Definition:Formal System

Definition
A formal system is a formal language together with a deductive apparatus.

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

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

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

A formal system is also known as:


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