A formula of the predicate calculus is in prenex [1] 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. [2]

前束范式（prenex normal form）是数理逻辑中使用谓词逻辑所描述的形式语言的一种格式。 前束范式亦称前束式，一种谓词演算公式。 指其一切量词都未被否定地处于公式的最前端且其辖域都延伸至公式的末端的谓词演算公式。 设Q∈ {∃，ᗄ}，一个公式α是前束范式，当且仅当存在一个不含量词的公式β，使得. α= (Q₁x₁) (Q₂x₂)… (Qₑxₑ)β. α= (∃x₁) (∃x₃)… (∃xₐ) (ᗄx₁) · (ᗄx₂)… (ᗄxₑ)β (a≥0,e≥0). [1] 一个公式，如果 量词 均在全式的开头，它们的作用域延伸到整个公式的末端，则 …

2025年3月5日 · 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.

2020年6月6日 · Prenex formulas are also called prenex normal forms or prenex forms. For each formula $ \phi $ of the language of the restricted predicate calculus there is a prenex formula that is logically equivalent to $ \phi $ in the classical predicate calculus. The procedure of finding a prenex formula is based on the following equivalences, which can be ...

2019年4月16日 · 一个公式，如果量词均在全式的开头，它们的作用域延伸到整个公式的末端，则该公式叫做前束范式(Prenex Normal Form)。

前束范式（prenex normal form）是数理逻辑中使用谓词逻辑所描述的形式语言的一种格式。 前束范式亦称前束式，一种谓词演算公式。 指其一切量词都未被否定地处于公式的最前端且其辖域都延伸至公式的末

How to obtain prenex normal form? Eliminate all occurrences of → and ↔ from the formula in question. Move all negations inward such that, in the end, negation only appear as part of literals.

例如，∀x∃y∀z ( (P (x,y)→Q (y,z)) → R (x,y)) 例如， ∃ ∀ → 是前束范式。

Prenex normal form is a way of structuring logical formulas in predicate logic so that all the quantifiers are at the front of the expression, followed by a quantifier-free part. This structure simplifies the process of understanding and manipulating logical statements, making it easier to apply various strategies for proofs and transformations ...

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