Definition:Semantic Consequence/Boolean Interpretations

Definition
Let $\mathcal F$ be a collection of WFFs of propositional logic.

Then a WFF $\mathbf A$ is a semantic consequence of $\mathcal F$ iff:


 * $v \models_{\mathrm{BI}} \mathcal F$ implies $v \models_{\mathrm{BI}} \mathbf A$

where $\models_{\mathrm{BI}}$ is the models relation.

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


 * $\mathcal F \models_{\mathbf{BI}} \mathbf A$

Also see

 * Definition:Semantic Equivalence (Boolean Interpretations)
 * Definition:Logical Consequence