### 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**

### Translation

#### Find a translation for the **prenex normal form** definition in other languages:

Select another language:

- - Select -
- 简体中文 (Chinese - Simplified)
- 繁體中文 (Chinese - Traditional)
- Español (Spanish)
- Esperanto (Esperanto)
- 日本語 (Japanese)
- Português (Portuguese)
- Deutsch (German)
- العربية (Arabic)
- Français (French)
- Русский (Russian)
- ಕನ್ನಡ (Kannada)
- 한국어 (Korean)
- עברית (Hebrew)
- Gaeilge (Irish)
- Українська (Ukrainian)
- اردو (Urdu)
- Magyar (Hungarian)
- मानक हिन्दी (Hindi)
- Indonesia (Indonesian)
- Italiano (Italian)
- தமிழ் (Tamil)
- Türkçe (Turkish)
- తెలుగు (Telugu)
- ภาษาไทย (Thai)
- Tiếng Việt (Vietnamese)
- Čeština (Czech)
- Polski (Polish)
- Bahasa Indonesia (Indonesian)
- Românește (Romanian)
- Nederlands (Dutch)
- Ελληνικά (Greek)
- Latinum (Latin)
- Svenska (Swedish)
- Dansk (Danish)
- Suomi (Finnish)
- فارسی (Persian)
- ייִדיש (Yiddish)
- հայերեն (Armenian)
- Norsk (Norwegian)
- English (English)

### Word of the Day

#### Would you like us to send you a **FREE** new word definition delivered to your inbox daily?

## Citation

#### Use the citation below to add this definition to your bibliography:

**Style:**MLAChicagoAPA

"prenex normal form." *Definitions.net.* STANDS4 LLC, 2024. Web. 4 Aug. 2024. <https://www.definitions.net/definition/prenex+normal+form>.

## Discuss these prenex normal form definitions with the community:

## Report Comment

We're doing our best to make sure our content is useful, accurate and safe.

If by any chance you spot an inappropriate comment while navigating through our website please use this form to let us know, and we'll take care of it shortly.

## Attachment

## You need to be logged in to favorite.

## Log In