proof theory
E1041771
Proof theory is a branch of mathematical logic that studies the structure, properties, and formalization of mathematical proofs using symbolic and syntactic methods.
Statements (51)
| Predicate | Object |
|---|---|
| instanceOf |
area of logic
ⓘ
branch of mathematical logic ⓘ field of mathematics ⓘ |
| aimsTo |
analyze proof systems
ⓘ
classify the strength of theories ⓘ establish completeness results ⓘ establish consistency results ⓘ establish decidability results ⓘ |
| appliesTo |
arithmetic theories
ⓘ
classical logic ⓘ intuitionistic logic ⓘ modal logics ⓘ set theories ⓘ type theories ⓘ |
| focusesOn |
formalization of proofs
ⓘ
properties of proofs ⓘ structure of proofs ⓘ |
| goal | understand the nature of mathematical reasoning ⓘ |
| hasSubfield |
ordinal proof theory
ⓘ
proof complexity theory ⓘ proof mining ⓘ reverse mathematics ⓘ structural proof theory ⓘ |
| historicallyDevelopedBy |
David Hilbert
NERFINISHED
ⓘ
Gerhard Gentzen NERFINISHED ⓘ Kurt Gödel NERFINISHED ⓘ Paul Bernays NERFINISHED ⓘ |
| isPartOf |
foundations of mathematics
ⓘ
mathematical logic ⓘ |
| relatedTo |
automated theorem proving
ⓘ
computability theory ⓘ model theory ⓘ recursion theory NERFINISHED ⓘ set theory ⓘ type theory ⓘ |
| studies |
Hilbert-style systems
NERFINISHED
ⓘ
consistency proofs ⓘ cut-elimination ⓘ deductive systems ⓘ formal systems ⓘ mathematical proofs ⓘ natural deduction systems ⓘ normalization of proofs ⓘ ordinal analysis ⓘ proof calculi ⓘ proof complexity ⓘ proof search ⓘ proof transformations ⓘ sequent calculi ⓘ |
| usesMethod |
symbolic methods
ⓘ
syntactic methods ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.