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Recent Advances in Datalog\(^\pm \)

  • Georg Gottlob
  • Michael Morak
  • Andreas Pieris
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9203)

Abstract

This tutorial, which is a continuation of the tutorial “Datalog and Its Extensions for Semantic Web Databases” presented in the Reasoning Web 2012 Summer School, discusses recent advances in the Datalog\(^\pm \) family of languages for knowledge representation and reasoning. These languages extend plain Datalog with key modeling features such as existential quantification (signified by the “+” symbol), and at the same time apply syntactic restrictions to achieve decidability of ontological reasoning and, in some relevant cases, also tractability (signified by the symbol “\(-\)”). In this tutorial, we first introduce the main Datalog\(^\pm \) languages that are based on the well-known notion of guardedness. Then, we discuss how these languages can be extended with important features such as disjunction and default negation.

Keywords

Turing Machine Conjunctive Query Query Answering Existential Quantification Datalog Program 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This research has received support from the EPSRC Programme Grant EP/M025268/ “VADA: Value Added Data Systems – Principles and Architecture”, and the Austrian Science Fund (FWF), project Y698 “Decodyn”.

References

  1. 1.
    Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Boston (1995)MATHGoogle Scholar
  2. 2.
    Alviano, M., Faber, W., Leone, N., Manna, M.: Disjunctive datalog with existential quantifiers: Semantics, decidability, and complexity issues. TPLP 12(4–5), 701–718 (2012)MathSciNetMATHGoogle Scholar
  3. 3.
    Alviano, M., Pieris, A.: Default negation for non-guarded existential rules. In: PODS (2015, to appear)Google Scholar
  4. 4.
    Andréka, H., Németi, I., van Benthem, J.: Modal languages and bounded fragments of predicate logic. J. Philos. Logic 27(3), 217–274 (1998)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Arenas, M., Gottlob, G., Pieris, A.: Expressive languages for querying the semantic web. In: PODS, pp. 14–26 (2014)Google Scholar
  6. 6.
    Baader, F., Calvanese, D., McGuinness, D.L., Nardi, D., Patel-Schneider, P.F. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, Cambridge (2003)MATHGoogle Scholar
  7. 7.
    Baget, J.F., Leclère, M., Mugnier, M.L., Salvat, E.: On rules with existential variables: Walking the decidability line. Artif. Intell. 175(9–10), 1620–1654 (2011)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Baget, J., Garreau, F., Mugnier, M., Rocher, S.: Extending acyclicity notions for existential rules. In: ECAI, pp. 39–44 (2014)Google Scholar
  9. 9.
    Bárány, V., Gottlob, G., Otto, M.: Querying the guarded fragment. Log. Meth. Comput. Sci. 10(2) (2014)Google Scholar
  10. 10.
    Beeri, C., Vardi, M.Y.: The implication problem for data dependencies. In: ICALP, pp. 73–85 (1981)Google Scholar
  11. 11.
    Bourhis, P., Morak, M., Pieris, A.: The impact of disjunction on query answering under guarded-based existential rules. In: IJCAI (2013)Google Scholar
  12. 12.
    Calì, A., Gottlob, G., Kifer, M.: Taming the infinite chase: Query answering under expressive relational constraints. J. Artif. Intell. Res. 48, 115–174 (2013)MathSciNetMATHGoogle Scholar
  13. 13.
    Calì, A., Gottlob, G., Lukasiewicz, T.: A general datalog-based framework for tractable query answering over ontologies. J. Web Sem. 14, 57–83 (2012)CrossRefGoogle Scholar
  14. 14.
    Calì, A., Gottlob, G., Lukasiewicz, T., Marnette, B., Pieris, A.: Datalog\(^\pm \): A family of logical knowledge representation and query languages for new applications. In: LICS, pp. 228–242 (2010)Google Scholar
  15. 15.
