Definition:Axiom/Formal Systems

Definition
 Let $\mathcal L$ be a formal language.

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

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

Also see

 * Definition:Proof System
 * Definition:Rule of Inference