### What does **prenex normal form** mean?

# Definitions for prenex normal form

prenex nor·mal form

#### This dictionary definitions page includes all the possible meanings, example usage and translations of the word **prenex normal form**.

### Wikipedia

Prenex normal form

A formula of the predicate calculus is in prenex normal form (PNF) if it is written as a string of quantifiers and bound variables, called the prefix, followed by a quantifier-free part, called the matrix. Together with the normal forms in propositional logic (e.g. disjunctive normal form or conjunctive normal form), it provides a canonical normal form useful in automated theorem proving. Every formula in classical logic is logically equivalent to a formula in prenex normal form. For example, if ϕ ( y ) {\displaystyle \phi (y)} , ψ ( z ) {\displaystyle \psi (z)} , and ρ ( x ) {\displaystyle \rho (x)} are quantifier-free formulas with the free variables shown then ∀ x ∃ y ∀ z ( ϕ ( y ) ∨ ( ψ ( z ) → ρ ( x ) ) ) {\displaystyle \forall x\exists y\forall z(\phi (y)\lor (\psi (z)\rightarrow \rho (x)))} is in prenex normal form with matrix ϕ ( y ) ∨ ( ψ ( z ) → ρ ( x ) ) {\displaystyle \phi (y)\lor (\psi (z)\rightarrow \rho (x))} , while ∀ x ( ( ∃ y ϕ ( y ) ) ∨ ( ( ∃ z ψ ( z ) ) → ρ ( x ) ) ) {\displaystyle \forall x((\exists y\phi (y))\lor ((\exists z\psi (z))\rightarrow \rho (x)))} is logically equivalent but not in prenex normal form.

### Numerology

Chaldean Numerology

The numerical value of prenex normal form in Chaldean Numerology is:

**1**Pythagorean Numerology

The numerical value of prenex normal form in Pythagorean Numerology is:

**9**

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"prenex normal form." *Definitions.net.* STANDS4 LLC, 2023. Web. 28 May 2023. <https://www.definitions.net/definition/prenex+normal+form>.

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