We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Data Access With Horn Ontologies: Where Description Logics Meet Existential Rules | SpringerLink
Skip to main content

Data Access With Horn Ontologies: Where Description Logics Meet Existential Rules

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

Two main families of ontology languages are considered in the context of data access, namely Horn description logics and existential rules. In this paper, we review the semantic relationships between these families in the light of the ontology-mediated query answering problem. To this end, we rely on the standard translation of description logics in first-order logic and on the notion of semantic emulation. We focus on description logics and classes of existential rules for which the conjunctive query answering problem has polynomial data complexity.

This is a preview of subscription content, access via your institution.

Fig. 1

Notes

  1. 1.

    If we make the simplifying assumption that I interprets constants by themselves, a match of q in I can be seen as a homomorphism from q to the instance naturally associated with I.

  2. 2.

    The framework in [10] considers more general equality rules, where \(x_1\) and \(x_2\) may also be constants.

  3. 3.

    Note that the core chase is not defined when it does not terminate [25].

  4. 4.

    First, computing the core of an extended instance is difficult. The associated decision problem is both NP-hard and coNP-hard, precisely DP-complete [30]. Second, the extended instance built by the core chase does not grow monotonically, which in practice does not allow to update it incrementally.

  5. 5.

    The equivalence between the rewritability into a union of CQs and first-order rewritability follows from the (Finite) Homomorphism Preservation Theorem [52].

  6. 6.

    The decidability of query answering in the bts class follows from a theorem by Courcelle [27], which states that satisfiability is decidable for any class of first-order formulas enjoying the bounded-treewidth model property (i.e., satisfiability implies the existence of a model with a bounded-treewidth).

  7. 7.

    Constants may occur in the initial instance but they may also be brought by the rules, since rule heads may contain constants.

  8. 8.

    For ba-fr1, 2ExpTime-hardness is still open in the unbounded arity case, while ExpTime-completeness holds in the bounded arity case [53].

  9. 9.

    To simplify the discussion, we chose not to include nominals nor role composition (except for its restricted use in the transitivity axiom which could be written \(r \circ r \sqsubseteq r\)).

  10. 10.

    Surpringly, ba-fr1 is not in a lower complexity class than ba-fg for data and bounded-arity combined complexity.

  11. 11.

    Actually, this result is established for a larger first-order logic fragment, itself included in the so-called guarded negation fragment.

References

  1. 1.

    Abiteboul S, Hull R, Vianu V (1994) Foundations of databases. Addison Wesley, New York

    Google Scholar 

  2. 2.

    Amarilli A, Benedikt M, Bourhis P, Vanden Boom M (2016) Query answering with transitive and linear-ordered data. In: Proceedings of the twenty-fifth international joint conference on artificial intelligence, IJCAI 2016, pp 893–899

  3. 3.

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

    MathSciNet  Article  Google Scholar 

  4. 4.

    Baader F, Brandt S, Lutz C (2005) Pushing the EL envelope. In: Proceedings of the nineteenth international joint conference on artificial intelligence, IJCAI 2005, pp 364–369

  5. 5.

    Baader F, Calvanese D, McGuinness D, Nardi D, Patel-Schneider P (eds) (2007) The description logic handbook: theory, implementation, and applications, 2nd edn. Cambridge University Press, Cambridge

  6. 6.

    Baader F, Horrocks I, Lutz C, Sattler U (2017) An introduction to description logic. Cambridge University Press, Cambridge

    Book  Google Scholar 

  7. 7.

    Baget J-F, Bienvenu M, Mugnier M-L, Rocher S (2015) Combining existential rules and transitivity: next steps. In: Proceedings of the 24th international joint conference on artificial intelligence, IJCAI 2015, pp 2720–2726

  8. 8.

    Baget J-F, Leclère M, Mugnier M-L (2010) Walking the decidability line for rules with existential variables. In: Principles of knowledge representation and reasoning: Proceedings of the twelfth international conference, KR 2010. AAAI Press, New York

  9. 9.

