Definition:Semantic Consequence/Predicate Logic

Definition
 Let $\FF$ be a collection of WFFs of predicate logic.

Then a WFF $\mathbf A$ is a semantic consequence of $\FF$ :


 * $\AA \models_{\mathrm{PL} } \FF$ implies $\AA \models_{\mathrm{PL} } \mathbf A$

for all structures $\AA$, where $\models_{\mathrm{PL} }$ is the models relation.

Notation
That $\mathbf A$ is a semantic consequence of $\FF$ is denoted as:


 * $\FF \models_{\mathrm{PL} } \mathbf A$

Also see

 * Semantic Consequence preserved in Supersignature, showing that this notion is indeed independent of the choice of signature which is left implicit above