Full Functional Dependency (Relational Algebra)

relational-algebra

Definition

Full Functional Dependency (Relational Algebra)

Let $\mathcal{R}$ be a schema of a relation $R$ and $\alpha ,\beta \subseteq \mathcal{R}$ (subsets of attributes of $\mathcal{R}$).

$\beta$ is called fully functional dependent on $\alpha$ if:

1. $\alpha \to \beta$ ($a$ functionally determines $\beta$) and
2. $\alpha$ cannot be reduced, meaning:

$$\forall A\in \alpha :(\alpha -\{A\})\cancel{\to }\beta$$