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Ockham algebra
A lattice $L$ is called an Ockham algebra if
1. $L$ is distributive
2. 3. there is a unary operator $\neg$ on $L$ with the following properties:
(a) (b) $\neg 0=1$ and $\neg 1=0$
Such a unary operator is an example of a dual endomorphism. When applied, $\neg$ interchanges the operations of $\vee$ and $\wedge$, and $0$ and $1$.
An Ockham algebra is a generalization of a Boolean algebra, in the sense that $\neg$ replaces ${}^{{\prime}}$, the complement operator, on a Boolean algebra.
Remarks.

An intermediate concept is that of a De Morgan algebra, which is an Ockham algebra with the additional requirement that $\neg(\neg a)=a$.

In the category of Ockham algebras, the morphism between any two objects is a $\{0,1\}$lattice homomorphism $f$ that preserves $\neg$: $f(\neg a)=\neg f(a)$. In fact, $f(0)=f(\neg 1)=\neg f(1)=\neg 1=0$, so that it is safe to drop the assumption that $f$ preserves $0$.
References
 1 T.S. Blyth, J.C. Varlet, Ockham Algebras, Oxford University Press, (1994).
 2 T.S. Blyth, Lattices and Ordered Algebraic Structures, Springer, New York (2005).
Mathematics Subject Classification
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