Definition:Formal System

Definition
A formal system is a formal language $\LL$ together with a deductive apparatus for $\LL$.

Let $\FF$ be a formal system consisting of a formal language with deductive apparatus $\DD$.

By applying the formal grammar of $\LL$, one constructs well-formed formulae in $\LL$.

Of such a well-formed formula, one can then use the deductive apparatus $\DD$ to determine whether or not it is a theorem in $\FF$.

Also see

 * Definition:Symbolic Logic, which is an important field of application for formal systems.