This note serves three purposes: (i) we provide a self-contained exposition of the fact that conjunctive queries are not efficiently learnable in the Probably-Approximately-Correct (PAC) model, paying clear attention to the complicating fact that this concept class lacks the polynomial-size fitting property, a property that is tacitly assumed in much of the computational learning theory literature; (ii) we establish a strong negative PAC learnability result that applies to many restricted classes of conjunctive queries (CQs), including acyclic CQs for a wide range of notions of acyclicity; (iii) we show that CQs (and UCQs) are efficiently PAC learnable with membership queries.

本注释有三个目的：（i）我们提供了一个独立的说明，说明连接查询在可能近似正确（PAC）模型中无法有效学习，并明确注意该概念类缺乏的复杂事实多项式大小拟合属性，这是许多计算学习理论文献中默认假设的属性；(ii) 我们建立了一个强大的负 PAC 可学习性结果，适用于许多受限类别的联合查询 (CQ)，包括用于各种非循环性概念的非循环 CQ；(iii) 我们证明 CQ（和 UCQ）可以通过成员资格查询有效地进行 PAC 学习。