A formula of the predicate calculus is in prenex[1] 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.[2] 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 logically 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.
^The term 'prenex' comes from the Latin praenexus "tied or bound up in front", past participle of praenectere [1] (archived as of May 27, 2011 at [2])
^Hinman, P. (2005), p. 110
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