\begin{definition}[Definition:Meet Semilattice]
Let $\struct {S, \preceq}$ be an ordered set.
Suppose that for all $a, b \in S$:
:$a \wedge b \in S$,
where $a \wedge b$ is the meet of $a$ and $b$.
Then the ordered structure $\struct {S, \wedge, \preceq}$ is called a '''meet semilattice'''.
\end{definition}