Herbrand base
E822884
The Herbrand base is the set of all ground (variable-free) atomic formulas that can be formed from the predicate and constant symbols of a first-order language, serving as the foundational domain for Herbrand semantics and automated theorem proving.
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
concept in automated theorem proving
ⓘ
concept in mathematical logic ⓘ concept in model theory ⓘ |
| appearsIn |
Skolemized form of first-order theories
ⓘ
first-order clause logic ⓘ |
| assumes | fixed first-order signature ⓘ |
| componentOf | Herbrand structure NERFINISHED ⓘ |
| constructedFrom |
Herbrand universe
NERFINISHED
ⓘ
predicate symbols applied to ground terms ⓘ |
| contextOfUse |
Horn clause logic
ⓘ
classical first-order logic ⓘ logic programming semantics ⓘ |
| contrastedWith |
non-ground atoms containing variables
ⓘ
set of all formulas of the language ⓘ |
| definedOver | first-order language ⓘ |
| dependsOn |
constant symbols of the language
ⓘ
function symbols of the language ⓘ predicate symbols of the language ⓘ |
| enables | reduction of first-order satisfiability to propositional satisfiability over ground instances ⓘ |
| field |
automated reasoning
ⓘ
first-order logic ⓘ mathematical logic ⓘ |
| formalDefinition | set of all ground atomic formulas over the signature of a first-order language ⓘ |
| hasElementType | ground atomic formula ⓘ |
| hasProperty |
contains all ground atomic formulas that can be formed from the language symbols
ⓘ
contains only variable-free formulas ⓘ is countable when the language signature is countable ⓘ is finite when the language has only finitely many constants and no function symbols of positive arity ⓘ is generally infinite when the language has function symbols of positive arity ⓘ is uniquely determined by the language signature ⓘ |
| namedAfter | Jacques Herbrand NERFINISHED ⓘ |
| relatedConcept |
Herbrand interpretation
NERFINISHED
ⓘ
Herbrand model ⓘ Herbrand theorem NERFINISHED ⓘ Herbrand universe NERFINISHED ⓘ ground atom ⓘ |
| roleInProofTheory |
basis for ground instantiations of clauses
ⓘ
underlies resolution-based theorem proving ⓘ |
| roleInSemantics |
provides canonical set of atoms for defining models of clauses
ⓘ
serves as domain of discourse for Herbrand interpretations ⓘ |
| typicalNotation |
B_L
ⓘ
HB ⓘ |
| usedBy |
SLD-resolution in logic programming
ⓘ
resolution calculus ⓘ tableaux methods ⓘ |
| usedIn |
Herbrand semantics
ⓘ
automated theorem proving ⓘ logic programming ⓘ model checking for first-order theories ⓘ |
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.