An algebraic lattice $left-parenthesis upper L comma logical-and comma logical-or right-parenthesis$ is a set $upper L$ with two binary operations meet and join, $logical-and$ and $logical-or$ such that both operations are commutative and associative and the absorption law holds.

I.e. $for-all a comma b comma c element-of upper L$

1. commutivity: $a logical-and b equals b logical-and a$, $a logical-or b equals b logical-or a$
2. associativity: $left-parenthesis a logical-and b right-parenthesis logical-and c equals a logical-and left-parenthesis b logical-and c right-parenthesis$, $left-parenthesis a logical-or b right-parenthesis logical-or c equals a logical-or left-parenthesis b logical-or c right-parenthesis$
3. absorption law: $a equals a logical-and left-parenthesis a logical-or b right-parenthesis equals a logical-or left-parenthesis a logical-and b right-parenthesis$