Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Chase

  • Alin Deutsch
  • Alan Nash
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_1250

Definition

The chase is a procedure that takes as input a set Σ of constraints and an instance I. The chase does not always terminate, but if it does it produces as output an instance U with the following properties:
  1. 1.

    U ⊨ Σ; that is, U satisfies Σ.

     
  2. 2.

    IU; that is, there is a homomorphism from I to U.

     
  3. 3.

    For every instance J (finite or infinite), if J ⊨ Σ and IJ, then UJ.

     

In [7], an instance that satisfies (1) and (2) above is called a model of Σ and I and an instance that satisfies (3) above is called strongly universal.

In summary, the chase is a procedure which – whenever it terminates – yields a strongly-universal model.

Comments

  1. 1.

    The set Σ of constraints is usually a set of tuple-generating dependencies (tgds) and equality-generating dependencies (egds) [5], or, equivalently, embedded dependencies [5, 10]. However, the chase has been extended to wider classes of constraints and to universality under functions other than homomorphisms [6, 7, 9]. In this case, the...

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Recommended Reading

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of California-San DiegoLa JollaUSA
  2. 2.Aleph One LLCLa JollaUSA

Section editors and affiliations

  • Leonid Libkin
    • 1
  1. 1.School of InformaticsUniversity of EdinburghEdinburghUK