logical equivalence

逻辑等价

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

Translation evidence: Literature usage

Meaning in context

Two propositional formulas are logically equivalent when they have equal truth values under every valuation.

两个命题公式在所有真值赋值下均有相同真值时称逻辑等价。

Example

P→QP\to Q is classically equivalent to ¬P∨Q\neg P\lor Q.

Usage and distinctions

Agreement under one valuation is weaker than logical equivalence.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Avigad, Hua, Lewis and van Doorn — Logic and Proof§2.4 The Language of Propositional Logic · Checked 2026-10-14

Translation sources

  1. 高等教育出版社 — 数学证明 通往高等数学的阶梯（第4版）影印版，官方中文目录官方中文目录：§2.8 逻辑等价（名称证据，非正文定义证据） · Checked 2026-10-14
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