syntactic consistency

一致

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

Other names / variants: consistency

Translation evidence: Literature usage

Meaning in context

A sentence set is syntactically consistent in a specified classical calculus if no derivation from it concludes falsity.

对于指定的经典演绎系统，若不能从一个语句集推出矛盾，则称它一致。

Example

{P(c),¬P(c)}\{P(c),\neg P(c)\} is inconsistent.

Usage and distinctions

Consistency is relative to proof rules; satisfiability is semantic. Completeness connects them.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Jeremy Avigad — Logic and Computation (January 2002)§6.3, Theorems 6.3.1–6.3.2; §7.2, Theorem 7.2.1 · Checked 2026-10-14

Translation sources

  1. 杨睿之（复旦大学）— 数理逻辑，第12讲PDF p.17 定义「不一致」；第17讲 PDF pp.5–6 使用「一致」 · Checked 2026-10-14
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