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Weight-based consistent query answering over inconsistent \({\mathcal {SHIQ}}\) knowledge bases

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Abstract

Non-standard query mechanisms that work under inconsistency are required in some important description logic (DL)-based applications, including those involving an inconsistent DL knowledge base ( KB) whose intensional knowledge is consistent but is violated by its extensional knowledge. This paper proposes a weight-based semantics for querying such an inconsistent KB. This semantics defines an answer of a conjunctive query posed upon an inconsistent KB as a tuple of individuals whose substitution for the variables in the query head makes the query body entailed by any subbase of the KB consisting of the intensional knowledge and a weight-maximally consistent subset of the extensional knowledge. A novel computational method for this semantics is proposed, which works for extensionally reduced \({\mathcal {SHIQ}}\) KBs and conjunctive queries without non-distinguished variables. The method first compiles the given KB to a propositional program; then, for any given conjunctive query, it reduces the problem of computing all answers of the given query to a set of propositional satisfiability (SAT) problems with PB-constraints, which are then solved by SAT solvers. A decomposition-based framework for optimizing the method is also proposed. The feasibility of this method is demonstrated in our experiments.

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References

  1. Arenas M, Bertossi LE Chomicki J (1999) Consistent query answers in inconsistent databases. In: Proceedings of the 18th ACM symposium on principles of database systems (PODS), pp 68–79

  2. Arenas M, Bertossi LE, Chomicki J (2003) Answer sets for consistent query answering in inconsistent databases. Theory Pract Logic Program 3(4–5): 393–424

    Article  MathSciNet  MATH  Google Scholar 

  3. Arieli O, Denecker M, NuffelenBV Bruynooghe M (2004) Coherent integration of databases by abductive logic programming. J Artif Intell Res 21: 245–286

    MATH  Google Scholar 

  4. Aspvall B, Plass MF, Tarjan RE (1979) A linear-time algorithm for testing the truth of certain quantified Boolean formulas. Inf Process Lett 8(3): 121–123

    Article  MathSciNet  MATH  Google Scholar 

  5. Baader, F, Calvanese, D, McGuinness, DL, Nardi, D, Patel-Schneider, PF (eds) (2003) The description logic handbook: theory, implementation, and applications. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  6. Bailleux O, Boufkhad Y, Roussel O (2006) A translation of pseudo boolean constraints to SAT. J Satisf Boolean Model Comput 2: 191–200

    MATH  Google Scholar 

  7. Benferhat S, Cayrol C, Dubois D, Lang J, Prade H (1993) Inconsistency management and prioritized syntax-based entailment. In: Bajcsy R (eds) Proceedings of the 13th international joint conference on artificial intelligence (IJCAI), pp 640–647

  8. Benferhat S, Dubois D, Prade H (1995) How to infer from inconsisent beliefs without revising? In: Proceedings of the 14th international joint conference on artificial intelligence (IJCAI), pp 1449–1457

  9. Bertossi LE, Chomicki J (2003) Query answering in inconsistent databases. In: Chomicki J, Meyden R, Saake G (eds) Logics for emerging applications of databases. Springer, pp 43–83

  10. Calvanese D, Giacomo G, Lembo D, Lenzerini M, Rosati R (2005) DL-Lite: tractable description logics for ontologies. In: Veloso M, Kambhampati S (eds) Proceedings of the 20th national conference on artificial intelligence (AAAI), pp 602–607

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

    Article  MATH  Google Scholar 

  12. Chai D, Kuehlmann A (2003) A fast pseudo-boolean constraint solver. In: Proceedings of the 40th design automation conference (DAC), pp 830–835

  13. Chomicki J (2007) Consistent query answering: five easy pieces. In: Schwentick T, Suciu D (eds) Proceedings of the 11th international conference on database theory (ICDT), pp 1–17

