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

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

\forall x_{1},\ldots ,x_{n}.\phi (x_{1},\ldots ,x_{n})\rightarrow \psi (y_{1},\ldots ,y_{m})

where $\{y_{1},\ldots ,y_{m}\}\subseteq \{x_{1},\ldots ,x_{n}\}$ , $\phi$ is a conjunction of relational and equality atoms and $\psi$ is a non-empty conjunction of equality atoms. A relational atom has the form $R(w_{1},\ldots ,w_{h})$ and an equality atom has the form $w_{i}=w_{j}$ where each of the terms $w,...,w_{h},w_{i},w_{j}$ are variables or constants.