Definition:Independent Rule of Inference
Jump to navigation
Jump to search
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.