Definition:Independent Rule of Inference

Definition

Let $\LL$ be a formal language.

Let $\mathscr P$ be a proof system for $\LL$.

Let $\RR$ be a rule of inference for $\mathscr P$.

Then $\RR$ is independent if and only if $\RR$ cannot be derived from the axioms and other rules of inference for $\mathscr P$.

Also see

• Results about independent rules of inference can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): independent: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): independent: 2.