    Baget J-F, Leclère M, Mugnier M-L, Salvat E (2009) Extending decidable cases for rules with existential variables. In: Proceedings of the 21st international joint conference on artificial intelligence, IJCAI 2009, pp 677–682

  10. 10.

    Baget J-F, Leclère M, Mugnier M-L, Salvat E (2011) On rules with existential variables: walking the decidability line. Artif Intell 175(9–10):1620–1654

    MathSciNet  Article  Google Scholar 

  11. 11.

    Baget J-F, Mugnier M-L, Rudolph S, Thomazo M (2011) Walking the complexity lines for generalized guarded existential rules. In: Proceedings of the 22nd international joint conference on artificial intelligence, IJCAI 2011, pp 712–717

  12. 12.

    Barceló P, Berger G, Lutz C, Pieris A (2018) First-order rewritability of frontier-guarded ontology-mediated queries. In: Proceedings of the 27th international joint conference on artificial intelligence, IJCAI 2018, pp 1707–1713

  13. 13.

    Beeri C, Vardi M (1981) The implication problem for data dependencies. In: Proceedings of automata, languages and programming, 8th colloquium (ICALP 1981). Lecture notes in computer science, vol 115, pp 73–85

  14. 14.

    Bienvenu M, Ortiz M (2015) Ontology-mediated query answering with data-tractable description logics. In: Reasoning web. Web logic rules—11th international summer school 2015. Lecture notes in computer science, vol 9203, pp 218–307

  15. 15.

    Bienvenu M, ten Cate B, Lutz C, Wolter F (2014) Ontology-based data access: a study through disjunctive datalog, csp, and MMSNP. ACM Trans. Database Syst. 39(4):33:1–33:44

    MathSciNet  Article  Google Scholar 

  16. 16.

    Bourhis P, Morak M, Pieris A (2013) The impact of disjunction on query answering under guarded-based existential rules. In: Proceedings of the 23rd international joint conference on artificial intelligence, IJCAI 2013, pp 796–802

  17. 17.

    Calì A, Gottlob G, Kifer M (2008) Taming the infinite chase: query answering under expressive relational constraints. Principles of knowledge representation and reasoning. Proceedings of the eleventh international conference, pp 70–80

  18. 18.

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

    MathSciNet  Article  Google Scholar 

  19. 19.

    Calì A, Gottlob G, Lukasiewicz T (2009) Datalog extensions for tractable query answering over ontologies. In: Semantic web information management—a model-based perspective. Springer, New York, pp 249–279

  20. 20.

    Calì A, Gottlob G, Lukasiewicz T (2009) A general datalog-based framework for tractable query answering over ontologies. In: Proceedings of the 28th ACM SIGMOD-SIGACT-SIGART symposium on principles of database systems, PODS 2009. ACM, New York, pp 77–86

  21. 21.

    Calì A, Gottlob G, Lukasiewicz T (2010) Datalog extensions for tractable query answering over ontologies. In: Semantic web information management: a model-based perspective. Springer, New York, pp 249–279

  22. 22.

    Calì A, Gottlob G, Lukasiewicz T, Marnette B, Pieris A (2010) Datalog+/-: a family of logical knowledge representation and query languages for new applications. In: Proceedings of the 25th annual IEEE symposium on logic in computer science, LICS 2010, pp 228–242

  23. 23.

    Calvanese D, De Giacomo G, Lembo D, Lenzerini M, Rosati R (2007) Tractable reasoning and efficient query answering in description logics: the DL-Lite family. J Autom Reas 39(3):385–429

    MathSciNet  Article  Google Scholar 

  24. 24.

    Carral D, Dragoste I, Krötzsch M (2017) Restricted chase (non)termination for existential rules with disjunctions. In: Proceedings of the twenty-sixth international joint conference on artificial intelligence, IJCAI 2017, pp 922–928

  25. 25.

