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Prenex normal form : ウィキペディア英語版
Prenex normal form
A formula of the predicate calculus is in prenex〔The term 'prenex' comes from the Latin ''praenexus'' "tied or bound up in front", past participle of ''praenectere'' ().〕 normal form if it is written as a string of quantifiers (referred to as the prefix) followed by a quantifier-free part (referred to as the matrix).
Every formula in classical logic is equivalent to a formula in prenex normal form. For example, if \phi(y), \psi(z), and \rho(x) are quantifier-free formulas with the free variables shown then
:\forall x \exists y \forall z (\phi(y) \lor (\psi(z) \rightarrow \rho(x)))
is in prenex normal form with matrix \phi(y) \lor (\psi(z) \rightarrow \rho(x)), while
:\forall x ((\exists y \phi(y)) \lor ((\exists z \psi(z) ) \rightarrow \rho(x)))
is logically equivalent but not in prenex normal form.
== Conversion to prenex form ==

Every first-order formula is logically equivalent (in classical logic) to some formula in prenex normal form. There are several conversion rules that can be recursively applied to convert a formula to prenex normal form. The rules depend on which logical connectives appear in the formula.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Prenex normal form」の詳細全文を読む



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