Document Open Access Logo

Right-Adjoints for Datalog Programs

Authors Balder ten Cate , Víctor Dalmau , Jakub Opršal

PDF
Thumbnail PDF

File

LIPIcs.ICDT.2024.10.pdf
  • Filesize: 0.84 MB
  • 20 pages

Document Identifiers

Author Details

Balder ten Cate
  • Institute for Logic, Language, and Computation, University of Amsterdam, The Netherlands
Víctor Dalmau
  • Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain
Jakub Opršal
  • School of Computer Science, University of Birmingham, UK

Funding

  • ten Cate, Balder: Supported by the European Union’s Horizon 2020 research and innovation programme (MSCA-101031081).
  • Dalmau, Víctor: Supported by the MiCin under grants PID2019-109137GB-C22 and PID2022-138506NB-C22, and the Maria de Maeztu program (CEX2021-001195-M).
  • Opršal, Jakub: Supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No 101034413.

Acknowledgements

Thanks to Pierre Bourrhis for detailed feedback and catching mistakes.

Cite AsGet BibTex

Balder ten Cate, Víctor Dalmau, and Jakub Opršal. Right-Adjoints for Datalog Programs. In 27th International Conference on Database Theory (ICDT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 290, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ICDT.2024.10

Abstract

A Datalog program can be viewed as a syntactic specification of a mapping from database instances over some schema to database instances over another schema. We establish a large class of Datalog programs for which this mapping admits a (generalized) right-adjoint. We employ these results to obtain new insights into the existence of, and methods for constructing, homomorphism dualities within restricted classes of instances. From this, we derive new results regarding the existence of uniquely characterizing data examples for database queries in the presence of integrity constraints.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and databases
Keywords
  • Datalog
  • Adjoints
  • Homomorphism Dualities
  • Database Constraints
  • Conjunctive Queries
  • Data Examples

