Definition:Proof System

Definition
Let $\LL$ be a formal language.

A proof system $\mathscr P$ for $\LL$ comprises:


 * Axioms and/or axiom schemata;
 * Rules of inference for deriving theorems.

It is usual that a proof system does this by declaring certain arguments concerning $\LL$ to be valid.

Informally, a proof system amounts to a precise account of what constitutes a (formal) proof.

Also known as
A proof system is referred to by some sources as an axiom system.

Others call it a mathematical theory.

Some sources consider the formal language $\LL$ as an implicit part of the proof system and do not define it separately.

Also see

 * Definition:Deductive Apparatus
 * Definition:Formal System


 * Definition:Formal Semantics