Formal system

A formal system is an abstract structure and formalization of an axiomatic system used for deducing, using rules of inference, theorems from axioms.

In 1921, David Hilbert proposed to use formal systems as the foundation of 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.

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