On query languages for linear queries definable with polynomial constraints

  • Luc Vandeurzen
  • Marc Gyssens
  • Dirk Van Gucht
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1118)


It has been argued that the linear database model, in which semi-linear sets are the only geometric objects, is very suitable for most spatial database applications. For querying linear databases, the language FO + linear has been proposed. We present both negative and positive results regarding the expressiveness of FO+linear. First, we show that the dimension query is definable in FO + linear, which allows us to solve several interesting queries. Next, we show the non-definability of a whole class of queries that are related to sets not definable in FO+linear. This result both sharpens and generalizes earlier results independently found by Afrati et al. and the present authors, and demonstrates the need for more expressive linear query languages if we want to sustain the desirability of the linear database model. In this paper, we show how FO + linear can be strictly extended within FO + poly in a safe way. Whether any of the proposed extensions is complete for the linear queries definable in FO + poly remains open. We do show, however, that it is undecidable whether an expression in FO + poly induces a linear query.


Convex Hull Query Language Spatial Database Atomic Formula Linear Formula 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Luc Vandeurzen
    • 1
  • Marc Gyssens
    • 1
  • Dirk Van Gucht
    • 2
  1. 1.Dept. WNIUniversity of LimburgDiepenbeekBelgium
  2. 2.Computer Science Dept.Indiana UniversityBloomingtonUSA

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