WIKI :: A formal system is used for inferring theorems from axioms according to a set of rules. Each formal system uses primitivesymbols(which collectively form analphabet) to finitely construct aformal languagefrom a set ofaxiomst through inferentialrules of formation. The system thus consists of valid formulas built up through finite combinations of the primitive symbols—combinations that are formed from the axioms in accordance with the stated rules.