first-order formula

合式公式

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

Other names / variants: well-formed formula

Translation evidence: Literature usage

Meaning in context

A finite expression of a fixed first-order language built from atomic formulas using its permitted connectives and quantifiers.

在固定一阶语言中，由原子公式按该语言的联结词和量词构成规则生成的有限表达式。

Example

∀x  (P(x)→P(f(x)))\forall x\;(P(x)\to P(f(x))) is a formula if PP is unary and ff unary.

Usage and distinctions

An expression with the wrong number of predicate arguments is not well formed.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Avigad, Hua, Lewis and van Doorn — Logic and Proof§7.1 Functions, Predicates, and Relations (terms and formulas); §§7.2–7.3 (quantified formulas) · Checked 2026-10-14
  2. 杨睿之（复旦大学）— 数理逻辑，第11讲PDF pp.15–16「合式公式」：原子公式及联结词、量词的递归构成规则 · Checked 2026-10-14

Translation sources

  1. 杨睿之（复旦大学）— 数理逻辑，2021年秋季PDF pp.15–16「合式公式」 · Checked 2026-10-14
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