# Definition:Model (Logic)/Logical Formula

## Definition

Let $\mathscr M$ be a formal semantics for a logical language $\mathcal L$.

Let $\mathcal M$ be a structure of $\mathscr M$.

Let $\phi$ be a logical formula of $\mathcal L$.

Then $\mathcal M$ is a model of $\phi$ iff:

$\mathcal M \models_{\mathscr M} \phi$

that is, if $\phi$ is valid in $\mathcal M$.