Category:Minimal Negation Operator
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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.