# Definition:Satisfiable/Boolean Interpretations

## Definition

Let $\mathbf A$ be a WFF of propositional logic.

$\mathbf A$ is called satisfiable (for boolean interpretations) if and only if:

$\map v {\mathbf A} = \T$

for some boolean interpretation $v$ for $\mathbf A$.

In terms of validity, this can be rendered:

$v \models_{\mathrm{BI}} \mathbf A$

that is, $\mathbf A$ is valid in the boolean interpretation $v$ of $\mathbf A$.