# Definition:Model (Logic)/Logical Formula

< Definition:Model (Logic)(Redirected from Definition:Model of Logical Formula)

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## 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 $\mathcal M$.