Definition:Semantic Consequence

Definition
Let $P$ and $Q$ be logical formulas.

Then:
 * $P$ is a logical consequence of $Q$, or $P$ is logically implied by $Q$

iff:
 * every model of $Q$ is a model of $P$

or alternatively, iff
 * $P$ is true in every model for $Q$.

We write:
 * $Q \models P$

and we can say:
 * $P$ follows from $Q$

Also known as
Instead of logical consequence, some sources use semantic consequence or semantic entailment.

Thus, $Q \models P$ means $Q$ semantically entails $P$.