Definition:Boolean Interpretation/Formal Semantics/Invalid

Definition

Let $\phi$ be a WFF of propositional logic.

$\phi$ is declared ($\mathrm{BI}$-)invalid in a boolean interpretation $v$ if and only if:

$\map v \phi = \F$

Symbolically, this can be expressed as:

$v \not\models_{\mathrm{BI}} \phi$