Prenex normal form

A first-order logic formula in which all quantifiers occur in a prefix before a quantifier-free matrix. Every first-order formula can be converted to an equivalent prenex form.

Quantifier: A logical operator that asserts that a predicate holds for all or some objects in a domain. Universal and existential quantifiers make up the prefix.
First-order logic: A formal system for reasoning about objects, predicates, relations, and functions using quantifiers. Prenex form is a normal form for formulas in this logic.
Skolem normal form: A first-order formula form obtained by eliminating existential quantifiers through Skolem functions or constants. Prenex conversion commonly precedes Skolemization in automated reasoning.
Conjunctive normal form: A propositional formula expressed as a conjunction of clauses, each clause being a disjunction of literals. It organizes connectives into clauses rather than gathering quantifiers into a prefix.
Free variable: A variable occurrence not bound by a quantifier or other binding operator. Renaming variables prevents outward moves from capturing free occurrences.
Universal quantification: A quantifier asserting that a predicate holds for every object in a specified domain. The universal quantifier is one possible prefix symbol.
Resolution (logic): A rule of inference that derives clauses by eliminating complementary literals. First-order resolution pipelines standardize formulas before Skolemization and clause conversion.
Negation normal form: A formula in which negation applies only to atomic formulas. It restricts negation placement but does not require a quantifier prefix.
Bound variable: A variable occurrence governed by a quantifier or another binding operator. Quantifiers can move across connectives only when variable-binding conditions are respected.
Existential quantification: A quantifier asserting that a predicate holds for at least one object in a specified domain. The existential quantifier is the other standard prefix symbol.

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Quantifier eliminationCompared with: It rearranges quantifiers instead of removing them.