# Definition:Logical Not/Boolean Interpretation

## Definition

Let $\mathbf A$ be a propositional formula.

Let $\neg$ denote the negation operator.

The truth value of $\neg \mathbf A$ under a boolean interpretation $v$ is given by:

$v \left({\neg \mathbf A}\right) = \begin{cases} T & : v \left({\mathbf A}\right) = F \\ F & : v \left({\mathbf A}\right) = T \end{cases}$