Definition:Minimal Negation Operator

Definition
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 exactly one of its arguments is false.

Notation
The symbol $\nu$ used for this is the Greek letter nu.

Also see

 * Definition:Logical Boundary Operator