    Carral D, Krötzsch M, Marx M, Ozaki A, Rudolph S (2018) Preserving constraints with the stable chase. In: 21st international conference on database theory, ICDT 2018. LIPIcs, vol 98, pp 12:1–12:19

  26. 26.

    Chein M, Mugnier M-L (2009) Graph-based Knowledge representation and reasoning—computational foundations of conceptual graphs. In: Advanced information and knowledge processing. Springer, New York

  27. 27.

    Courcelle B (1990) The monadic second-order logic of graphs: I. Recognizable sets of finite graphs. Inf. Comput. 85(1):12–75

    MathSciNet  Article  Google Scholar 

  28. 28.

    Deutsch A, Nash A, Remmel J (2008) The chase revisited. In: Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on principles of database systems (PODS) 2008, pp 149–158

  29. 29.

    Fagin R, Kolaitis PG, Miller RJ, Popa L (2005) Data exchange: semantics and query answering. Theor Comput Sci 336(1):89–124

    MathSciNet  Article  Google Scholar 

  30. 30.

    Fagin R, Kolaitis PG, Popa L (2005) Data exchange: getting to the core. ACM Trans Database Syst 30(1):174–210

    Article  Google Scholar 

  31. 31.

    Glimm B, Horrocks I, Lutz C, Sattler U (2008) Conjunctive query answering for the description logic SHIQ. J Artif Intell Res 31:150–197

    MathSciNet  Article  Google Scholar 

  32. 32.

    Gogacz T, Marcinkowski J (2014) All-instances termination of chase is undecidable. In: Proceedings of automata, languages, and programming—41st international colloquium, ICALP 2014, Part II. Lecture notes in computer science, vol 8573. Springer, New York, pp 293–304

  33. 33.

    Gottlob G, Orsi G, Pieris A, Simkus M (2012) Datalog and its extensions for semantic web databases. In: Reasoning web. Semantic technologies for advanced query answering—8th international summer school 2012, proceedings. Lecture notes in computer science, vol 7487. Springer, New York, pp 54–77

  34. 34.

    Gottlob G, Pieris A, Tendera L (2013) Querying the guarded fragment with transitivity. In Automata, languages, and programming—40th international colloquium, ICALP 2013, proceedings, part II, pp 287–298

  35. 35.

    Gottlob G, Rudolph S, Simkus M (2014) Expressiveness of guarded existential rule languages. In: Proceedings of the 33rd ACM SIGMOD-SIGACT-SIGART symposium on principles of database systems, PODS’14. ACM, New York, pp 27–38

  36. 36.

    Grahne G, Onet A (2018) Anatomy of the chase. Fund Inform 157(3):221–270

    MathSciNet  MATH  Google Scholar 

  37. 37.

    Hitzler P, Krötzsch M, Rudolph S (2009) Foundations of semantic web technologies. Chapman & Hall/CRC, London

    Book  Google Scholar 

  38. 38.

    Hustadt U, Motik B, Sattler U (2005) Data complexity of reasoning in very expressive description logics. In Proceedings of the 19th international joint conference on artificial intelligence (IJCAI’05), pp 466–471

  39. 39.

    Kontchakov R, Rodriguez-Muro M, Zakharyaschev M (2013) Ontology-based data access with databases: a short course. In: Reasoning web. Semantic technologies for intelligent data access—9th international summer school 2013, proceedings. Lecture notes in computer science, vol 8067. Springer, New York, pp 194–229

  40. 40.

    Krötzsch M, Rudolph S (2016) Is your database system a semantic web reasoner? KI 30(2):169–176

    Google Scholar 

  41. 41.

    Krötzsch M, Rudolph S, Hitzler P (2013) Complexities of Horn description logics. ACM Trans Comput Logic 14(1):2:1–2:36

    MathSciNet  Article  Google Scholar 

  42. 42.

    Krötzsch M, Rudolph S, Schmitt PH (2015) A closer look at the semantic relationship between datalog and description logics. Semantic Web 6(1):63–79

    Article  Google Scholar 

  43. 43.

