Definition:Pseudocomplement

Definition
Let $(L, \wedge, \vee, \preceq)$ 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 $x \wedge x^* = \bot$.