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On the Complexity of Ontological Reasoning under Disjunctive Existential Rules

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Mathematical Foundations of Computer Science 2012 (MFCS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7464))

Abstract

Ontology-based data access is an emerging yet powerful technology that allows to enhance a classical relational database with an ontology in order to infer new intensional knowledge. Recently, Datalog+/- was introduced with the purpose of providing tractable reasoning algorithms for expressive ontology languages. In this framework, Datalog is extended by features such as existential quantification in rule heads, and at the same time the rule syntax is restricted to guarantee decidability, and also tractability, of relevant reasoning tasks. In this paper, we enrich Datalog even more by allowing not only existential quantification but also disjunction in rule heads, and we investigate the complexity of reasoning under the obtained formalism.

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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. In: TPLP (to appear, 2012)

    Google Scholar 

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

    Article  MATH  Google Scholar 

  4. Baader, F.: Least common subsumers and most specific concepts in a description logic with existential restrictions and terminological cycles. In: Proc. of IJCAI, pp. 319–324 (2003)

    Google Scholar 

  5. Baader, F., Brandt, S., Lutz, C.: Pushing the \(\mathcal{EL}\) envelope. In: Proc. of IJCAI, pp. 364–369 (2005)

    Google Scholar 

  6. Baader, F., Calvanese, D., McGuinness, D.L., Nardi, D., Patel-Schneider, P.F.: The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press (2003)

    Google Scholar 

  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)

    Article  MATH  Google Scholar 

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

    Google Scholar 

  9. Beeri, C., Vardi, M.Y.: The Implication Problem for Data Dependencies. In: Even, S., Kariv, O. (eds.) ICALP 1981. LNCS, vol. 115, pp. 73–85. Springer, Heidelberg (1981)

    Chapter  Google Scholar 

  10. Berardi, D., Calvanese, D., Giacomo, G.D.: Reasoning on UML class diagrams. Artif. Intell. 168(1-2), 70–118 (2005)

    Article  MATH  Google Scholar 

  11. Cabibbo, L.: The expressive power of stratified logic programs with value invention. Inf. Comput. 147(1), 22–56 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  12. Calì, A., Gottlob, G., Kifer, M.: Taming the infinite chase: Query answering under expressive relational constraints. In: Proc. of KR, pp. 70–80 (2008)

    Google Scholar 

  13. Calì, A., Gottlob, G., Lukasiewicz, T.: A general Datalog-based framework for tractable query answering over ontologies. In: Proc. of PODS, pp. 77–86 (2009)

    Google Scholar 

  14. Calì, A., Gottlob, G., Lukasiewicz, T., Marnette, B., Pieris, A.: Datalog±: A family of logical knowledge representation and query languages for new applications. In: Proc. of LICS, pp. 228–242 (2010)

    Google Scholar 

  15. Calì, A., Gottlob, G., Pieris, A.: Advanced processing for ontological queries. VLDB 3(1), 554–565 (2010)

    Google Scholar 

  16. Calì, A., Gottlob, G., Pieris, A.: Query Answering under Non-guarded Rules in Datalog±. In: Hitzler, P., Lukasiewicz, T. (eds.) RR 2010. LNCS, vol. 6333, pp. 1–17. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  17. Calvanese, D., Giacomo, G.D., Lembo, D., Lenzerini, M., Rosati, R.: Data complexity of query answering in description logics. In: Proc. of KR, pp. 260–270 (2006)

    Google Scholar 

  18. Calvanese, D., Giacomo, G.D., Lembo, D., Lenzerini, M., Rosati, R.: Tractable reasoning and efficient query answering in description logics: The DL-Lite family. J. Autom. Reasoning 39(3) (2007)

    Google Scholar 

  19. Chen, P.P.: The Entity-Relationship model - Toward a unified view of data. ACM Trans. Database Syst. 1(1), 9–36 (1976)

    Article  Google Scholar 

  20. Deutsch, A., Nash, A., Remmel, J.B.: The chase revisited. In: Proc. of PODS, pp. 149–158 (2008)

    Google Scholar 

  21. Eiter, T., Gottlob, G., Mannila, H.: Disjunctive Datalog. ACM Trans. Database Syst. 22(3), 364–418 (1997)

    Article  Google Scholar 

  22. 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  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  24. Johnson, D.S., Klug, A.C.: Testing containment of conjunctive queries under functional and inclusion dependencies. J. Comput. Syst. Sci. 28(1), 167–189 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  25. Krisnadhi, A., Lutz, C.: Data complexity in the EL family of DLs. In: Proc. of DL (2007)

    Google Scholar 

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

    Google Scholar 

  27. Leone, N., Manna, M., Terracina, G., Veltri, P.: Efficiently computable Datalog ∃  programs. In: Proc. of KR, pp. 13–23 (2012)

    Google Scholar 

  28. Marnette, B.: Generalized schema-mappings: From termination to tractability. In: Proc. of PODS, pp. 13–22 (2009)

    Google Scholar 

  29. 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 

  30. Poggi, A., Lembo, D., Calvanese, D., Giacomo, G.D., Lenzerini, M., Rosati, R.: Linking data to ontologies. J. Data Semantics 10, 133–173 (2008)

    Google Scholar 

  31. Vardi, M.Y.: The complexity of relational query languages (extended abstract). In: Proc. of STOCS, pp. 137–146 (1982)

    Google Scholar 

  32. Vardi, M.Y.: On the complexity of bounded-variable queries. In: Proc. of PODS, pp. 266–276 (1995)

    Google Scholar 

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Author information

Authors and Affiliations

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

    Georg Gottlob, Marco Manna, Michael Morak & Andreas Pieris

  2. Oxford-Man Institute of Quantitative Finance, University of Oxford, UK

    Georg Gottlob

  3. Institute for the Future of Computing, Oxford Martin School, UK

    Georg Gottlob

  4. Department of Mathematics, University of Calabria, Italy

    Marco Manna

Authors
  1. Georg Gottlob
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  2. Marco Manna
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  3. Michael Morak
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  4. Andreas Pieris
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Comenius University, Mlynska Dolina, 84248, Bratislava, Slovakia

    Branislav Rovan

  2. Department of Electronics and Computer Science, University of Southampton, SO17 1BJ, Southampton, UK

    Vladimiro Sassone

  3. Institute of Theoretical Computer Science, ETH Zürich, CAB H 39.2, Universitätstrasse 6, 8092, Zürich, Switzerland

    Peter Widmayer

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Gottlob, G., Manna, M., Morak, M., Pieris, A. (2012). On the Complexity of Ontological Reasoning under Disjunctive Existential Rules. In: Rovan, B., Sassone, V., Widmayer, P. (eds) Mathematical Foundations of Computer Science 2012. MFCS 2012. Lecture Notes in Computer Science, vol 7464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32589-2_1

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  • DOI: https://doi.org/10.1007/978-3-642-32589-2_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32588-5

  • Online ISBN: 978-3-642-32589-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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