\begin{definition}[Definition:Complement (Lattice Theory)]
Let $\left({S, \vee, \wedge, \preceq}\right)$ be a bounded lattice.
Denote by $\bot$ and $\top$ the bottom and top of $S$, respectively.
Let $a \in S$.
Then $b \in S$ is called a '''complement of $a$''' {{iff}}:
:$b \vee a = \top$
:$b \wedge a = \bot$
If $a$ has a unique '''complement''', it is denoted by $\neg a$.
\end{definition}