Definition:Complemented Lattice

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Let $\struct {S, \vee, \wedge, \preceq}$ be a bounded lattice.

Suppose that every $a \in S$ admits a complement.

Then $\struct {S, \vee, \wedge, \preceq}$ is called a complemented lattice.

Also see

Linguistic Note

The word complement comes from the idea of complete-ment, it being the thing needed to complete something else.

It is a common mistake to confuse the words complement and compliment. Usually the latter is mistakenly used when the former is meant.