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Let $\mathcal L$ be a logical language.

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

A logical formula $\phi$ of $\mathcal L$ is falsifiable for $\mathscr M$ iff:

$\phi$ is not valid in some structure $\mathcal M$ of $\mathscr M$

That is, there exists some structure $\mathcal M$ of $\mathscr M$ such that:

$\mathcal M \not\models_{\mathscr M} \phi$

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