Definition:Multiplicative Relation

Definition
Let $L = \struct {S, \wedge, \preceq}$ be a meet semilattice.

Let $\RR$ be a relation on $S$.

Then $\RR$ is multiplicative (relation)
 * $\forall a, x, y \in S: \paren {\tuple {a, x}, \tuple {a, y} \in \RR \implies \tuple {a, x \wedge y} \in \RR}$