Skip to main content
Springer Nature Link
Log in

Computing Repairs Under Functional and Inclusion Dependencies via Argumentation

  • Conference paper
  • First Online:
Foundations of Information and Knowledge Systems (FoIKS 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14589))

Abstract

We discover a connection between finding subset-maximal repairs for sets of functional and inclusion dependencies, and computing extensions within argumentation frameworks (AFs). We study the complexity of existence of a repair, and deciding whether a given tuple belongs to some (or every) repair, by simulating the instances of these problems via AFs. We prove that subset-maximal repairs under functional dependencies correspond to the naive extensions, which also coincide with the preferred and stable extensions in the resulting AFs. For inclusion dependencies one needs a pre-processing step on the resulting AFs in order for the extensions to coincide. Allowing both types of dependencies breaks this relationship between extensions and only preferred semantics captures the repairs. Finally, we establish that the complexities of the above decision problems are \( {\textbf {NP}}\)-complete and \(\boldsymbol{\mathrm {\Pi }}^{ {\textbf {P}}}_2\)-complete, when both functional and inclusion dependencies are allowed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    We borrow this notation and write \(\textsf{dep}(\boldsymbol{x};\boldsymbol{y})\) and \(\boldsymbol{x}\subseteq \boldsymbol{y}\) for FDs and IDs, respectively.

  2. 2.

    We disallow the empty set (\(\emptyset \)) in extensions for the sake of compatibility with repairs. Nevertheless, one can allow \(\emptyset \) as an extension in AFs and the empty database as repairs, without affecting our complexity results.

References

  1. Afrati, F.N., Kolaitis, P.G.: Repair checking in inconsistent databases: algorithms and complexity. In: Fagin, R. (ed.) Database Theory - ICDT 2009, 12th International Conference, Proceedings. ACM International Conference Proceeding Series, St. Petersburg, Russia, 23–25 March 2009, vol. 361, pp. 31–41. ACM (2009). https://doi.org/10.1145/1514894.1514899

  2. Arenas, M., Bertossi, L.E., Chomicki, J.: Scalar aggregation in FD-inconsistent databases. In: den Bussche, J.V., Vianu, V. (eds.) ICDT 2001. LNCS, vol. 1973, pp. 39–53. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44503-X_3

    Chapter  Google Scholar 

  3. Arieli, O., Borg, A., Heyninck, J.: A review of the relations between logical argumentation and reasoning with maximal consistency. Ann. Math. Artif. Intell. 87(3), 187–226 (2019). https://doi.org/10.1007/S10472-019-09629-7

    Article  MathSciNet  Google Scholar 

  4. Arioua, A., Croitoru, M.: Dialectical characterization of consistent query explanation with existential rules. In: Markov, Z., Russell, I. (eds.) Proceedings of the Twenty-Ninth International Florida Artificial Intelligence Research Society Conference, FLAIRS 2016, Key Largo, Florida, USA, 16–18 May 2016, pp. 621–625. AAAI Press (2016). http://www.aaai.org/ocs/index.php/FLAIRS/FLAIRS16/paper/view/12800

  5. Arioua, A., Croitoru, M., Vesic, S.: Logic-based argumentation with existential rules. Int. J. Approx. Reason. 90, 76–106 (2017). https://doi.org/10.1016/J.IJAR.2017.07.004

    Article  MathSciNet  Google Scholar 

  6. Arioua, A., Tamani, N., Croitoru, M.: Query answering explanation in inconsistent datalog +/- knowledge bases. In: Chen, Q., Hameurlain, A., Toumani, F., Wagner, R.R., Decker, H. (eds.) DEXA 2015. LNCS, vol. 9261, pp. 203–219. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-22849-5_15

    Chapter  Google Scholar 

  7. Arioua, A., Tamani, N., Croitoru, M., Buche, P.: Query failure explanation in inconsistent knowledge bases using argumentation. In: Parsons, S., Oren, N., Reed, C., Cerutti, F. (eds.) Computational Models of Argument - Proceedings of COMMA 2014. Frontiers in Artificial Intelligence and Applications, Atholl Palace Hotel, Scottish Highlands, UK, 9–12 September 2014, vol. 266, pp. 101–108. IOS Press (2014). https://doi.org/10.3233/978-1-61499-436-7-101

  8. Barceló, P., Fontaine, G.: On the data complexity of consistent query answering over graph databases. J. Comput. Syst. Sci. 88, 164–194 (2017)

    Article  MathSciNet  Google Scholar 

  9. Bertossi, L.E.: Consistent query answering in databases. SIGMOD Rec. 35(2), 68–76 (2006). https://doi.org/10.1145/1147376.1147391

