Formal system

A formal system is an abstract structure and formalization of an axiomatic system used for inferring theorems from axioms by a set of inference rules.

In 1921, David Hilbert proposed to use the formal system as the foundation for the knowledge in mathematics.

The term formalism is sometimes a rough synonym for formal system, but it also refers to a given style of notation, for example, Paul Dirac's bra–ket notation.