Category:Minimal Negation Operator

From ProofWiki
Jump to navigation Jump to search

This category contains results about 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 if and only if exactly one of its arguments is false.

Subcategories

This category has only the following subcategory.