formal system
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any well-defined system of abstract thought based on the model of mathematics
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A formal system (or deductive 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. However, in 1931 Kurt Gödel proved that any consistent formal system sufficiently powerful to express basic arithmetic cannot prove its own completeness. This effectively showed that Hilbert's program was impossible as stated.
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axiom
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mathematical logic
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recursive set
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structure
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semantic theory of truth
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formal language
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string
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first-order logic
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Peano axioms
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foundations of mathematics
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formal grammar
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formal methods
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rule of inference
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interpretation
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semantics of logic
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recursively enumerable set
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substitution
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ground expression
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diagram
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Europe
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