Definition:Falsifiable/Formula

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Definition

Let $\LL$ be a logical language.

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


A logical formula $\phi$ of $\LL$ is falsifiable for $\mathscr M$ if and only if:

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

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

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



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