Recherches sur la théorie de la démonstration
E238238
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Recherches sur la théorie de la démonstration canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T2139590 — 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: Recherches sur la théorie de la démonstration Context triple: [Jacques Herbrand, notableWork, Recherches sur la théorie de la démonstration]
-
A.
Lectures on the Logic of Arithmetic
Lectures on the Logic of Arithmetic is an educational work by Mary Everest Boole that explores the foundations and teaching of arithmetic through logical and psychological principles.
-
B.
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.
-
C.
Remarks on the Foundations of Mathematics
Remarks on the Foundations of Mathematics is a posthumously published collection of Ludwig Wittgenstein’s later writings that critically examines the nature of mathematical truth, proof, and practice from a philosophical and language-centered perspective.
-
D.
Hilbert and Ackermann’s "Grundzüge der theoretischen Logik"
Hilbert and Ackermann’s "Grundzüge der theoretischen Logik" is a foundational early 20th-century textbook that systematically developed first-order logic and helped establish mathematical logic as a rigorous formal discipline.
-
E.
Frege’s system in "Grundgesetze der Arithmetik"
Frege’s system in "Grundgesetze der Arithmetik" is a foundational logical framework for arithmetic based on second-order logic and Basic Law V, whose inconsistency—revealed by Russell’s paradox—marked a turning point in the development of modern logic and set theory.
- 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: Recherches sur la théorie de la démonstration Target entity description: 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.
-
A.
Lectures on the Logic of Arithmetic
Lectures on the Logic of Arithmetic is an educational work by Mary Everest Boole that explores the foundations and teaching of arithmetic through logical and psychological principles.
-
B.
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.
-
C.
Remarks on the Foundations of Mathematics
Remarks on the Foundations of Mathematics is a posthumously published collection of Ludwig Wittgenstein’s later writings that critically examines the nature of mathematical truth, proof, and practice from a philosophical and language-centered perspective.
-
D.
Hilbert and Ackermann’s "Grundzüge der theoretischen Logik"
Hilbert and Ackermann’s "Grundzüge der theoretischen Logik" is a foundational early 20th-century textbook that systematically developed first-order logic and helped establish mathematical logic as a rigorous formal discipline.
-
E.
Frege’s system in "Grundgesetze der Arithmetik"
Frege’s system in "Grundgesetze der Arithmetik" is a foundational logical framework for arithmetic based on second-order logic and Basic Law V, whose inconsistency—revealed by Russell’s paradox—marked a turning point in the development of modern logic and set theory.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical logic monograph
ⓘ
work in proof theory ⓘ |
| academicDiscipline |
foundations of mathematics
ⓘ
logic ⓘ |
| author | Jacques Herbrand ⓘ |
| citedIn |
historical studies of proof theory
ⓘ
literature on automated deduction ⓘ textbooks on first-order logic and proof theory ⓘ |
| countryOfOrigin | France ⓘ |
| field |
mathematical logic
ⓘ
proof theory ⓘ |
| genre | doctoral thesis ⓘ |
| hasPart |
proofs concerning the structure of formal derivations
ⓘ
results on the reduction of quantifiers to propositional combinations ⓘ statement of Herbrand's theorem for first-order logic ⓘ |
| historicalPeriod | early 20th century logic ⓘ |
| impact |
established a bridge between syntactic proof systems and semantic models
ⓘ
provided a basis for later completeness and decidability results in logic ⓘ |
| influenced |
automated theorem proving
ⓘ
development of proof theory in the 20th century ⓘ model theory techniques for first-order logic ⓘ resolution methods in logic ⓘ |
| introducesConcept |
Herbrand disjunction
ⓘ
Herbrand expansion ⓘ Herbrand universe ⓘ Herbrand's theorem ⓘ |
| keyResult |
equivalence between provability and existence of a finite disjunction of ground instances
ⓘ
reduction of first-order validity to propositional validity via Herbrand expansions ⓘ |
| language | French ⓘ |
| mainSubject |
first-order logic
ⓘ
foundations of mathematics ⓘ predicate calculus ⓘ proof theory ⓘ |
| notableFor | formulation of Herbrand's theorem ⓘ |
| originalTitleLanguage | French ⓘ |
| relatedTo |
Hilbert’s program
ⓘ
surface form:
Hilbert's program
consistency problem for arithmetic ⓘ formalization of mathematical reasoning ⓘ |
| title | Recherches sur la théorie de la démonstration self-link ⓘ |
| topic |
consistency proofs
ⓘ
elimination of quantifiers in proofs ⓘ relationship between syntactic proofs and semantic validity ⓘ |
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: Recherches sur la théorie de la démonstration Description of subject: 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.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
Recherches sur la théorie de la démonstration
→
title
→
Recherches sur la théorie de la démonstration
self-link
ⓘ