Restriction (Database)

Definition

Functional dependency

Let $F$ be the set of functional dependencies on schema $R$, and let $R_1,\cdots ,R_n$ be a decomposition of $R$.

The restriction of $F$ to $R_i$, denoted as $F_i$, is the set of all functional dependencies in the closure $F^{+}$ (Note: not $F$) that include only attributes of $R_i$.

Multivalued dependency

Let $D$ be the set of functional and multivalued dependencies on schema $R$, and let $R_1,\cdots ,R_n$ be a decomposition of $R$.

The restriction of $D$ to $R_i$, denoted as $D_i$, is the set of all functional and multivalued dependencies in the closure $D^{+}$ that include only attributes of $R_i$.

That is,

• All functional dependencies in $D^{+}$ that include only attributes of $R_i$.
• All multivalued dependencies of the form $\alpha \twoheadrightarrow (\beta \cap R_i)$, where $\alpha \subseteq R_i$ and $\alpha \twoheadrightarrow \beta \in D^{+}$.