    Lutz C (2008) The complexity of conjunctive query answering in expressive description logics. In: Armando A, Baumgartner P, Dowek G (eds) Proceedings of the 4th international joint conference on automated reasoning (IJCAR’08). Lecture notes in artificial intelligence, vol 5195. Springer, New York, pp 179–193

  44. 44.

    Lutz C, Toman D, Wolter F (2009) Conjunctive query answering in the description logic \({\cal{EL}}\) using a relational database system. In: Proceedings of the 21st international joint conference on artificial intelligence, IJCAI 2009, pp 2070–2075

  45. 45.

    Magka D, Krötzsch M, Horrocks I (2013) Computing stable models for nonmonotonic existential rules. In: Proceedings of the 23rd international joint conference on artificial intelligence, IJCAI 2013, pp 1031–1038

  46. 46.

    Maier D (1983) The theory of relational databases. Computer Science Press, Rockville

    MATH  Google Scholar 

  47. 47.

    Marnette B (2009) Generalized schema-mappings: from termination to tractability. In: Proceedings of the twenty-eigth ACM SIGMOD-SIGACT-SIGART symposium on principles of database systems, PODS 2009, pp 13–22

  48. 48.

    Mugnier M-L (2011) Ontological query answering with existential rules. In: Web reasoning and rule systems—5th international conference, RR 2011. Proceedings. Lecture notes in computer science, vol 6902. Springer, New York, pp 2–23

  49. 49.

    Mugnier M-L, Thomazo M (2014) An introduction to ontology-based query answering with existential rules. In: Reasoning web. Reasoning on the web in the Big Data era—10th international summer school 2014. Proceedings. Lecture notes in computer science, vol 8714. Springer, New York, pp 245–278

  50. 50.

    Ortiz M, Rudolph S, Simkus M (2011) Query answering in the horn fragments of the description logics \({\cal{SHOIQ}}\) and \({\cal{SROIQ}}\). In Walsh T (ed) Proceedings of the 22nd international joint conference on artificial intelligence, IJCAI 2011, pp 1039–1044. IJCAI/AAAI

  51. 51.

    Rocher S (2016) Querying existential rule knowledge bases: decidability and complexity (Interrogation de Bases de Connaissances avec Règles Existentielles : Décidabilité et Complexité). PhD thesis, University of Montpellier, France

  52. 52.

    Rossman B (2008) Homomorphism preservation theorems. J. ACM 55(3):15:1–15:53

    MathSciNet  Article  Google Scholar 

  53. 53.

    Rudolph S, Thomazo M, Baget J-F, Mugnier M-L (2014) Worst-case optimal query answering for greedy sets of existential rules and their subclasses. CoRR. arXiv:abs/1412.4485

  54. 54.

    Thomazo M (2013) Conjunctive Query Answering Under Existential Rules—Decidability, Complexity, and Algorithms. PhD thesis, University of Montpellier 2

  55. 55.

    Thomazo M, Baget J-F, Mugnier M-L, Rudolph S (2012) A generic querying algorithm for greedy sets of existential rules. In: Principles of knowledge representation and reasoning. Proceedings of the thirteenth international conference, KR 2012

  56. 56.

    W3C OWL Working Group (2009) OWL 2 web ontology language: document overview. W3C recommendation. http://www.w3.org/TR/owl2-overview/. Accessed 27 Oct 2009

Download references

Acknowledgements

Many thanks to the anonymous reviewers for their helpful comments and suggestions. This work was partially funded by the ANR project CQFD (ANR-18-CE23-0003).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Marie-Laure Mugnier.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mugnier, ML. Data Access With Horn Ontologies: Where Description Logics Meet Existential Rules. Künstl Intell 34, 475–489 (2020). https://doi.org/10.1007/s13218-020-00678-3

Download citation

Keywords

  • Data access
  • Ontology-mediated query answering
  • Existential rules
  • Horn description logics