\begin{definition}[Definition:Pseudocomplement]
Let $\struct {L, \wedge, \vee, \preceq}$ be a lattice with smallest element $\bot$.
Let $x, x^* \in L$.
Then $x^*$ is the '''pseudocomplement''' of $x$ {{iff}}
: $x^*$ is the greatest element of $L$ such that $x \wedge x^* = \bot$.
\end{definition}