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Towards Efficient Reasoning Under Guarded-Based Disjunctive Existential Rules

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Mathematical Foundations of Computer Science 2014 (MFCS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8634))

Abstract

The complete picture of the complexity of answering (unions of) conjunctive queries under the main guarded-based classes of disjunctive existential rules has been recently settled. It has been shown that the problem is very hard, namely 2ExpTime-complete, even for fixed sets of rules expressed in lightweight formalisms. This gives rise to the question whether its complexity can be reduced by restricting the query language. Several subclasses of conjunctive queries have been proposed with the aim of reducing the complexity of classical database problems such as query evaluation and query containment. Three of the most prominent subclasses of this kind are queries of bounded hypertree-width, queries of bounded treewidth and acyclic queries. The central objective of the present paper is to understand whether the above query languages have a positive impact on the complexity of query answering under the main guarded-based classes of disjunctive existential rules.

We show that (unions of) conjunctive queries of bounded hypertree-width and of bounded treewidth do not reduce the complexity of our problem, even if we focus on predicates of bounded arity, or on fixed sets of disjunctive existential rules. Regarding acyclic queries, although our problem remains 2ExpTime-complete in general, in some relevant settings the complexity reduces to ExpTime-complete; in fact, this requires to bound the arity of the predicates, and for some expressive guarded-based formalisms, to fix the set of rules.

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References

  1. Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley (1995)

    Google Scholar 

  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)

    MATH  MathSciNet  Google Scholar 

  3. Andréka, H., van Benthem, J., Németi, I.: Modal languages and bounded fragments of predicate logic. J. Philosophical Logic 27, 217–274 (1998)

    Article  MATH  Google Scholar 

  4. Artale, A., Calvanese, D., Kontchakov, R., Zakharyaschev, M.: The DL-Lite family and relations. J. Artif. Intell. Res. 36, 1–69 (2009)

    MATH  MathSciNet  Google Scholar 

  5. Baeza, P.B.: Querying graph databases. In: PODS, pp. 175–188 (2013)

    Google Scholar 

  6. 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)

    Article  MATH  Google Scholar 

  7. Baget, J.F., Mugnier, M.L., Rudolph, S., Thomazo, M.: Walking the complexity lines for generalized guarded existential rules. In: IJCAI, pp. 712–717 (2011)

    Google Scholar 

  8. Bárány, V., Gottlob, G., Otto, M.: Querying the guarded fragment. In: LICS, pp. 1–10 (2010)

    Google Scholar 

  9. Bárány, V., ten Cate, B., Segoufin, L.: Guarded negation. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 356–367. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  10. Beeri, C., Vardi, M.Y.: The implication problem for data dependencies. In: Even, S., Kariv, O. (eds.) ICALP. LNCS, vol. 115, pp. 73–85. Springer, Heidelberg (1981)

    Google Scholar 

  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. Calì, A., Gottlob, G., Kifer, M.: Taming the infinite chase: Query answering under expressive relational constraints. J. Artif. Intell. Res. 48, 115–174 (2013)

    MATH  Google Scholar 

  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)

    Article  Google Scholar 

  14. Calì, A., Gottlob, G., Pieris, A.: Towards more expressive ontology languages: The query answering problem. Artif. Intell. 193, 87–128 (2012)

    Article  MATH  Google Scholar 

  15. 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)

    Article  MATH  Google Scholar 

  16. Chekuri, C., Rajaraman, A.: Conjunctive query containment revisited. Theor. Comput. Sci. 239(2), 211–229 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  17. Deutsch, A., Tannen, V.: Reformulation of XML queries and constraints. In: Calvanese, D., Lenzerini, M., Motwani, R. (eds.) ICDT 2003. LNCS, vol. 2572, pp. 225–241. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  18. Fagin, R., Kolaitis, P.G., Miller, R.J., Popa, L.: Data exchange: Semantics and query answering. Theor. Comput. Sci. 336(1), 89–124 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  19. Gottlob, G., Leone, N., Scarcello, F.: The complexity of acyclic conjunctive queries. J. ACM 48(3), 431–498 (2001)

    Article  MathSciNet  Google Scholar 

  20. Gottlob, G., Leone, N., Scarcello, F.: Hypertree decompositions and tractable queries. J. Comput. Syst. Sci. 64(3), 579–627 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  21. Gottlob, G., Leone, N., Scarcello, F.: Robbers, marshals, and guards: game theoretic and logical characterizations of hypertree width. J. Comput. Syst. Sci. 66(4), 775–808 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  22. 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)

    Chapter  Google Scholar 

  23. Gottlob, G., Manna, M., Pieris, A.: Combining decidability paradigms for existential rules. TPLP 13(4-5), 877–892 (2013)

    MATH  MathSciNet  Google Scholar 

  24. Grädel, E.: On the restraining power of guards. J. Symb. Log. 64(4), 1719–1742 (1999)

    Article  MATH  Google Scholar 

  25. Grau, B.C., Horrocks, I., Krötzsch, M., Kupke, C., Magka, D., Motik, B., Wang, Z.: Acyclicity notions for existential rules and their application to query answering in ontologies. J. Artif. Intell. Res. 47, 741–808 (2013)

    MATH  Google Scholar 

  26. Krötzsch, M., Rudolph, S.: Extending decidable existential rules by joining acyclicity and guardedness. In: IJCAI, pp. 963–968 (2011)

    Google Scholar 

  27. Leone, N., Manna, M., Terracina, G., Veltri, P.: Efficiently computable Datalog ∃  programs. In: KR (2012)

    Google Scholar 

  28. Patel-Schneider, P.F., Horrocks, I.: A comparison of two modelling paradigms in the semantic web. J. Web Sem. 5(4), 240–250 (2007)

    Article  Google Scholar 

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Authors and Affiliations

  1. CNRS LIFL Université Lille 1/INRIA Lille, France

    Pierre Bourhis

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

    Michael Morak & Andreas Pieris

Authors
  1. Pierre Bourhis
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  2. Michael Morak
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  3. Andreas Pieris
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Editor information

Editors and Affiliations

  1. Faculty of Informatics, Eötvös Loránd University, Pázmány Péter sétány 1/C, 1117, Budapest, Hungary

    Erzsébet Csuhaj-Varjú

  2. Fakultät für Informatik und Automatisierung, Technische Universität Ilmenau, Helmholtzplatz, 598693, Ilmenau, Germany

    Martin Dietzfelbinger

  3. Institute of Informatics, Szeged University, Tisza Lajos krt. 103, 6720, Szeged, Hungary

    Zoltán Ésik

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Bourhis, P., Morak, M., Pieris, A. (2014). Towards Efficient Reasoning Under Guarded-Based Disjunctive Existential Rules. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44522-8_9

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  • DOI: https://doi.org/10.1007/978-3-662-44522-8_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44521-1

  • Online ISBN: 978-3-662-44522-8

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