Definition:Falsifiable/Boolean Interpretations

Definition

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

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

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

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

In terms of validity, this can be rendered:

$v \not\models_{\mathrm{BI}} \mathbf A$

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