# Definition:Boolean Interpretation/Truth Value

## Definition

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 $\map v \phi$.