Conjunctive Queries: Unique Characterizations and Exact Learnability

Authors Balder ten Cate , Victor Dalmau

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Balder ten Cate
  • Google, Mountain View, CA, USA
Victor Dalmau
  • Universitat Pompeu Fabra, Barcelona, Spain


This paper largely grew out of discussions at Dagstuhl Seminar 19361 ("Logic and Learning") in Sept. 2019. We thank Carsten Lutz and Phokion Kolaitis for helpful discussions.

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Balder ten Cate and Victor Dalmau. Conjunctive Queries: Unique Characterizations and Exact Learnability. In 24th International Conference on Database Theory (ICDT 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 186, pp. 9:1-9:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We answer the question of 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Machine learning theory
  • Theory of computation → Logic
  • Information systems → Query languages
  • Conjunctive Queries
  • Homomorphisms
  • Frontiers
  • Unique Characterizations
  • Exact Learnability
  • Schema Mappings
  • Description Logic


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