\begin{definition}[Definition:Formal System]
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 $\FF$.
\end{definition}