Definition:Multiplicative Relation

Definition

Let $L = \left({S, \wedge, \preceq}\right)$ be a meet semilattice.

Let $\mathcal R$ be a relation on $S$.

Then $\mathcal R$ is multiplicative (relation) if and only if

$\forall a, x, y \in S: \left({\left({a, x}\right), \left({a, y}\right) \in \mathcal R \implies \left({a, x \wedge y}\right) \in \mathcal R}\right)$