Skolemization
E822885
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.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Skolemization canonical | 3 |
| Skolem normal form | 2 |
| Skolem function | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9809599 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Skolemization Context triple: [Herbrand's theorem, relatedTo, Skolemization]
-
A.
Herbrand expansion
Herbrand expansion is a method in mathematical logic that transforms first-order formulas into equivalent (often infinite) propositional combinations by systematically instantiating quantified variables with terms from the Herbrand universe.
-
B.
Herbrand's theorem
Herbrand's theorem is a fundamental result in mathematical logic and proof theory that characterizes the validity of first-order formulas via finite sets of ground instances, forming a basis for automated theorem proving.
-
C.
Herbrand universe
The Herbrand universe is a fundamental concept in mathematical logic and automated theorem proving, consisting of all ground (variable-free) terms that can be built from the function symbols and constants of a given first-order language.
-
D.
Herbrand disjunction
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.
-
E.
Herbrand function
The Herbrand function is a numerical tool in local class field theory that measures the ramification filtration of Galois groups, playing a key role in understanding how ramification behaves in extensions of local fields.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Skolemization Target entity description: 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.
-
A.
Herbrand expansion
Herbrand expansion is a method in mathematical logic that transforms first-order formulas into equivalent (often infinite) propositional combinations by systematically instantiating quantified variables with terms from the Herbrand universe.
-
B.
Herbrand's theorem
Herbrand's theorem is a fundamental result in mathematical logic and proof theory that characterizes the validity of first-order formulas via finite sets of ground instances, forming a basis for automated theorem proving.
-
C.
Herbrand universe
The Herbrand universe is a fundamental concept in mathematical logic and automated theorem proving, consisting of all ground (variable-free) terms that can be built from the function symbols and constants of a given first-order language.
-
D.
Herbrand disjunction
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.
-
E.
Herbrand function
The Herbrand function is a numerical tool in local class field theory that measures the ramification filtration of Galois groups, playing a key role in understanding how ramification behaves in extensions of local fields.
- F. None of above. chosen
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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Skolemization Description of subject: 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.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Skolem normal form
this entity surface form:
Skolem function
this entity surface form:
Skolem normal form