De Morgan algebra

Summary

A De Morgan algebra is a bounded distributive lattice with a negation $\sim$ that is an involution and satisfies De Morgan's laws. Unlike the complement of a Boolean algebra, this negation need not satisfy $a \wedge {\sim} a = 0$ or $a \vee {\sim} a = 1$. De Morgan algebras give the algebraic semantics of several many-valued and relevance logics. Every Boolean algebra is a De Morgan algebra.