Definition:Logical Complement

Context
Logic and boolean algebra.

Boolean Algebra
Let $$f: \mathbb{B}^k \to \mathbb{B}$$ be a boolean function.

The (logical) complement of $$f$$ is the function $$f'$$ (or $$\overline f$$) defined as:
 * $$\forall p \in \operatorname{Dom} \left({f}\right): f' \left({p}\right) = \neg \left({f \left({p}\right)}\right)$$

Logic
The (logical) complement of a statement $$p$$ is the negation of $$p$$, that is, $$\neg p$$.

From Double Negation, it follows that the complement of $$\neg p$$ is $$p$$.