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 | 7 |
| Herbrand universe of the underlying language | 1 |
Statements (39)
| Predicate | Object |
|---|---|
| instanceOf |
concept in automated theorem proving
ⓘ
concept in mathematical logic ⓘ |
| appearsIn |
Herbrand's theorem
ⓘ
surface form:
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 interpretation
ⓘ
surface form:
Herbrand models
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 (8)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Herbrand universe of the underlying language