Deduction

logic

Definition

Deduction

Deduction is reasoning in which a conclusion $\phi$ follows necessarily from a set of premises $\Gamma$. A deductively valid inference satisfies

$$\Gamma \models \phi ,$$

meaning that every interpretation that makes all premises in $\Gamma$ true also makes $\phi$ true. Deduction therefore preserves truth: if its premises are true and its reasoning is valid, its conclusion must be true.