Model (Predicate Logic)

If $\mathcal{I}$ satisfies $\varphi$, $\mathcal{I}$ is said to be a model of $\varphi$. If $\mathcal{I}$ does not satisfy $\varphi$, it can be denoted by $\mathcal{I}/\models \varphi$.

For an interpretation $\mathcal{I}$ and a formula $\varphi$, we can also write $\mathcal{I}(\varphi )=1$ and $\mathcal{I}(\varphi )=0$ to say that $\mathcal{I}$ satisfies and does not satisfy $\varphi$ respectively.