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.
U ⊨ Σ; that is, U satisfies Σ.
- 2.
I → U; that is, there is a homomorphism from I to U.
- 3.
For every instance J (finite or infinite), if J ⊨ Σ and I → J, then U → J.
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.
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 chase...
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Deutsch, A., Nash, A. (2018). Chase. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_1250
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