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.
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 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.