  14. Cimiano P (2006) Ontology learning and population from text algorithms evaluation and applications. Springer, Berlin

    Google Scholar 

  15. Cimiano P, Völker J (2005) Text2onto—a framework for ontology learning and data-driven change discovery. In: Montoyo A, Muñoz R, Métais E (eds) Proceedings of the 10th international conference on applications of natural language to information systems (NLDB), pp 227–238

  16. de Saint-Cyr F, Lang J, Schiex T (1994) Penalty logic and its link with dempster-shafer theory. In: Mántaras R, Poole D (eds) Proceedings of the 10th annual conference on uncertainty in artificial intelligence (UAI), pp 204–211

  17. Dolby J, Fokoue A, Kalyanpur A, Ma L, Schonberg E, Srinivas K, Sun X (2008) Scalable grounded conjunctive query evaluation over large and expressive knowledge bases. In: Sheth AP, Staab S, Dean M, Paolucci M, Maynard D, Finin TW, Thirunarayan K (eds) Proceedings of the 7th international semantic web conference (ISWC), pp 403–418

  18. Du J, Shen Y (2008) Computing minimum cost diagnoses to repair populated DL-based ontologies. In: Huai J, Chen R, Hon H, Liu Y, Ma W, Tomkins A, Zhang X (eds) Proceedings of the 17th international world wide web conference (WWW), pp 575–584

  19. Eén N, Sörensson N (2006) Translating pseudo-boolean constraints into SAT. J Satisf Boolean Model Comput 2: 1–26

    MATH  Google Scholar 

  20. Eiter T, Gottlob G (1995) The complexity of logic-based abduction. J ACM 42(1): 3–42

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  22. Eiter T, Leone N, Mateis C, Pfeifer G, Scarcello F (1997) A deductive system for non-monotonic reasoning. In: Dix J, Furbach U, Nerode A (eds) Proceedings of the 4th international conference on logic programming and nonmonotonic reasoning (LPNMR), pp 364–375

  23. Feldman R, Rosenfeld B, Fresko M (2006) TEG—a hybrid approach to information extraction. Knowl Inf Syst 9(1): 1–18

    Article  Google Scholar 

  24. Fitting M (1996) First-order logic and automated theorem proving. Springer, Secaucus

    Book  MATH  Google Scholar 

  25. Guo Y, Pan Z, Heflin J (2005) LUBM: a benchmark for OWL knowledge base systems. J Web Semant 3(2–3): 158–182

    Article  Google Scholar 

  26. Haarslev V, Möller R (2001) Racer system description. In: Goré R, Leitsch A, Nipkow T (eds) Proceedings of the 1st international joint conference on automated reasoning (IJCAR), pp 701–706

  27. Horrocks I, Patel-Schneider PF, van Harmelen F (2003) From \({\mathcal{SHIQ} }\) and RDF to OWL: the making of a web ontology language. J Web Semant 1(1): 7–26

    Article  Google Scholar 

  28. Horrocks I, Sattler U, Tobies S (2000) Practical reasoning for very expressive description logics. Logic J IGPL 8(3): 239–263

    Article  MathSciNet  MATH  Google Scholar 

  29. Huang Z, van Harmelen F, ten Teije A (2005) Reasoning with inconsistent ontologies. In: Kaelbling LP, Saffiotti A (eds) Proceedings of the 19th international joint conference on artificial intelligence (IJCAI), pp 454–459

  30. Hustadt U, Motik B, Sattler U (2004) Reducing \({\mathcal{SHIQ}^-}\) description logic to disjunctive datalog programs. In: Proceedings of the 9th international conference on principles of knowledge representation and reasoning (KR), pp 152–162

  31. Hustadt U, Motik B, Sattler U (2007) Reasoning in description logics by a reduction to disjunctive datalog. J Autom Reason 39(3): 351–384

    Article  MathSciNet  MATH  Google Scholar 

  32. Kazakov Y, Motik B (2008) A resolution-based decision procedure for \({\mathcal{SHOIQ}}\). J Autom Reason 40(2–3): 89–116

