Return a CommutativeRig using join and meet.
Return a CommutativeRig using join and meet. Note this must obey the commutative rig laws since meet(a, one) = a, and meet and join are associative, commutative and distributive.
This is the lattice with meet and join swapped
This is the lattice with meet and join swapped
De Morgan algebras are bounded lattices that are also equipped with a De Morgan involution.
De Morgan involution obeys the following laws:
However, in De Morgan algebras this involution does not necessarily provide the law of the excluded middle. This means that there is no guarantee that (a ∨ ¬a) = 1. De Morgan algebra do not not necessarily provide the law of non contradiction either. This means that there is no guarantee that (a ∧ ¬a) = 0.
De Morgan algebras are useful to model fuzzy logic. For a model of classical logic, see the boolean algebra type class implemented as Bool.