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The prenex normal form can now be obtained by moving all quantifiers to the front of the formula. To accomplish Step 1 (eliminate the ,), make use of the following logical equivalences: A B |=| A B. A B |=| (A B)
Prenex Normal Form is a type of strongly correct normalization in predicate logic that involves moving quantifiers to the front of a formula. AI generated definition based on: Handbook of Automated Reasoning, 2001.
Prenexing rules. (If x occurs in P, but P is not in the scope of (Qx), then the sentence P0 that results from replacing x throughout P with a different variable is equivalent to P.)
Another traditional first-order form is prenex normal form. Here, the aim consists in separating the quantifiers from a quantifier-free part, the so-called matrix. Unlike to NNF, the propositional structure of the formula remains unchanged. ( x ) ( ( y ) ( P ( x , y ) R ( x ) ) ( u ) P ( u , u ) ) .
Each of the following formulas is in prenex normal form: x y (P(x) Q(y)); x y R(x, y); S(x, y). On the other hand, the following formulas are not in prenex normal form: x P(x) x Q(x); x R(x, y).
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Noun. prenex (plural prenexes) (mathematics, logic) The initial part of a prenex formula where all of the formulas bound variables are bound by logical quantifiers. is the prenex of the formula.

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