Tautology

logic

Definition

Tautology

A formula is a tautology if it is true under every interpretation. Then we write:

$$\models F$$

Formally, a formula $F$ is a tautology if

$$\forall v(v(F)=1)$$

In that case, $F$ is valid.

Duality

Duality

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