Definition:Formal System

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

Let $\mathcal F$ be a formal system consisting of a formal language with deductive apparatus $\mathcal D$.

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

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

Also known as
A formal system is also known as:


 * A logical system;
 * A logistic system;
 * A logical calculus;
 * A logic.