Normal forms (logic)

Prenex normal form

A formula of the predicate calculus is in prenex normal form (PNF) if it is written as a string of quantifiers and bound variables, called the prefix, followed by a quantifier-free part, called the matrix. Together with the normal forms in propositional logic (e.g. disjunctive normal form or conjunctive normal form), it provides a canonical normal form useful in automated theorem proving. Every formula in classical logic is equivalent to a formula in prenex normal form. For example, if , , and are quantifier-free formulas with the free variables shown then is in prenex normal form with matrix , while is logically equivalent but not in prenex normal form. (Wikipedia).

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Related pages

Conjunctive normal form | Tarski's axioms | Scope (logic) | Normal form (abstract rewriting) | Herbrandization | Propositional calculus | Tautology (logic) | Rewriting | Automated theorem proving | Arithmetical hierarchy | Analytical hierarchy | Predicate calculus | Canonical normal form | Logical disjunction | Material conditional | Decidability (logic) | Alfred Tarski | Natural number | Ring (mathematics) | Existential quantification | Disjunctive normal form | Proof calculus | Quantifier (logic) | Logical connective | Gödel's completeness theorem | Intuitionistic logic | Universal quantification | Logical conjunction | Classical logic | First-order logic