Definition:Formal System

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.