Herbrand semantics
E822886
Herbrand semantics is a formal framework in logic and automated theorem proving that interprets first-order formulas over the Herbrand universe of ground terms to define truth and satisfiability.
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
framework in automated theorem proving
ⓘ
semantics in mathematical logic ⓘ |
| advantage |
avoids arbitrary non-denumerable domains by using syntactic terms as domain elements
ⓘ
reduces semantic reasoning to combinatorics over ground atoms ⓘ |
| appliesTo | first-order logic ⓘ |
| assumes |
fixed function symbols and constants of the underlying language
ⓘ
standard syntactic formation rules of first-order logic ⓘ |
| basedOn |
Herbrand base
ⓘ
Herbrand universe NERFINISHED ⓘ |
| characteristicFeature |
restricts interpretations to ground terms built from the language’s function symbols and constants
ⓘ
treats predicate symbols as the only non-fixed part of interpretations ⓘ |
| clarifies | relationship between syntactic derivations and semantic models in first-order logic ⓘ |
| concerns | truth of ground atoms in Herbrand interpretations ⓘ |
| defines |
satisfiability for first-order formulas over the Herbrand universe
ⓘ
truth for first-order formulas over the Herbrand universe ⓘ |
| field |
mathematical logic
ⓘ
theoretical computer science ⓘ |
| formalObject | Herbrand structure NERFINISHED ⓘ |
| historicalContext | developed in the context of early 20th-century proof theory ⓘ |
| implies | a formula is satisfiable iff it has a Herbrand model (under suitable conditions) ⓘ |
| interprets | first-order formulas ⓘ |
| namedAfter | Jacques Herbrand NERFINISHED ⓘ |
| relatedConcept |
Herbrand interpretation
NERFINISHED
ⓘ
Herbrand model NERFINISHED ⓘ Herbrand’s theorem NERFINISHED ⓘ ground instantiation of clauses ⓘ least Herbrand model ⓘ |
| relatedTo |
Tarskian semantics
NERFINISHED
ⓘ
model-theoretic semantics ⓘ |
| roleIn |
connecting syntactic derivability with semantic satisfiability
ⓘ
formalizing semantics of Horn clause programs ⓘ providing a basis for completeness proofs in first-order logic ⓘ |
| supports |
construction of countermodels via ground instances
ⓘ
formal analysis of logic programs ⓘ |
| typicalUse |
analyzing satisfiability of clause sets via ground instances
ⓘ
reasoning about sets of clauses ⓘ |
| usedBy |
logic programming systems such as Prolog (at the semantic level)
ⓘ
resolution-based theorem provers ⓘ |
| usedIn |
automated theorem proving
ⓘ
logic programming ⓘ model theory for logic programming languages ⓘ proof theory ⓘ |
| usesDomain |
Herbrand universe
NERFINISHED
ⓘ
set of ground terms ⓘ |
| varies | interpretations of predicate symbols ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.