Definition:Unsatisfiable/Boolean Interpretations

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

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


 * $\map v {\mathbf A} = F$

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

In terms of validity, this can be rendered:


 * $v \not \models_{\mathrm {BI} } \mathbf A$

that is, $\mathbf A$ is invalid in every boolean interpretation of $\mathbf A$.

Also known as
Unsatisfiable formulae are more commonly referred to as contradictions.

To avoid ambiguity with inconsistent formulae, the latter term is discouraged on when specifically referring to unsatisfiability.

Also see

 * Definition:Contradiction


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