A formula of firstorder logic is in prenex
normal form if it is of the form

(1)

where each
is a quantifier ("for all") or
("exists")
and
is quantifierfree.
For example, the formula

(2)

is in prenex normal form, whereas formula

(3)

is not, where
denotes OR.
Every formula of firstorder logic can be converted
to an equivalent formula in prenex normal form.
This entry contributed by Alex
Sakharov (author's link)
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References
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.Referenced on WolframAlpha
Prenex Normal Form
Cite this as:
Sakharov, Alex. "Prenex Normal Form." From MathWorldA Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/PrenexNormalForm.html
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