    Article  Google Scholar 

  10. Bertossi, L.E.: Database repairs and consistent query answering: origins and further developments. In: Suciu, D., Skritek, S., Koch, C. (eds.) Proceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, PODS 2019, Amsterdam, The Netherlands, 30 June–5 July 2019, pp. 48–58. ACM (2019). https://doi.org/10.1145/3294052.3322190

  11. Bienvenu, M., Bourgaux, C.: Querying and repairing inconsistent prioritized knowledge bases: complexity analysis and links with abstract argumentation. In: Calvanese, D., Erdem, E., Thielscher, M. (eds.) Proceedings of the 17th International Conference on Principles of Knowledge Representation and Reasoning, KR 2020, Rhodes, Greece, 12–18 September 2020, pp. 141–151 (2020). https://doi.org/10.24963/KR.2020/15

  12. Bienvenu, M., Bourgaux, C.: Inconsistency handling in prioritized databases with universal constraints: complexity analysis and links with active integrity constraints. In: Proceedings of the 20th International Conference on Principles of Knowledge Representation and Reasoning, pp. 97–106 (2023). https://doi.org/10.24963/kr.2023/10

  13. Bienvenu, M., Bourgaux, C., Goasdoué, F.: Computing and explaining query answers over inconsistent DL-lite knowledge bases. J. Artif. Intell. Res. 64, 563–644 (2019)

    Article  MathSciNet  Google Scholar 

  14. ten Cate, B., Fontaine, G., Kolaitis, P.G.: On the data complexity of consistent query answering. In: Proceedings of the 15th International Conference on Database Theory, ICDT 2012, pp. 22–33 (2012)

    Google Scholar 

  15. Chomicki, J., Marcinkowski, J.: Minimal-change integrity maintenance using tuple deletions. Inf. Comput. 197(1), 90–121 (2005). https://doi.org/10.1016/j.ic.2004.04.007. https://www.sciencedirect.com/science/article/pii/S0890540105000179

  16. Coste-Marquis, S., Devred, C., Marquis, P.: Symmetric argumentation frameworks. In: Godo, L. (ed.) ECSQARU 2005. LNCS (LNAI), vol. 3571, pp. 317–328. Springer, Heidelberg (2005). https://doi.org/10.1007/11518655_28

    Chapter  Google Scholar 

  17. Croitoru, M., Thomopoulos, R., Vesic, S.: Introducing preference-based argumentation to inconsistent ontological knowledge bases. In: Chen, Q., Torroni, P., Villata, S., Hsu, J., Omicini, A. (eds.) PRIMA 2015. LNCS (LNAI), vol. 9387, pp. 594–602. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-25524-8_42

    Chapter  Google Scholar 

  18. Croitoru, M., Vesic, S.: What can argumentation do for inconsistent ontology query answering? In: Liu, W., Subrahmanian, V.S., Wijsen, J. (eds.) SUM 2013. LNCS (LNAI), vol. 8078, pp. 15–29. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40381-1_2

    Chapter  Google Scholar 

  19. Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. AI 77(2), 321–357 (1995)

    MathSciNet  Google Scholar 

  20. Dvorák, W., Dunne, P.E.: Computational problems in formal argumentation and their complexity. FLAP 4(8), 2557–2622 (2017)

    Google Scholar 

  21. Fagin, R., Kimelfeld, B., Kolaitis, P.G.: Dichotomies in the complexity of preferred repairs. In: Milo, T., Calvanese, D. (eds.) Proceedings of the 34th ACM Symposium on Principles of Database Systems, PODS 2015, Melbourne, Victoria, Australia, 31 May–4 June 2015, pp. 3–15. ACM (2015). https://doi.org/10.1145/2745754.2745762

  22. Hannula, M., Hella, L.: Complexity thresholds in inclusion logic. Inf. Comput. 287, 104759 (2022). https://doi.org/10.1016/J.IC.2021.104759

    Article  MathSciNet  Google Scholar 

  23. Hannula, M., Wijsen, J.: A dichotomy in consistent query answering for primary keys and unary foreign keys. In: Libkin, L., Barceló, P. (eds.) PODS 2022: International Conference on Management of Data, Philadelphia, PA, USA, 12–17 June 2022, pp. 437–449. ACM (2022). https://doi.org/10.1145/3517804.3524157

  24. Ho, L., Arch-Int, S., Acar, E., Schlobach, S., Arch-Int, N.: An argumentative approach for handling inconsistency in prioritized datalog\(\pm \)ontologies. AI Commun. 35(3), 243–267 (2022). https://doi.org/10.3233/AIC-220087

    Article  MathSciNet  Google Scholar 

  25. Kimelfeld, B., Livshits, E., Peterfreund, L.: Detecting ambiguity in prioritized database repairing. In: Benedikt, M., Orsi, G. (eds.) 20th International Conference on Database Theory (ICDT 2017). Leibniz International Proceedings in Informatics (LIPIcs), vol. 68, pp. 17:1–17:20. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl (2017). https://doi.org/10.4230/LIPIcs.ICDT.2017.17. http://drops.dagstuhl.de/opus/volltexte/2017/7048

