# Definition:Satisfiable/Formula

< Definition:Satisfiable(Redirected from Definition:Satisfiable Formula)

Jump to navigation
Jump to search
## Definition

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:

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

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

This article is complete as far as it goes, but it could do with expansion.You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Expand}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

## 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.