\begin{definition}[Definition:Boolean Interpretation/Truth Value]
Let $\LL_0$ be the language of propositional logic.
Let $\PP_0$ be the vocabulary of $\LL_0$.
Let $\phi$ be a WFF of propositional logic.
Let $v: \LL_0 \to \set {\T, \F}$ be a boolean interpretation of $\phi$.
The '''truth value of $\phi$ under $v$''' is $\map v \phi$.
\end{definition}