Definition:Model (Logic)

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

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

Model of Logical Formula
Let $\phi$ be a logical formula of $\mathcal L$.

Then $\mathcal M$ is a model of $\phi$ iff:


 * $\mathcal M \models_{\mathscr M} \phi$

that is, if $\phi$ is valid in $\mathcal M$.

Model of Set of Logical Formulas
Let $\mathcal F$ be a set of logical formulas of $\mathcal L$.

Then $\mathcal M$ is a model of $\mathcal F$ iff:


 * $\mathcal M \models_{\mathscr M} \phi$ for every $\phi \in \mathcal F$

that is, if it is a model of every logical formulas $\phi \in \mathcal F$.

Also known as
If $\mathcal M$ is a model of $\phi$, respectively $\mathcal F$, one sometimes says that $\mathcal M$ models $\phi$, respectively $\mathcal F$.

Also see

 * Definition:Valid (Formal Systems)