    Calì, A., Gottlob, G., Pieris, A.: Towards more expressive ontology languages: The query answering problem. Artif. Intell. 193, 87–128 (2012)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Tractable reasoning and efficient query answering in description logics: The DL-Lite family. J. Autom. Reasoning 39(3), 385–429 (2007)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Data complexity of query answering in description logics. Artif. Intell. 195, 335–360 (2013)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Casanova, M.A., Fagin, R., Papadimitriou, C.H.: Inclusion dependencies and their interaction with functional dependencies. J. Comput. Syst. Sci. 28(1), 29–59 (1984)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Ceri, S., Gottlob, G., Tanca, L.: Logic Programming and Databases. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  20. 20.
    Chandra, A.K., Kozen, D., Stockmeyer, L.J.: Alternation. J. ACM 28(1), 114–133 (1981)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Deutsch, A., Tannen, V.: Reformulation of XML queries and constraints. In: Calvanese, D., Lenzerini, M., Motwani, R. (eds.) ICDT 2003. LNCS, vol. 2572, pp. 225–238. Springer, Heidelberg (2002) CrossRefGoogle Scholar
  22. 22.
    Eiter, T., Gottlob, G., Mannila, H.: Disjunctive datalog. ACM Trans. Database Syst. 22(3), 364–418 (1997)CrossRefGoogle Scholar
  23. 23.
    Eiter, T., Leone, N., Mateis, C., Pfeifer, G., Scarcello, F.: A deductive system for non-monotonic reasoning. In: LPNMR, pp. 364–375 (1997)Google Scholar
  24. 24.
    Eiter, T., Simkus, M.: FDNC: decidable nonmonotonic disjunctive logic programs with function symbols. ACM Trans. Comput. Log., 11(2) (2010)Google Scholar
  25. 25.
    Gebser, M., Kaufmann, B., Kaminski, R., Ostrowski, M., Schaub, T., Schneider, M.T.: Potassco: The potsdam answer set solving collection. AI Commun. 24(2), 107–124 (2011)MathSciNetMATHGoogle Scholar
  26. 26.
    Gottlob, G., Hernich, A., Kupke, C., Lukasiewicz, T.: Stable model semantics for guarded existential rules and description logics. In: KRGoogle Scholar
  27. 27.
    Gottlob, G., Hernich, A., Kupke, C., Lukasiewicz, T.: Equality-friendly well-founded semantics and applications to description logics. In: AAAI (2012)Google Scholar
  28. 28.
    Gottlob, G., Manna, M., Morak, M., Pieris, A.: On the complexity of ontological reasoning under disjunctive existential rules. In: Rovan, B., Sassone, V., Widmayer, P. (eds.) MFCS 2012. LNCS, vol. 7464, pp. 1–18. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  29. 29.
    Gottlob, G., Orsi, G., Pieris, A., Šimkus, M.: Datalog and its extensions for semantic web databases. In: Eiter, T., Krennwallner, T. (eds.) Reasoning Web 2012. LNCS, vol. 7487, pp. 54–77. Springer, Heidelberg (2012) Google Scholar
  30. 30.
    Grädel, E.: On the restraining power of guards. J. Symbolic Logic 64(4), 1719–1742 (1999)MathSciNetCrossRefMATHGoogle Scholar
  31. 31.
    Hernich, A., Kupke, C., Lukasiewicz, T., Gottlob, G.: Well-founded semantics for extended datalog and ontological reasoning. In: PODS, pp. 225–236 (2013)Google Scholar
  32. 32.
    Lloyd, J.W.: Foundations of Logic Programming. Springer, New York (1987) CrossRefMATHGoogle Scholar
  33. 33.
    Magka, D., Krötzsch, M., Horrocks, I.: Computing stable models for nonmonotonic existential rules. In: IJCAI (2013)Google Scholar
  34. 34.
    Morak, M.: The Impact of Disjunction on Reasoning under Existential Rules. Ph.D. Thesis, University of Oxford, Oxford, Oxfordshire, UK (2015)Google Scholar
  35. 35.
    Patel-Schneider, P.F., Horrocks, I.: A comparison of two modelling paradigms in the semantic web. J. Web Sem. 5(4), 240–250 (2007)CrossRefGoogle Scholar
  36. 36.
    Vardi, M.Y.: On the complexity of bounded-variable queries. In: PODS, pp. 266–276 (1995)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of OxfordOxfordUK
  2. 2.Institute of Information SystemsVienna University of TechnologyViennaAustria

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