. These properties are then considered in the light of the data furnished by the experiment. The paper concludes with a discussion of the significance of the analyses and the scope for further work in this area.

Keywords

Nearness qualitative spatial reasoning landmarks data mining similarity relation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A.G. Cohn, A hierarchical representation of qualitative shape based on connection and convexity, Spatial Information Theory: A Theoretical Basis for GIS (A.U. Frank and W. Kuhn, eds.), Lecture Notes in Computer Science, no. 988, Springer-Verlag, Berlin, 1995, pp. 311–326.Google Scholar
  2. 2.
    A.G. Cohn and N.M. Gotts, The’ egg-yolk’ representation of regions with indeterminate boundaries, Geographic Objects with Indeterminate Boundaries (Burrough, P.A. and Frank, A.U., eds.), GIS Data 2, Taylor and Francis, London, 1996.Google Scholar
  3. 3.
    M.J. Egenhofer and R.D. Franzosa, Point-set topological spatial relations, International Journal of Geographical Information Systems 5 (1991), no. 2, 161–174.CrossRefGoogle Scholar
  4. 4.
    P.F. Fisher, Sorites paradox and vague geographies, Fuzzy Sets and Systems 113 (2000), no. 1, 7–18.CrossRefGoogle Scholar
  5. 5.
    P.F. Fisher and T.M. Orf, An investigation of the meaning of near and close on a university campus, Computers, Environment and Urban Systems 15 (1991), 23–35.CrossRefGoogle Scholar
  6. 6.
    A.U. Frank, Qualitative spatial reasoning about distances and directions in geographic space, Journal of Visual Languages and Computing 3 (1992), 343–371.CrossRefGoogle Scholar
  7. 7.
    M. Gahegan, Proximity operators for qualitative spatial reasoning, Spatial Information Theory: A Theoretical Basis for GIS (A.U. Frank and W. Kuhn, eds.), Lecture Notes in Computer Science, no. 988, Springer-Verlag, Berlin, 1995, pp. 31–44.Google Scholar
  8. 8.
    —, Experiments using context and significance to enhance the reporting capabilities of GIS, Spatial Information Theory: A Theoretical Basis for GIS (S.C. Hirtle and A.U. Frank, eds.), Lecture Notes in Computer Science, no. 988, Springer-Verlag, Berlin, 1997, pp. 485–496.CrossRefGoogle Scholar
  9. 9.
    D. Hernández, E. Clementini, and P. Di Felice, Qualitative distances, Spatial Information Theory: A Theoretical Basis for GIS (A.U. Frank and W. Kuhn, eds.), Lecture Notes in Computer Science, no. 988, Springer-Verlag, Berlin, 1995, pp. 45–57.Google Scholar
  10. 10.
    S.C. Hirtle, Representational structures for cognitive spaces: trees, ordered trees and semi-lattices, Spatial Information Theory: A Theoretical Basis for GIS (A.U. Frank and W. Kuhn, eds.), Lecture Notes in Computer Science, no. 988, Springer-Verlag, Berlin, 1995, pp. 327–340.Google Scholar
  11. 11.
    S.C. Hirtle and T. Gärling, Heuristic rules for sequential spatial decisions, Geoforum 23 (1992), no. 2, 227–238.CrossRefGoogle Scholar
  12. 12.
    S.C. Hirtle and J. Jonides, Evidence of hierarchies in cognitive maps, Memory and Cognition 13 (1985), no. 3, 208–217.Google Scholar
  13. 13.
    S.C. Hirtle and M.F. Mascolo, Effect of semantic clustering on the memory of spatial locations, Journal of Experimental Psychology: Learning, Memory and Cognition 12 (1986), no. 2, 182–189.CrossRefGoogle Scholar
  14. 14.
    G.F. Ligozat, Qualitative triangulation for spatial reasoning, Spatial Information Theory: A Theoretical Basis for GIS (A.U. Frank and I. Campari, eds.), Lecture Notes in Computer Science, no. 716, Springer-Verlag, Berlin, 1993, pp. 54–68.Google Scholar
  15. 15.
    D. Medyckyj-Scott and M. Blades, Human spatial cognition: its relevance to the design and use of spatial information systems, Geoforum 23 (1992), no. 2, 215–226.CrossRefGoogle Scholar
  16. 16.
    T. Munakata, Fundamentals of the New Artificial Intelligence, Springer-Verlag, 1998.Google Scholar
  17. 17.
    J.R. Quinlan, Learning efficient classification procedures and their application to chess end games, Machine Learning: An Artificial Intelligence Approach (R.S. Michalski, J.G. Carbonell, and T.M. Mitchell, eds.), Morgan Kauffmann, California, 1983, pp. 463–482.Google Scholar
  18. 18.
    V.B. Robinson, Interactive machine acquisition of a fuzzy spatial relation, Computers and Geosciences 16 (1990), no. 6, 857–872.CrossRefGoogle Scholar
  19. 19.
    1—, Individual and multipersonal fuzzy spatial relations acquired using humanmachine interaction, Fuzzy Sets and Systems (2000), no. 113, 133–145.Google Scholar
  20. 20.
    S. Russell and P. Norvig, Artificial Intelligence: A Modern Approach, Prentice Hall, New Jersey, 1995.zbMATHGoogle Scholar
  21. 21.
    E.K. Sadalla, W.J. Burroughs, and L.J. Staplin, Reference points in spatial cognition, Journal of Experimental Psychology: Human Learning and Memory 6 (1980), no. 5, 516–528.CrossRefGoogle Scholar
  22. 22.
    C.E. Shannon, A mathematical theory of communication, The Bell System Technical Journal 27 (1948), 379–423, 623–656.MathSciNetGoogle Scholar
  23. 23.
    A. Stevens and P. Coupe, Distortions in judged spatial relations, Cognitive Psychology 10 (1978), no. 4, 422–437.CrossRefGoogle Scholar
  24. 24.
    B. Tversky, Distortions in cognitive maps, Geoforum 23 (1992), no. 2, 131–138.CrossRefGoogle Scholar
  25. 25.
    M.F. Worboys, Nearness relations in environmental space, International Journal of Geographical Information Science (2001), In press.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Matt Duckham
    • 1
  • Michael Worboys
    • 1
  1. 1.Department of Computer ScienceKeele UniversityStaffordshireUK

Personalised recommendations