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Let $\LL$ be a logical language.

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

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

$\phi$ is valid in some structure $\MM$ of $\mathscr M$

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

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

Also known as

It is sometimes convenient to refer to satisfiability for $\mathscr M$ in a single adjective.

In such cases, $\mathscr M$-satisfiable is often seen.

Also see