Query Languages for Constraint Databases: First-Order Logic, Fixed-Points, and Convex Hulls

  • Stephan Kreutzer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1973)

Abstract

We define various extensions of first-order logic on linear as well as polynomial constraint databases. First, we extend first-order logic by a convex closure operator and show this logic, FO(conv), to be closed and to have Ptime data-complexity. We also show that a weak form of multiplication is definable in this language and prove the equivalence between this language and the multiplication part of PFOL. We then extend FO(conv) by fixed-point operators to get a query languages expressive enough to capture Ptime. In the last part of the paper we lift the results to polynomial constraint databases.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Stephan Kreutzer
    • 1
  1. 1.Lehrgebiet Mathematische Grundlagen der InformatikAachen

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