  26. Kimelfeld, B., Livshits, E., Peterfreund, L.: Counting and enumerating preferred database repairs. Theor. Comput. Sci. 837, 115–157 (2020). https://doi.org/10.1016/J.TCS.2020.05.016

    Article  MathSciNet  Google Scholar 

  27. Livshits, E., Kimelfeld, B., Roy, S.: Computing optimal repairs for functional dependencies. ACM Trans. Database Syst. 45(1), 4:1–4:46 (2020). https://doi.org/10.1145/3360904

  28. Lopatenko, A., Bertossi, L.: Complexity of consistent query answering in databases under cardinality-based and incremental repair semantics. In: Schwentick, T., Suciu, D. (eds.) ICDT 2007. LNCS, vol. 4353, pp. 179–193. Springer, Heidelberg (2006). https://doi.org/10.1007/11965893_13

    Chapter  Google Scholar 

  29. Mahmood, Y.: Parameterized aspects of team-based formalisms and logical inference (2022). https://doi.org/10.15488/13064. https://www.tib.eu/de/suchen/id/base%3Ae4c211ee856f89407f6d9a67b4c100e3fb7eafdd

  30. Staworko, S., Chomicki, J., Marcinkowski, J.: Prioritized repairing and consistent query answering in relational databases. Ann. Math. Artif. Intell. 64(2–3), 209–246 (2012). https://doi.org/10.1007/S10472-012-9288-8

    Article  MathSciNet  Google Scholar 

  31. Staworko, S., Chomicki, J.: Consistent query answers in the presence of universal constraints. Inf. Syst. 35(1), 1–22 (2010). https://doi.org/10.1016/J.IS.2009.03.004

    Article  Google Scholar 

  32. Väänänen, J.: Dependence Logic. Cambridge University Press, Cambridge (2007)

    Book  Google Scholar 

  33. Wijsen, J.: Condensed representation of database repairs for consistent query answering. In: Calvanese, D., Lenzerini, M., Motwani, R. (eds.) ICDT 2003. LNCS, vol. 2572, pp. 378–393. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36285-1_25

    Chapter  Google Scholar 

  34. Young, A.P., Modgil, S., Rodrigues, O.: Prioritised default logic as argumentation with partial order default priorities. CoRR abs/1609.05224 (2016). http://arxiv.org/abs/1609.05224

  35. Yun, B., Vesic, S., Croitoru, M.: Sets of attacking arguments for inconsistent datalog knowledge bases. In: Prakken, H., Bistarelli, S., Santini, F., Taticchi, C. (eds.) Computational Models of Argument - Proceedings of COMMA 2020. Frontiers in Artificial Intelligence and Applications, Perugia, Italy, 4–11 September 2020, vol. 326, pp. 419–430. IOS Press (2020). https://doi.org/10.3233/FAIA200526

Download references

Acknowledgment

The work has received funding from the European Union’s Horizon Europe research and innovation programme within project ENEXA (101070305) and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation): TRR 318/1 2021 - 438445824 and VI 1045-1/1 - 432788559. The first author expresses gratitude to Arne Meier (Leibniz University Hannover) for the invitation to discuss the topic in Hannover, as well as for motivating and guiding the discussion on this subject.

Author information

Authors and Affiliations

  1. DICE Group, Department of Computer Science, Paderborn University, Paderborn, Germany

    Yasir Mahmood & Axel-Cyrille Ngonga Ngomo

  2. Department of Computer Science, University of Sheffield, Sheffield, UK

    Jonni Virtema

  3. Institut für Theoretische Informatik, Leibniz Universität Hannover, Hannover, Germany

    Timon Barlag

Authors
  1. Yasir Mahmood
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jonni Virtema
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Timon Barlag
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Axel-Cyrille Ngonga Ngomo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yasir Mahmood .

Editor information

Editors and Affiliations

  1. Leibniz University Hannover, Hanover, Germany

    Arne Meier

  2. TU Wien, Wien, Austria

    Magdalena Ortiz

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Mahmood, Y., Virtema, J., Barlag, T., Ngomo, AC.N. (2024). Computing Repairs Under Functional and Inclusion Dependencies via Argumentation. In: Meier, A., Ortiz, M. (eds) Foundations of Information and Knowledge Systems. FoIKS 2024. Lecture Notes in Computer Science, vol 14589. Springer, Cham. https://doi.org/10.1007/978-3-031-56940-1_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-56940-1_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-56939-5

  • Online ISBN: 978-3-031-56940-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics