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.
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 Wolfram|Alpha
Prenex Normal Form Cite this as:
Sakharov, Alex. "Prenex Normal Form." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/PrenexNormalForm.html
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