\begin{definition}[Definition:Minimal Negation Operator]
Let $\Bbb B$ be a Boolean domain:
:$\Bbb B = \set {\F, \T}$
The '''minimal negation operator''' $\nu$ is a multiary operator:
:$\nu_k: \Bbb B^k \to \Bbb B$
where:
:$k \in \N$ is a natural number
:$\nu_k$ is a boolean function defined as:
::$\map {\nu_k} {x_1, x_2, \ldots, x_k} = \begin {cases}
\T & : \exists! x_j \in \set {x_1, x_2, \ldots, x_k}: x_j = \F \\
\F & : \text {otherwise}
\end{cases}$
That is:
:$\map {\nu_k} {x_1, x_2, \ldots, x_k}$ is true {{iff}} exactly one of its arguments is false.
\end{definition}