bound variable occurrence

约束出现

Foundations & Logic · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

An occurrence of a variable within the scope of a quantifier for that variable, bound by the nearest such quantifier.

变元在相应量词作用域内、由最近的同名量词约束的一次出现。

Example

The second xx in ∀x  (x=y)\forall x\;(x=y) is bound.

Usage and distinctions

Renaming must avoid capture; changing a bound name is not the same as changing a free parameter.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Avigad, Hua, Lewis and van Doorn — Logic and Proof§7.2 The Universal Quantifier; §7.3 The Existential Quantifier · Checked 2026-10-14

Translation sources

  1. 杨睿之（复旦大学）— 数理逻辑，2021年秋季PDF pp.17–20: 一阶逻辑的语言；自由出现与约束出现 · Checked 2026-10-14
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