De Morgan algebras are bounded lattices that are also equipped with a De Morgan involution.
De Morgan algebras are bounded lattices that are also equipped with a De Morgan involution.
De Morgan involution obeys the following laws:
- ¬¬a = a
- ¬(x∧y) = ¬x∨¬y
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.
- Companion
- object
Value members
Inherited methods
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.
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.
- Inherited from
- BoundedDistributiveLattice