Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
125 tokens/sec
GPT-4o
53 tokens/sec
Gemini 2.5 Pro Pro
42 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
47 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

The Data Complexity of Description Logic Ontologies (1611.02453v3)

Published 8 Nov 2016 in cs.AI

Abstract: We analyze the data complexity of ontology-mediated querying where the ontologies are formulated in a description logic (DL) of the ALC family and queries are conjunctive queries, positive existential queries, or acyclic conjunctive queries. Our approach is non-uniform in the sense that we aim to understand the complexity of each single ontology instead of for all ontologies formulated in a certain language. While doing so, we quantify over the queries and are interested, for example, in the question whether all queries can be evaluated in polynomial time w.r.t. a given ontology. Our results include a PTime/coNP-dichotomy for ontologies of depth one in the description logic ALCFI, the same dichotomy for ALC- and ALCI-ontologies of unrestricted depth, and the non-existence of such a dichotomy for ALCF-ontologies. For the latter DL, we additionally show that it is undecidable whether a given ontology admits PTime query evaluation. We also consider the connection between PTime query evaluation and rewritability into (monadic) Datalog.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (65)
  1. The complexity of satisfiability problems: Refining Schaefer’s theorem. In MFCS, pages 71–82, 2005.
  2. The DL-Lite family and relations. J. Artif. Intell. Res. (JAIR), 36:1–69, 2009.
  3. On datalog vs. polynomial time. In PODS, pages 13–25, 1991.
  4. Albert Atserias. On digraph coloring problems and treewidth duality. Eur. J. Comb., 29(4):796–820, 2008.
  5. Libor Barto. Constraint satisfaction problem and universal algebra. SIGLOG News, 1(2):14–24, 2014.
  6. Query and predicate emptiness in ontology-based data access. J. Artif. Intell. Res. (JAIR), 56:1–59, 2016.
  7. Pushing the ℰ⁢ℒℰℒ\mathcal{EL}caligraphic_E caligraphic_L envelope. In IJCAI, pages 364–369. Professional Book Center, 2005.
  8. Querying the guarded fragment. In LICS, pages 1–10, 2010.
  9. First order-rewritability and containment of conjunctive queries in Horn description logics. In IJCAI, pages 965–971, 2016.
  10. Andrei A. Bulatov. A dichotomy theorem for nonuniform CSPs. In FOCS, 2017.
  11. Classifying the complexity of constraints using finite algebras. SIAM J. Comput., 34(3):720–742, 2005.
  12. First-order rewritability of atomic queries in horn description logics. In IJCAI, pages 754–760, 2013.
  13. Walking the complexity lines for generalized guarded existential rules. In IJCAI, pages 712–717, 2011.
  14. Ontology-mediated query answering with data-tractable description logics. In Reasoning Web, volume 9203 of LNCS, pages 218–307. Springer, 2015.
  15. Ontology-based data access: A study through disjunctive datalog, CSP, and MMSNP. ACM Trans. Database Syst., 39(4):33:1–33:44, 2014.
  16. Query-Based Entailment and Inseparability for ALC Ontologies In IJCAI, pages 1001–1007, 2016.
  17. Andrei A. Bulatov. A dichotomy theorem for constraints on a three-element set. In FOCS, pages 649–658, 2002.
  18. Andrei A. Bulatov. On the CSP dichotomy conjecture. In CSR, pages 331–344, 2011.
  19. Tractable reasoning and efficient query answering in description logics: The DL-Lite family. J. of Autom. Reasoning, 39(3):385–429, 2007.
  20. Data complexity of query answering in description logics. Artificial Intelligence, 195:335–360, 2013.
  21. Taming the infinite chase: Query answering under expressive relational constraints. J. Artif. Intell. Res. (JAIR), 48:115–174, 2013.
  22. View-based query processing and constraint satisfaction. In LICS, pages 361–371, 2000.
  23. Reasoning on regular path queries. SIGMOD Record, 32(4):83–92, 2003.
  24. View-based query containment. In PODS, pages 56–67, 2003.
  25. What you always wanted to know about datalog (and never dared to ask). IEEE Trans. Knowl. Data Eng., 1(1):146–166, 1989.
  26. Model Theory, volume 73 of Studies in Logic and the Foundations of Mathematics. Elsevier, 1990.
  27. Query answering in the description logic Horn-𝒮⁢ℋ⁢ℐ⁢𝒬𝒮ℋℐ𝒬\mathcal{SHIQ}caligraphic_S caligraphic_H caligraphic_I caligraphic_Q. In JELIA, pages 166–179, 2008.
  28. Rewritability in monadic disjunctive datalog, MMSNP, and expressive description logics. In ICDT, pages 1–17, 2017.
