satisfiability

可满足

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

Translation evidence: Literature usage

Meaning in context

A set of first-order sentences is satisfiable if one structure satisfies all of them together.

存在一个结构同时满足全部语句时，该语句集称可满足。

Example

{∃x P(x),∃x ¬P(x)}\{\exists x\,P(x),\exists x\,\neg P(x)\} has a two-element model.

Usage and distinctions

Separate models for individual sentences need not give a simultaneous model for the set.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Avigad, Hua, Lewis and van Doorn — Logic and Proof§10.2 Truth in a Model; §10.4 Validity and Logical Consequence; §10.5 Soundness and Completeness · Checked 2026-10-14

Translation sources

  1. 杨睿之（复旦大学）— 数理逻辑，第17讲PDF pp.21–22：「可满足」与紧致性定理 · Checked 2026-10-14
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