Abbreviation: InvLat
An \emph{involutive lattice} is a structure $\mathbf{A}=\langle A,\vee,\wedge,\neg\rangle$ such that
$\langle A,\vee,\wedge\rangle$ is a lattices
$\neg$ is a De Morgan involution: $\neg( x\wedge y) =\neg x\vee \neg y$, $\neg\neg x=x$
Remark: It follows that $\neg ( x\vee y) =\neg x\wedge \neg y$. Thus $\neg$ is a dual automorphism.
Let $\mathbf{A}$ and $\mathbf{B}$ be involutive lattices. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism:
$h(x\vee y)=h(x)\vee h(y)$, $h(\neg x)=\neg h(x)$
Example 1:
$\begin{array}{lr}
f(1)= &1
f(2)= &1
f(3)= &1
f(4)= &
f(5)= &
f(6)= &
f(7)= &
f(8)= &
f(9)= &
f(10)= &
\end{array}$