  29. Data exchange: semantics and query answering. Theor. Comput. Sci., 336(1):89–124, 2005.
  30. The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory SIAM J. Comput., 28(1):57–104, 1998.
  31. Homomorphism closed vs. existential positive. In LICS, pages 311–320, 2003.
  32. Conjunctive query answering for the description logic 𝒮⁢ℋ⁢ℐ⁢𝒬𝒮ℋℐ𝒬\mathcal{SHIQ}caligraphic_S caligraphic_H caligraphic_I caligraphic_Q. JAIR, 31:157–204, 2008.
  33. Model theory of modal logic. In Handbook of Modal Logic, pages 249–329. Elsevier, 2007.
  34. Efficient query rewriting in the description logic ℰ⁢ℒℰℒ\mathcal{EL}caligraphic_E caligraphic_L and beyond. In IJCAI, pages 3034–3040, 2015.
  35. Dichotomies in Ontology-Mediated Querying with the Guarded Fragment. In PODS, pages 185–199, 2017.
  36. Horn Rewritability vs PTime Query Answering for Description Logic TBoxes. In Description Logics, 2017.
  37. Reasoning in description logics by a reduction to disjunctive datalog. J. Autom. Reasoning, 39(3):351–384, 2007.
  38. On the complexity of h-coloring. J. Comb. Theory, Ser. B, 48(1):92–110, 1990.
  39. Datalog rewritability of Disjunctive Datalog programs and non-Horn ontologies. Artificial Intelligence, 236: 90–118, 2016.
  40. Yevgeny Kazakov. Consequence-driven reasoning for Horn-𝒮⁢ℋ⁢ℐ⁢𝒬𝒮ℋℐ𝒬\mathcal{SHIQ}caligraphic_S caligraphic_H caligraphic_I caligraphic_Q ontologies. In Craig Boutilier, editor, IJCAI, pages 2040–2045, 2009.
  41. Data complexity in the ℰ⁢ℒℰℒ\mathcal{EL}caligraphic_E caligraphic_L family of description logics. In LPAR, pages 333–347, 2007.
  42. The combined approach to query answering in DL-Lite. In KR, 2010.
  43. Complexity boundaries for Horn description logics. In AAAI, pages 452–457, 2007.
  44. Andrei A. Krokhin. Tree dualities for constraint satisfaction. In CSL, pages 32–33, 2010.
  45. Markus Krötzsch. Efficient inferencing for OWL EL. In JELIA, pages 234–246, 2010.
  46. A new line of attack on the dichotomy conjecture. In STOC, pages 725–734, 2009.
  47. An introduction to description logics and query rewriting. In Reasoning Web, volume 8714 of LNCS, pages 195–244. Springer, 2014.
  48. A characterisation of first-order constraint satisfaction problems. Logical Methods in Computer Science, 3(4), 2007.
  49. Description logic tboxes: Model-theoretic characterizations and rewritability. In IJCAI, 2011.
  50. Ontology-based data access with closed predicates is inherently intractable (sometimes). In IJCAI, pages 1024–1030. IJCAI/AAAI, 2013.
  51. Ontology-Mediated Querying with the Description Logic ℰ⁢ℒℰℒ\mathcal{EL}caligraphic_E caligraphic_L: Trichotomy and Linear Datalog Rewritability. In IJCAI, pages 1181–1187. IJCAI/AAAI, 2017.
  52. Ontology-mediated queries with closed predicates. In IJCAI, pages 3120–3126. AAAI Press, 2015.
  53. Conjunctive query answering in the description logic ℰ⁢ℒℰℒ\mathcal{EL}caligraphic_E caligraphic_L using a relational database system. In IJCAI, pages 2070–2075, 2009.
  54. Deciding inseparability and conservative extensions in the description logic ℰ⁢ℒℰℒ\mathcal{EL}caligraphic_E caligraphic_L. J. Symb. Comput., 45(2):194–228, 2010.
  55. Non-uniform data complexity of query answering in description logics. In Description Logics, 2011.
  56. Non-uniform data complexity of query answering in description logics. In KR. AAAI Press, 2012.
  57. Johann A. Makowsky. Why Horn formulas matter in computer science: Initial structures and generic examples. J. Comput. Syst. Sci., 34(2/3):266–292, 1987.
  58. Anatoli I. Malcev. The metamathematics of algebraic systems, collected papers:1936-1967. North-Holland, 1971.
  59. Initiality, induction, and computability. In Algebraic Methods in Semantics, pages 459–541. Cambridge University Press, 1985.
  60. Data complexity of query answering in expressive description logics via tableaux. J. of Autom. Reasoning, 41(1):61–98, 2008.
  61. Linking data to ontologies. J. Data Semantics, 10:133–173, 2008.
  62. Riccardo Rosati. The limits of querying ontologies. In ICDT, volume 4353 of LNCS, pages 164–178. Springer, 2007.
  63. Thomas J. Schaefer. The complexity of satisfiability problems. In STOC, pages 216–226, 1978.
  64. Andrea Schaerf. On the complexity of the instance checking problem in concept languages with existential quantification. J. of Intel. Inf. Systems, 2:265–278, 1993.
  65. Dmitriy Zhuk. The Proof of CSP Dichotomy Conjecture. In FOCS, 2017.
Citations (23)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now