Equality-generating dependency

In relational database theory, an equality-generating dependency (EGD) is a certain kind of constraint on data. It is a subclass of the class of embedded dependencies (ED).

An algorithm known as the chase takes as input an instance that may or may not satisfy a set of EGDs (or, more generally, a set of EDs), and, if it terminates (which is a priori undecidable), output an instance that does satisfy the EGDs.

An important subclass of equality-generating dependencies are functional dependencies.

Definition

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An equality-generating dependency is a sentence in first-order logic of the form:

 

where  ,   is a conjunction of relational and equality atoms and   is a non-empty conjunction of equality atoms. A relational atom has the form   and an equality atom has the form  , where each of the terms   are variables or constants.

Actually, one can remove all equality atoms from the body of the dependency without loss of generality.[1] For instance, if the body consists in the conjunction  , then it can be replaced with   (analogously replacing possible occurrences of the variables   and   in the head).

An equivalent definition is the following:[2]

 

where  . Indeed, generating a conjunction of equalities is equivalent to have multiple dependencies which generate only one equality.

References

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  1. ^ (Abiteboul, Hull & Vianu 1995, p. 217)
  2. ^ Calì, Andrea; Pieris, Andreas (2011). On Equality-Generating Dependencies in Ontology Querying - Preliminary Report (PDF). Alberto Mendelzon International Workshop on Foundations of Data Management (AMW 2011).

Further reading

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