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Serge Abiteboul, Richard Hull, and Victor Vianu. Foundations of Databases. Addison Wesley, 1995. Google Scholar
  2. Bogdan Alexe, Balder ten Cate, Phokion G. Kolaitis, and Wang-Chiew Tan. Characterizing schema mappings via data examples. ACM Trans. Database Syst., 36(4):23:1-23:48, dec 2011. URL: https://doi.org/10.1145/2043652.2043656.
  3. Albert Atserias. On digraph coloring problems and treewidth duality. Eur. J. Comb., 29(4):796-820, 2008. URL: https://doi.org/10.1016/j.ejc.2007.11.004.
  4. Richard N. Ball, Jaroslav Nešetřil, and Aleš Pultr. Dualities in full homomorphisms. European Journal of Combinatorics, 31(1):106-119, 2010. URL: https://doi.org/10.1016/j.ejc.2009.04.004.
  5. Michael Benedikt, Pierre Bourhis, Balder Ten Cate, Gabrieled Puppis, and Michael Vanden Boom. Inference from visible information and background knowledge. ACM Trans. Comput. Logic, 22(2), jun 2021. URL: https://doi.org/10.1145/3452919.
  6. Meghyn Bienvenu, Balder Ten Cate, Carsten Lutz, and Frank Wolter. Ontology-based data access: A study through Disjunctive Datalog, CSP, and MMSNP. ACM Trans. Database Syst., 39(4), dec 2015. URL: https://doi.org/10.1145/2661643.
  7. Manuel Bodirsky, Simon Knäuer, and Sebastian Rudolph. Datalog-expressibility for monadic and guarded second-order logic. In ICALP 2021, pages 120:1-120:17, 2021. URL: https://doi.org/10.4230/LIPIcs.ICALP.2021.120.
  8. Andrei A. Bulatov, Andrei A. Krokhin, and Benoît Larose. Dualities for constraint satisfaction problems. In Nadia Creignou, Phokion G. Kolaitis, and Heribert Vollmer, editors, Complexity of Constraints - An Overview of Current Research Themes [Result of a Dagstuhl Seminar], volume 5250 of LNCS, pages 93-124. Springer, 2008. URL: https://doi.org/10.1007/978-3-540-92800-3_5.
  9. Balder ten Cate and Victor Dalmau. Conjunctive queries: Unique characterizations and exact learnability. ACM Trans. Database Syst., 47(4), nov 2022. URL: https://doi.org/10.1145/3559756.
  10. Balder ten Cate, Victor Dalmau, Maurice Funk, and Carsten Lutz. Extremal fitting problems for conjunctive queries. In Proceedings of the 42nd ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, PODS'23, 2023. URL: https://doi.org/10.1145/3584372.3588655.
  11. Balder ten Cate, Víctor Dalmau, and Jakub Opršal. Right-adjoints for datalog programs, and homomorphism dualities over restricted classes, 2023. URL: https://doi.org/10.48550/arXiv.2302.06366.
  12. Surajit Chaudhuri and Moshe Y Vardi. On the equivalence of recursive and nonrecursive Datalog programs. Journal of Computer and System Sciences, 54(1):61-78, 1997. URL: https://doi.org/10.1006/jcss.1997.1452.
  13. Victor Dalmau, Andrei Krokhin, and Jakub Opršal. Functors on relational structures which admit both left and right adjoints, 2023. URL: https://doi.org/10.48550/arXiv.2302.13657.
  14. Víctor Dalmau and Jakub Opršal. Local consistency as a reduction between constraint satisfaction problems, 2023. URL: https://doi.org/10.48550/arXiv.2301.05084.
  15. Péter L. Erdös, Dömötör Pálvölgyi, Claude Tardif, and Gábor Tardos. Regular families of forests, antichains and duality pairs of relational structures. Comb., 37(4):651-672, 2017. URL: https://doi.org/10.1007/s00493-015-3003-4.
  16. Jan Foniok, Jaroslav Nešetřil, and Claude Tardif. Generalised dualities and maximal finite antichains in the homomorphism order of relational structures. Eur. J. Comb., 29(4):881-899, 2008. URL: https://doi.org/10.1016/j.ejc.2007.11.017.
  17. Jan Foniok and Claude Tardif. Digraph functors which admit both left and right adjoints. Discrete Mathematics, 338(4):527-535, 2015. URL: https://doi.org/10.1016/j.disc.2014.10.018.
  18. Maurice Funk, Jean Christoph Jung, and Carsten Lutz. Frontiers and exact learning of ELI queries under DL-Lite ontologies. In Proceedings of the 31st International Joint Conference on Artificial Intelligence, IJCAI-22, 2022. URL: https://doi.org/10.24963/ijcai.2022/364.
  19. Georg Gottlob and Christoph Koch. Monadic Datalog and the expressive power of languages for web information extraction. J. ACM, 51(1):74-113, jan 2004. URL: https://doi.org/10.1145/962446.962450.
  20. Pavol Hell and Jaroslav Nešetřil. Graphs and homomorphisms, volume 28 of Oxford lecture series in mathematics and its applications. Oxford University Press, 2004. Google Scholar
  21. Andrei A. Krokhin, Jakub Opršal, Marcin Wrochna, and Stanislav Živný. Topology and adjunction in promise constraint satisfaction. SIAM Journal on Computing, 52(1):38-79, 2023. URL: https://doi.org/10.1137/20M1378223.
  22. Aleš Pultr. The right adjoints into the category of relational systems. In Reports of the Midwest Category Seminar IV, volume 137 of Lecture Notes in Mathematics, pages 100-113. Springer, 1970. Google Scholar
  23. Sebastian Rudolph and Markus Krötzsch. Flag & check: Data access with monadically defined queries. In Proceedings of the 32nd ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, PODS '13, pages 151-162. ACM, 2013. URL: https://doi.org/10.1145/2463664.2465227.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact