Definition:Boolean Lattice/Definition 3

Definition
A Boolean lattice is a bounded lattice $\left({S, \vee, \wedge, \preceq, \bot, \top}\right)$ together with a unary operation $\neg$ called complementation, subject to:

$(1): \quad$ For all $a, b \in S$, $a \preceq \neg b$ $a \wedge b = \bot$

$(2): \quad$ For all $a \in S$, $\neg \neg a = a$.

Also see

 * Equivalence of Definitions of Boolean Lattice