Definition:Tautology/Formal Semantics/Boolean Interpretations

Definition
 Let $\mathbf A$ be a WFF of propositional logic.

Then $\mathbf A$ is called a tautology (for boolean interpretations) iff:


 * $v \left({\mathbf A}\right) = T$

for every boolean interpretation $v$ of $\mathbf A$.

That $\mathbf A$ is a tautology may be denoted as:


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

Also known as
A tautology in this context may also be described as valid (for boolean interpretations).

On, we have chosen to only use validity in the context of a single boolean interpretation.

Also denoted as
If only boolean interpretations are under discussion, $\models \mathbf A$ is also often encountered.

Also see

 * Method of Truth Tables: Proof of Tautology


 * Definition:Contradiction (Boolean Interpretations)
 * Definition:Valid (Boolean Interpretation)
 * Definition:Satisfiable (Boolean Interpretations)