Definition:Semantic Consequence

Logical Formula
Let $$P$$ and $$Q$$ be logical formulas.

If $$P$$ is true in every model for $$Q$$, then $$P$$ is a logical consequence of $$Q$$, or $$P$$ is logically implied by $$Q$$.

We can then write $$Q \models P$$.

Set of Logical Formulas
Let $$U$$ be a set of logical formulas.

Let $$P$$ be a logical formula.

If $$P$$ is true in every model of $$U$$, then $$P$$ is a logical consequence of $$U$$, or $$P$$ is logically implied by $$U$$.

We can then write $$U \models P$$.

Alternative term
An alternative term to logical consequence is semantic consequence or semantic entailment.

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