\begin{definition}[Definition:Multiplicative Relation]
Let $L = \struct {S, \wedge, \preceq}$ be a meet semilattice.
Let $\RR$ be a relation on $S$.
Then $\RR$ is '''multiplicative (relation)''' {{iff}}
:$\forall a, x, y \in S: \paren {\tuple {a, x}, \tuple {a, y} \in \RR \implies \tuple {a, x \wedge y} \in \RR}$
\end{definition}