Skolemization

E822885

logical transformation technique method in first-order logic technique in automated theorem proving

Skolemization is a logical transformation technique that eliminates existential quantifiers by introducing Skolem functions or constants, commonly used in automated theorem proving and first-order logic.

Try in SPARQL Jump to: Surface forms Statements Referenced by

Observed surface forms (2)

Surface form	Occurrences
Skolem normal form	2
Skolem function	1

Statements (47)

Predicate	Object
instanceOf	logical transformation technique ⓘ method in first-order logic ⓘ technique in automated theorem proving ⓘ
appliedAfter	prenex normal form transformation ⓘ
appliedBefore	Herbrand expansion NERFINISHED ⓘ clausal form conversion ⓘ
assumes	non-empty domain of discourse ⓘ
assumption	classical first-order logic semantics ⓘ
commonUsage	standard preprocessing step in automated theorem provers ⓘ standard step in converting formulas to CNF ⓘ
conditionForSkolemConstant	existential quantifier not within scope of universal quantifiers ⓘ
conditionForSkolemFunction	existential quantifier within scope of universal quantifiers ⓘ
doesNotPreserve	logical equivalence in general ⓘ
effectOnQuantifiers	removes existential quantifiers ⓘ retains universal quantifiers or moves them outward ⓘ
field	automated reasoning ⓘ first-order logic ⓘ mathematical logic ⓘ
historicalOrigin	work of Thoralf Skolem in early 20th century ⓘ
input	first-order logic formula in prenex form ⓘ
introduces	new constant symbols ⓘ new function symbols ⓘ
limitation	not directly applicable to second-order quantifiers ⓘ
namedAfter	Thoralf Skolem NERFINISHED ⓘ
output	first-order logic formula without existential quantifiers ⓘ
preserves	satisfiability ⓘ
property	can increase signature of the language ⓘ produces equisatisfiable formula ⓘ
purpose	eliminate existential quantifiers ⓘ prepare formulas for resolution-based theorem proving ⓘ transform formulas into equisatisfiable form ⓘ
relatedConcept	Herbrand’s theorem NERFINISHED ⓘ Skolem constant NERFINISHED ⓘ Skolem function NERFINISHED ⓘ Skolem normal form NERFINISHED ⓘ clausal normal form ⓘ prenex normal form ⓘ
replaces	existentially quantified variables ⓘ
typicalStepIn	conversion to clausal normal form GENERATED ⓘ preprocessing for resolution calculus GENERATED ⓘ
usedIn	Prolog implementation ⓘ logic programming ⓘ model checking preprocessors ⓘ resolution theorem proving ⓘ tableaux methods ⓘ
uses	Skolem constants NERFINISHED ⓘ Skolem functions NERFINISHED ⓘ

Referenced by (6)

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

Thoralf Skolem → knownFor → Skolemization ⓘ

this entity surface form: Skolem normal form

Thoralf Skolem → knownFor → Skolemization ⓘ

Thoralf Skolem → notableWork → Skolemization ⓘ

this entity surface form: Skolem normal form

Thoralf Skolem → notableWork → Skolemization ⓘ

this entity surface form: Skolem function

Thoralf Skolem → notableWork → Skolemization ⓘ

Herbrand's theorem → relatedTo → Skolemization ⓘ