    Article  MathSciNet  MATH  Google Scholar 

  33. Lembo D, Ruzzi M (2007) Consistent query answering over description logic ontologies. In: Marchiori M, Pan JZ, Marie C (eds) Proceedings of the 1st international conference on web reasoning and rule systems (RR), pp 194–208

  34. Lopatenko A, Bertossi LE (2007) Complexity of consistent query answering in databases under cardinality-based and incremental repair semantics. In: Schwentick T, Suciu D (eds) Proceedings of the 11th international conference on database theory (ICDT), pp 179–193

  35. Ma L, Yang Y, Qiu Z, Xie G, Pan Y, Liu S (2006) Towards a complete OWL ontology benchmark. In: Sure Y, Domingue J (eds) Proceedings of the 3rd European semantic web conference (ESWC), pp 125–139

  36. Ma Y, Hitzler P, Lin Z (2007) Algorithms for paraconsistent reasoning with OWL. In: Franconi E, Kifer M, May W (eds) Proceedings of the 4th European semantic web conference (ESWC), pp 399–413

  37. McDowell L, Cafarella MJ (2008) Ontology-driven, unsupervised instance population. J Web Semant 6(3): 218–236

    Article  Google Scholar 

  38. Meyer T, Lee K, Booth R (2005) Knowledge integration for description logics. In: Veloso M, Kambhampati S (eds) Proceedings of the 20th national conference on artificial intelligence (AAAI), pp 645–650

  39. Odintsov SP, Wansing H (2003) Inconsistency-tolerant description logic: motivation and basic systems. Kluwer, Dordrecht, pp 301–335

    Google Scholar 

  40. Patel-Schneider PF, Hayes P, Horrocks I (eds) (2004) OWL web ontology language semantics and abstract syntax. W3C recommendation. http://www.w3.org/TR/owl-semantics/

  41. Popov B, Kiryakov A, Kirilov A, Manov D, Ognyanoff D, Goranov M (2003) Kim—semantic annotation platform. In: Fensel D, Sycara KP, Mylopoulos J (eds) Proceedings of the 2nd international semantic web conference (ISWC), pp 834–849

  42. Qi G, Ji Q, Pan JZ, Du J (2011) Extending description logics with uncertainty reasoning in possibilistic logic. Int J Intell Syst 26(4): 353–381

    Article  MATH  Google Scholar 

  43. Qi G, Liu W, Bell D (2006) A revision-based approach to handling inconsistency in description logics. Artif Intell Rev 26(1–2): 115–128

    Article  Google Scholar 

  44. Rao AS, Foo NY (1989) Minimal change and maximal coherence: a basis for belief revision and reasoning about actions. In: Sridharan NS (eds) Proceedings of the 11th international joint conference on artificial intelligence (IJCAI), pp 966–971

  45. Sattler K, Geist I, Schallehn E (2005) Concept-based querying in mediator systems. VLDB J 14(1): 97–111

    Article  Google Scholar 

  46. Shadbolt N, Berners-Lee T, Hall W (2006) The semantic web revisited. IEEE Intell Syst 21(3): 96–101

    Article  Google Scholar 

  47. Shchekotykhin K, Jannach D, Friedrich G (2010) xCrawl: a high-recall crawling method for web mining. Knowl Inf Syst 25(2): 303–326

    Article  Google Scholar 

  48. Sheini HM, Sakallah KA (2006) Pueblo: a hybrid pseudo-boolean SAT solver. J Satisf Boolean Model Comput 2: 157–181

    Google Scholar 

  49. Song M, Rudniy A (2010) Detecting duplicate biological entities using Markov random field-based edit distance. Knowl Inf Syst 25(2): 371–387

    Article  Google Scholar 

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Correspondence to Jianfeng Du.

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Du, J., Qi, G. & Shen, YD. Weight-based consistent query answering over inconsistent \({\mathcal {SHIQ}}\) knowledge bases. Knowl Inf Syst 34, 335–371 (2013). https://doi.org/10.1007/s10115-012-0478-9

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  • DOI: https://doi.org/10.1007/s10115-012-0478-9

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