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.


  1. 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.

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How to say prenex normal form in sign language?


  1. Chaldean Numerology

    The numerical value of prenex normal form in Chaldean Numerology is: 1

  2. 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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    applied to a fish depicted horizontally
    • A. naiant
    • B. motile
    • C. lank
    • D. bonzer

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