Herbrand interpretation

E238813

model-theoretic construct semantic notion in logic

A Herbrand interpretation is a foundational model-theoretic construct in logic and automated theorem proving that interprets formulas over the Herbrand universe built from a theory’s own function symbols and constants.

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All labels observed (4)

Label	Occurrences
Herbrand interpretation canonical	3
Herbrand model	1
Herbrand models	1
Herbrand structure	1

Statements (36)

Predicate	Object
instanceOf	model-theoretic construct ⓘ semantic notion in logic ⓘ
appliesTo	Skolemized formulas ⓘ clause sets ⓘ
associatesTruthValuesWith	ground atomic formulas ⓘ
assumes	standard syntactic signature of a theory ⓘ
basedOn	Herbrand base ⓘ Herbrand universe ⓘ
characterizedAs	interpretation determined by truth values of ground atoms ⓘ interpretation with canonical domain of ground terms ⓘ
constrains	interpretation of constants to be themselves as ground terms ⓘ interpretation of function symbols to be term-forming operations ⓘ
contrastedWith	arbitrary first-order structures ⓘ
domainOfInterpretation	Herbrand universe ⓘ
enables	reduction of satisfiability to ground instances ⓘ search procedures over ground clauses ⓘ
formalizedIn	model theory ⓘ
interprets	ground atoms ⓘ ground terms ⓘ
interpretsOver	constant symbols of a theory ⓘ function symbols of a theory ⓘ
namedAfter	Jacques Herbrand ⓘ
relatedTo	Herbrand interpretation self-linksurface differs ⓘ surface form: Herbrand model Herbrand semantics ⓘ
roleIn	Herbrand's theorem ⓘ surface form: Herbrand’s theorem completeness results for first-order logic ⓘ
truthAssignmentType	two-valued truth assignment ⓘ
usedBy	Prolog ⓘ logic programming semantics ⓘ resolution calculus ⓘ tableaux methods ⓘ
usedFor	decidability investigations of fragments of first-order logic ⓘ soundness and completeness proofs of automated deduction calculi ⓘ
usedIn	automated theorem proving ⓘ first-order logic ⓘ proof theory ⓘ

Referenced by (6)

Full triples — surface form annotated when it differs from this entity's canonical label.

Jacques Herbrand → developedConcept → Herbrand interpretation ⓘ

Jacques Herbrand → conceptNamedAfter → Herbrand interpretation ⓘ

this entity surface form: Herbrand structure

Herbrand universe → usedIn → Herbrand interpretation ⓘ

this entity surface form: Herbrand models

Herbrand universe → relatedConcept → Herbrand interpretation ⓘ

Herbrand expansion → closelyRelatedTo → Herbrand interpretation ⓘ

Herbrand interpretation → relatedTo → Herbrand interpretation self-linksurface differs ⓘ

this entity surface form: Herbrand model