\begin{definition}[Definition:Biconditional/Boolean Interpretation]
Let $\mathbf A$ and $\mathbf B$ be propositional formulas.
Let $\mathbf A \iff \mathbf B$ denote the biconditional operator.
The truth value of $\mathbf A \iff \mathbf B$ under a boolean interpretation $v$ is given by:
:$\map v {\mathbf A \iff \mathbf B} = \begin{cases}
\T & : \map v {\mathbf A} = \map v {\mathbf B} \\
\F & : \text{otherwise}
\end{cases}$
\end{definition}