Herbrand universe
E238235
The Herbrand universe is a fundamental concept in mathematical logic and automated theorem proving, consisting of all ground (variable-free) terms that can be built from the function symbols and constants of a given first-order language.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Herbrand universe canonical | 13 |
| Herbrand universe of the underlying language | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2139570 — 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: Herbrand universe Context triple: [Jacques Herbrand, knownFor, Herbrand universe]
-
A.
von Neumann universe
The von Neumann universe is a cumulative, well-founded hierarchy of sets used as a standard model of the set-theoretic universe in axiomatic set theory.
-
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.
Tarski's undefinability theorem
Tarski's undefinability theorem is a fundamental result in mathematical logic showing that, in sufficiently strong formal systems, the notion of truth for the language of the system cannot be defined within that same language.
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D.
Jacques Herbrand
Jacques Herbrand was a French mathematician and logician known for his foundational contributions to proof theory and mathematical logic, particularly Herbrand's theorem.
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E.
completeness theorem for first-order logic
The completeness theorem for first-order logic is a fundamental result in mathematical logic, proved by Kurt Gödel, which states that every logically valid first-order formula is provable from the axioms of first-order logic.
- 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: Herbrand universe Target entity description: The Herbrand universe is a fundamental concept in mathematical logic and automated theorem proving, consisting of all ground (variable-free) terms that can be built from the function symbols and constants of a given first-order language.
-
A.
von Neumann universe
The von Neumann universe is a cumulative, well-founded hierarchy of sets used as a standard model of the set-theoretic universe in axiomatic set theory.
-
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.
Tarski's undefinability theorem
Tarski's undefinability theorem is a fundamental result in mathematical logic showing that, in sufficiently strong formal systems, the notion of truth for the language of the system cannot be defined within that same language.
-
D.
Jacques Herbrand
Jacques Herbrand was a French mathematician and logician known for his foundational contributions to proof theory and mathematical logic, particularly Herbrand's theorem.
-
E.
completeness theorem for first-order logic
The completeness theorem for first-order logic is a fundamental result in mathematical logic, proved by Kurt Gödel, which states that every logically valid first-order formula is provable from the axioms of first-order logic.
- F. None of above. chosen
Statements (39)
| Predicate | Object |
|---|---|
| instanceOf |
concept in automated theorem proving
ⓘ
concept in mathematical logic ⓘ |
| appearsIn |
Herbrand’s theorem
ⓘ
linked to:
Herbrand's theorem
|
| assumes | given first-order signature ⓘ |
| assumption | language has at least one constant symbol or 0-ary function symbol ⓘ |
| builtFrom |
constant symbols of the language
ⓘ
function symbols of the language ⓘ |
| cardinalityProperty |
can be countably infinite
ⓘ
can be finite ⓘ |
| consistsOf |
ground terms
ⓘ
variable-free terms ⓘ |
| context | first-order predicate logic ⓘ |
| definedInTermsOf | first-order language ⓘ |
| dependsOn |
set of constant symbols
ⓘ
set of function symbols ⓘ |
| elementType | terms built from constants and function symbols only ⓘ |
| excludes |
non-ground terms
ⓘ
variables ⓘ |
| field |
automated theorem proving
ⓘ
mathematical logic ⓘ |
| formalProperty | closed under application of function symbols ⓘ |
| ifLanguageHasNoConstants | often a new constant is added to define a non-empty Herbrand universe ⓘ |
| is | set of all ground terms over a given signature ⓘ |
| mathematicalStructure | set ⓘ |
| namedAfter | Jacques Herbrand ⓘ |
| relatedConcept |
Herbrand base
ⓘ
Herbrand interpretation ⓘ |
| relatedTo |
ground instances of clauses
ⓘ
term algebra ⓘ |
| role |
provides canonical domain for Herbrand models
ⓘ
reduces first-order satisfiability to propositional satisfiability under Herbrand’s theorem ⓘ |
| usedBy |
automated deduction systems
ⓘ
logic programming languages such as Prolog ⓘ |
| usedIn |
Herbrand models
ⓘ
linked to:
Herbrand interpretation
Herbrand semantics ⓘ logic programming semantics ⓘ model theory for first-order logic ⓘ proof theory ⓘ resolution-based theorem proving ⓘ |
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: Herbrand universe Description of subject: The Herbrand universe is a fundamental concept in mathematical logic and automated theorem proving, consisting of all ground (variable-free) terms that can be built from the function symbols and constants of a given first-order language.
Referenced by (14)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Herbrand universe