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A formal system is an abstract structure and formalization of an axiomatic system used for deducing, using rules of inference, theorems from axioms by a set of inference rules.[1]
In 1921, David Hilbert proposed to use formal systems as the foundation of knowledge in mathematics.[2]
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.
- ^ "Formal system | Logic, Symbols & Axioms | Britannica". www.britannica.com. Retrieved 2023-10-10.
- ^ Zach, Richard (31 July 2003). "Hilbert's Program". Hilbert's Program, Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University.