Fourth normal form

Definition

Let $R$ be a relation schema, and $D$ be a set of functional and multivalued dependencies of $R$. Let $D^{+}$ be the closure of $D$.

Then, $R$ is said to be in fourth normal form(4NF) if, for all multivalued dependencies $\alpha \twoheadrightarrow \beta \in D^{+}$, at least one of the followings hold:

• $\alpha \twoheadrightarrow \beta$ is trivial. (i.e., $\beta \subseteq \alpha$, or $\alpha \cup \beta =R$)
• $\alpha$ is a superkey of $R$. (i.e., $\alpha \to R$)

Decomposition into 4NF