Definition:Semantic Consequence/Boolean Interpretations/Single Formula/Definition 2

Definition
Let $\mathbf A, \mathbf B$ be WFFs of propositional logic.

Then $\mathbf A$ is a semantic consequence of $\mathbf B$ :


 * $\mathbf A \implies \mathbf B$ is a tautology

where $\implies$ is the conditional connective.

Notation
That $\mathbf A$ is a semantic consequence of $\mathbf B$ can be denoted as:


 * $\mathbf B \models_{\mathrm{BI}} \mathbf A$

Also see

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