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.
All labels observed (2)
| Label | Occurrences |
|---|---|
| proof theory canonical | 2 |
| foundations of structural proof theory | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T13444213 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: proof theory Context triple: [Per Martin-Löf, areaOfInfluence, proof theory]
-
A.
Gentzen-style proof systems
Gentzen-style proof systems are formal logical calculi, such as natural deduction and sequent calculi, that rigorously structure proofs using inference rules to clarify the foundations of mathematics and logic.
-
B.
Recherches sur la théorie de la démonstration
Recherches sur la théorie de la démonstration is Jacques Herbrand’s foundational work in mathematical logic, introducing key results in proof theory and what is now known as Herbrand’s theorem.
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C.
Gentzen’s consistency proof for arithmetic
Gentzen’s consistency proof for arithmetic is a landmark 1930s result in proof theory that established the consistency of Peano arithmetic using transfinite induction up to the ordinal ε₀.
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D.
Curry–Howard correspondence
The Curry–Howard correspondence is a foundational principle in logic and computer science that establishes a deep analogy between proofs and programs, and between logical propositions and types in programming languages.
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E.
Hilbert’s program
Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: proof theory Target entity description: Proof theory is a branch of mathematical logic that studies the structure, properties, and formalization of mathematical proofs using symbolic and syntactic methods.
-
A.
Gentzen-style proof systems
Gentzen-style proof systems are formal logical calculi, such as natural deduction and sequent calculi, that rigorously structure proofs using inference rules to clarify the foundations of mathematics and logic.
-
B.
Recherches sur la théorie de la démonstration
Recherches sur la théorie de la démonstration is Jacques Herbrand’s foundational work in mathematical logic, introducing key results in proof theory and what is now known as Herbrand’s theorem.
-
C.
Gentzen’s consistency proof for arithmetic
Gentzen’s consistency proof for arithmetic is a landmark 1930s result in proof theory that established the consistency of Peano arithmetic using transfinite induction up to the ordinal ε₀.
-
D.
Curry–Howard correspondence
The Curry–Howard correspondence is a foundational principle in logic and computer science that establishes a deep analogy between proofs and programs, and between logical propositions and types in programming languages.
-
E.
Hilbert’s program
Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
- F. None of above. chosen
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
ⓘ
Gerhard Gentzen ⓘ Kurt Gödel ⓘ Paul Bernays ⓘ |
| isPartOf |
foundations of mathematics
ⓘ
mathematical logic ⓘ |
| relatedTo |
automated theorem proving
ⓘ
computability theory ⓘ model theory ⓘ recursion theory ⓘ
linked to:
Computability Theory
set theory ⓘ type theory ⓘ |
| studies |
Hilbert-style systems
ⓘ
linked to:
Hilbert-style deductive systems
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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: proof theory Description of subject: Proof theory is a branch of mathematical logic that studies the structure, properties, and formalization of mathematical proofs using symbolic and syntactic methods.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
Untersuchungen über das logische Schließen
→
contributedTo
→
foundations of structural proof theory
ⓘ
linked to: proof theory