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Date: 15-2-2022
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A formula of first-order logic is in prenex normal form if it is of the form
(1) |
where each is a quantifier ("for all") or ("exists") and is quantifier-free.
For example, the formula
(2) |
is in prenex normal form, whereas formula
(3) |
is not, where denotes OR.
Every formula of first-order logic can be converted to an equivalent formula in prenex normal form.
Chang, C.-L. and Lee, R. C.-T. Symbolic Logic and Mechanical Theorem Proving. New York: Academic Press, 1997.
Kleene, S. C. Mathematical Logic. New York: Dover, 2002.
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