Definition:Boolean Interpretation/Truth Value

Definition
Let $\mathcal L_0$ be the language of propositional logic.

Let $\mathcal P_0$ be the vocabulary of $\mathcal L_0$. Let $\phi$ be a WFF of propositional logic.

Let $v: \mathcal L_0 \to \left\{{T, F}\right\}$ be a boolean interpretation of $\phi$.

The truth value of $\phi$ under $v$ is $v (\phi)$.