Herbrand disjunction
E238239
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Herbrand disjunction canonical | 3 |
Statements (30)
| Predicate | Object |
|---|---|
| instanceOf |
concept in automated reasoning
ⓘ
concept in proof theory ⓘ logical formula ⓘ |
| appearsIn | proofs of first-order validity via Herbrand's theorem ⓘ |
| constructedFrom |
instances of the matrix of a Skolemized formula
ⓘ
substitutions of ground terms for variables ⓘ |
| formalizationLanguage | classical first-order logic ⓘ |
| hasComponent |
finite disjunction
ⓘ
ground instances of a first-order formula ⓘ |
| hasDomain |
Herbrand universe
ⓘ
surface form:
Herbrand universe of the underlying language
|
| hasOppositeConcept | Herbrand conjunction (for universal formulas) ⓘ |
| hasProperty |
contains no variables (is ground)
ⓘ
is a finite disjunction ⓘ is built from instances of a given first-order formula ⓘ |
| isCentralTo | Herbrand's theorem ⓘ |
| isDefinedInContextOf | first-order logic ⓘ |
| namedAfter | Jacques Herbrand ⓘ |
| occursIn |
Herbrand's theorem
ⓘ
surface form:
Herbrand-style proof calculi
cut-elimination style arguments involving Herbrand's theorem ⓘ |
| relatedTo |
Herbrand base
ⓘ
Herbrand expansion ⓘ Herbrand universe ⓘ |
| roleInHerbrandTheorem |
serves as a propositional counterpart of a first-order formula
ⓘ
witnesses the unsatisfiability of a first-order formula ⓘ |
| usedFor |
reducing first-order validity to propositional validity
ⓘ
search procedures in automated theorem proving ⓘ semantic characterization of first-order consequence ⓘ |
| usedIn |
automated reasoning
ⓘ
automated theorem proving ⓘ proof theory ⓘ |
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.