Definition:Axiom/Formal Systems

Definition
Let $\LL$ be a formal language.

Part of defining a proof system $\mathscr P$ for $\LL$ is to specify its axioms.

An axiom of $\mathscr P$ is a well-formed formula of $\LL$ that $\mathscr P$ approves of by definition.

Also known as
When $\LL$ is a logical language, then one also speaks of logical axioms.

Also see

 * Definition:Proof System
 * Definition:Rule of Inference