Definition:Formal System
From ProofWiki
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.
