Conjunctive Queries: Unique Characterizations and Exact Learnability

TL;DR

This paper characterizes which conjunctive queries can be uniquely identified with polynomially many examples and introduces an efficient learning algorithm based on new polynomial-time algorithms for constructing frontiers in the homomorphism lattice.

Contribution

It provides the first polynomial-time algorithms for constructing frontiers in the homomorphism lattice, enabling efficient exact learning of certain conjunctive queries.

Findings

Polynomially many examples suffice for unique characterization.

New polynomial-time algorithms for frontier construction.

Implications for schema mappings and description logic.

Abstract

We answer the question which conjunctive queries are uniquely characterized by polynomially many positive and negative examples, and how to construct such examples efficiently. As a consequence, we obtain a new efficient exact learning algorithm for a class of conjunctive queries. At the core of our contributions lie two new polynomial-time algorithms for constructing frontiers in the homomorphism lattice of finite structures. We also discuss implications for the unique characterizability and learnability of schema mappings and of description logic concepts.