Herbrand conjunction (for universal formulas)
E822898
A Herbrand conjunction (for universal formulas) is a finite conjunction of ground instances of a universally quantified formula, used in Herbrand’s theorem and automated reasoning to represent universal information over a Herbrand universe.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Herbrand conjunction (for universal formulas) canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9809810 — 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 conjunction (for universal formulas) Context triple: [Herbrand disjunction, hasOppositeConcept, Herbrand conjunction (for universal formulas)]
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A.
Herbrand disjunction
Herbrand disjunction is a logical formula formed as a finite disjunction of ground instances of a first-order formula, central to Herbrand’s theorem in proof theory and automated reasoning.
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B.
Herbrand universe
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.
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C.
Herbrand's theorem
Herbrand's theorem is a fundamental result in mathematical logic and proof theory that characterizes the validity of first-order formulas via finite sets of ground instances, forming a basis for automated theorem proving.
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D.
Herbrand expansion
Herbrand expansion is a method in mathematical logic that transforms first-order formulas into equivalent (often infinite) propositional combinations by systematically instantiating quantified variables with terms from the Herbrand universe.
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E.
Herbrand function
The Herbrand function is a numerical tool in local class field theory that measures the ramification filtration of Galois groups, playing a key role in understanding how ramification behaves in extensions of local fields.
- 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 conjunction (for universal formulas) Target entity description: A Herbrand conjunction (for universal formulas) is a finite conjunction of ground instances of a universally quantified formula, used in Herbrand’s theorem and automated reasoning to represent universal information over a Herbrand universe.
-
A.
Herbrand disjunction
Herbrand disjunction is a logical formula formed as a finite disjunction of ground instances of a first-order formula, central to Herbrand’s theorem in proof theory and automated reasoning.
-
B.
Herbrand universe
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.
-
C.
Herbrand's theorem
Herbrand's theorem is a fundamental result in mathematical logic and proof theory that characterizes the validity of first-order formulas via finite sets of ground instances, forming a basis for automated theorem proving.
-
D.
Herbrand expansion
Herbrand expansion is a method in mathematical logic that transforms first-order formulas into equivalent (often infinite) propositional combinations by systematically instantiating quantified variables with terms from the Herbrand universe.
-
E.
Herbrand function
The Herbrand function is a numerical tool in local class field theory that measures the ramification filtration of Galois groups, playing a key role in understanding how ramification behaves in extensions of local fields.
- F. None of above. chosen
Statements (37)
| Predicate | Object |
|---|---|
| instanceOf |
concept in automated reasoning
ⓘ
concept in mathematical logic ⓘ logical construct ⓘ |
| appearsIn |
completeness proofs for first-order logic
ⓘ
proof of Herbrand’s theorem ⓘ |
| assumes |
fixed Herbrand base
ⓘ
fixed Herbrand universe ⓘ |
| constructedBy | instantiating universal quantifiers with ground terms ⓘ |
| constructedFrom | universally quantified formula ⓘ |
| definedOver | Herbrand universe NERFINISHED ⓘ |
| formalizes | finite conjunction of ground instances of a universal formula ⓘ |
| hasComponent | ground instance of a universally quantified formula ⓘ |
| hasDomain |
automated theorem proving
ⓘ
first-order logic ⓘ proof theory ⓘ |
| hasProperty |
built from ground atoms
ⓘ
contains no free variables ⓘ contains no function symbols outside the Herbrand universe ⓘ finite conjunction ⓘ quantifier-free ⓘ |
| hasRole |
bridge between syntactic formulas and semantic models
ⓘ
intermediate representation in automated theorem proving ⓘ |
| isPartOf | Herbrand semantics NERFINISHED ⓘ |
| namedAfter | Jacques Herbrand NERFINISHED ⓘ |
| relatedTo |
Herbrand disjunction
NERFINISHED
ⓘ
Herbrand expansion NERFINISHED ⓘ Herbrand model NERFINISHED ⓘ |
| represents | universal information over a Herbrand universe ⓘ |
| usedFor |
constructing countermodels
ⓘ
reducing first-order validity to propositional validity ⓘ representing sets of universal consequences ⓘ |
| usedIn |
Herbrand’s theorem
NERFINISHED
ⓘ
automated reasoning ⓘ model-theoretic proofs ⓘ proof search ⓘ resolution-based theorem proving ⓘ satisfiability reasoning ⓘ |
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 conjunction (for universal formulas) Description of subject: A Herbrand conjunction (for universal formulas) is a finite conjunction of ground instances of a universally quantified formula, used in Herbrand’s theorem and automated reasoning to represent universal information over a Herbrand universe.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.