Definition:Satisfiable/Boolean Interpretations

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

$\mathbf A$ is called satisfiable (for boolean interpretations) iff:


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

for some boolean interpretation $v$ for $\mathbf A$.

In terms of validity, this can be rendered:


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

that is, $\mathbf A$ is valid in the boolean interpretation $v$ of $\mathbf A$.

Also see

 * Definition:Valid (Boolean Interpretation)
 * Definition:Tautology (Boolean Interpretations)
 * Definition:Unsatisfiable (Boolean Interpretations)