\begin{definition}[Definition:Logical Not/Boolean Interpretation]
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:
:$\map v {\neg \mathbf A} = \begin{cases}
\T & : \map v {\mathbf A} = \F \\
\F & : \map v {\mathbf A} = \T
\end{cases}$
\end{definition}