Definition:Model (Logic)/Logical Formula

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

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

Let $\phi$ be a logical formula of $\LL$.

Then $\MM$ is a model of $\phi$ if and only if:

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

that is, if and only if $\phi$ is valid in $\MM$.