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.

翻译：本文撰写目的有三：(i) 我们提供了合取查询在概率近似正确（PAC）模型中不可高效学习的自包含论证，清晰关注此类概念类缺乏多项式规模拟合性质这一复杂事实，该性质在计算学习理论文献中常被默示假设；(ii) 我们建立了适用于多种受限合取查询（CQs）类的强PAC不可学习性结论，包括针对多种"无环性"概念定义的无环CQ；(iii) 我们证明CQ（以及UCQ）在成员查询条件下是高效PAC可学习的。