Contradiction

logic

Definition

Contradiction

A formula is a contradiction if it is false under every interpretation. Then we write:

$$/\models F$$

Formally, a formula $F$ is a contradiction if

$$\forall v(v(F)=0)$$

In that case, $F$ is unsatisfiable.

Duality

Duality

$P$ is a tautology iff $\neg P$ is contradictory.