On topological elementary equivalence of spatial databases

  • Bart Kuijpers
  • Jan Paredaens
  • Jan Van den Bussche
Contributed Papers Session 10: Spatial Data and Bulk Data
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1186)


We consider spatial databases and queries definable using first-order logic and real polynomial inequalities. We are interested in topological queries: queries whose result only depends on the topological aspects of the spatial data. Two spatial databases are called topologically elementary equivalent if they cannot be distinguished by such topological first-order queries. Our contribution is a natural and effective characterization of topological elementary equivalence of closed databases in the real plane. As far as topological elementary equivalence is concerned, it does not matter whether we use first-order logic with full polynomial inequalities, or first-order logic with simple order comparisons only.


Transformation Rule Spatial Database Real Plane Clockwise Order Polynomial Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. Abel and B.C. Ooi, editors. Advances in spatial databases — 3rd Symposium SSD'93, volume 692 of Lecture Notes in Computer Science. Springer-Verlag, 1993.Google Scholar
  2. 2.
    D.S. Arnon. Geometric reasoning with logic and algebra. Artificial Intelligence, 37:37–60, 1988.Google Scholar
  3. 3.
    M. Benedikt, G. Dong, L. Libkin, and L. Wong. Relational expressive power of constraint query languages. In Proceedings 15th ACM Symposium on Principles of Database Systems, pages 5–16. ACM Press, 1996.Google Scholar
  4. 4.
    J. Bochnak, M. Coste, and M.-F. Roy. Géométrie algébrique réelle. Springer-Verlag, 1987.Google Scholar
  5. 5.
    A. Buchmann, editor. Design and implementation of large spatial databases — First Symposium SSD '89, volume 409 of Lecture Notes in Computer Science. Springer-Verlag, 1989.Google Scholar
  6. 6.
    G.E. Collins. Quantifier elimination for real closed fields by cylindrical algebraic decomposition. Lecture Notes in Computer Science, 33:134–183, 1975.Google Scholar
  7. 7.
    M. Coste. Ensembles semi-algébriques. In Géometrie algébrique réelle et formes quadratiques, volume 959 of Lecture Notes in Mathematics, pages 109–138. Springer, 1982.Google Scholar
  8. 8.
    M.J. Egenhofer and R.D. Franzosa. Point-set topological spatial relations. Int. J. Geographical Information Systems, 5(2):161–174, 1991.Google Scholar
  9. 9.
    M.J. Egenhofer and J.R. Herring, editors. Advances in Spatial Databases, volume 951 of Lecture Notes in Computer Science. Springer, 1995.Google Scholar
  10. 10.
    J. Flum and M. Ziegler. Topological Model Theory, volume 769 of Lecture Notes in Mathematics. Springer-Verlag, 1980.Google Scholar
  11. 11.
    S. Grumbach and J. Su. First-order definability over constraint databases. In U. Montanari and F. Rossi, editors, Principles and practice of constraint programming, volume 976 of Lecture Notes in Computer Science, pages 121–136. Springer, 1995.Google Scholar
  12. 12.
    O. Gunther and H.-J. Schek, editors. Advances in spatial databases — 2nd Symposium SSD '91, volume 525 of Lecture Notes in Computer Science. Springer-Verlag, 1991.Google Scholar
  13. 13.
    C.W. Henson, C.G. Jockusch, Jr., L.A. Rubel, and G. Takeuti. First order topology, volume CXLIII of Dissertationes Mathematicae. 1977.Google Scholar
  14. 14.
    P.C. Kanellakis, G.M. Kuper, and P.Z. Revesz. Constraint query languages. Journal of Computer and System Sciences, 51(1):26–52, August 1995.Google Scholar
  15. 15.
    E.E. Moise. Geometric topology in dimensions 2 and 3, volume 47 of Graduate Texts in Mathematics. Springer, 1977.Google Scholar
  16. 16.
    C.H. Papadimitriou, D. Suciu, and V. Vianu. Topological queries in spatial databases. In Proceedings 15th ACM Symposium on Principles of Database Systems, pages 81–92. ACM Press, 1996.Google Scholar
  17. 17.
    J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a theory of spatial database queries. In Proceedings 13th ACM Symposium on Principles of Database Systems, pages 279–288. ACM Press, 1994.Google Scholar
  18. 18.
    A. Pillay. First order topological structures and theories. Journal of Symbolic Logic, 52(3), September 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Bart Kuijpers
    • 1
  • Jan Paredaens
    • 1
  • Jan Van den Bussche
    • 2
  1. 1.Dept. Math. & Computer Sci.University of Antwerp (UIA)AntwerpBelgium
  2. 2.Dept. WNIUniversity of Limburg (LUC)DiepenbeekBelgium

Personalised recommendations