On the non-efficient PAC learnability of conjunctive queries

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...

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Bibliographic Details
Published in:	Information processing letters Vol. 183; p. 106431
Main Authors:	ten Cate, Balder, Funk, Maurice, Jung, Jean Christoph, Lutz, Carsten
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.01.2024
Subjects:	Computational learning theory Conjunctive queries Inductive logic programming Computational learning theory Databases Inductive logic programming Conjunctive queries
ISSN:	0020-0190, 1872-6119
Online Access:	Get full text
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Summary:	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. •Conjunctive Queries (CQs) are known to be not efficiently PAC learnable. We give a self-contained exposition.•Acyclic CQs are not efficiently PAC learnable, even for very restrictive notions of acyclicity.•Conjunctive Queries (CQs), and Unions of Conjunctive Queries (UCQs), are efficiently PAC learnable with membership queries.
ISSN:	0020-0190 1872-6119
DOI:	10.1016/j.ipl.2023.106431