Papers
Topics
Authors
Recent
Search
2000 character limit reached

Exploiting Uncertainty for Querying Inconsistent Description Logics Knowledge Bases

Published 15 Jun 2023 in cs.AI and cs.LO | (2306.09138v6)

Abstract: The necessity to manage inconsistency in Description Logics Knowledge Bases (KBs) has come to the fore with the increasing importance gained by the Semantic Web, where information comes from different sources that constantly change their content and may contain contradictory descriptions when considered either alone or together. Classical reasoning algorithms do not handle inconsistent KBs, forcing the debugging of the KB in order to remove the inconsistency. In this paper, we exploit an existing probabilistic semantics called DISPONTE to overcome this problem and allow queries also in case of inconsistent KBs. We implemented our approach in the reasoners TRILL and BUNDLE and empirically tested the validity of our proposal. Moreover, we formally compare the presented approach to that of the repair semantics, one of the most established semantics when considering DL reasoning tasks.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (84)
  1. Efficient MUS enumeration of horn formulae with applications to axiom pinpointing. In Marijn Heule and Sean A. Weaver, editors, SAT 2015, volume 9340 of LNCS, pages 324–342. Springer, 2015. doi:10.1007/978-3-319-24318-4_24.
  2. Inconsistency-tolerant querying of description logic knowledge bases. In Jeff Z. Pan, Diego Calvanese, Thomas Eiter, Ian Horrocks, Michael Kifer, Fangzhen Lin, and Yuting Zhao, editors, RW 2016, volume 9885 of LNCS, pages 156–202. Springer, 2016. doi:10.1007/978-3-319-49493-7_5.
  3. Querying inconsistent prioritized data with ORBITS: algorithms, implementation, and experiments. In Gabriele Kern-Isberner, Gerhard Lakemeyer, and Thomas Meyer, editors, KR-2022, 2022. URL: https://proceedings.kr.org/2022/54/.
  4. Querying inconsistent description logic knowledge bases under preferred repair semantics. In Carla E. Brodley and Peter Stone, editors, AAAI-2014, pages 996–1002. AAAI Press, 2014. URL: http://www.aaai.org/ocs/index.php/AAAI/AAAI14/paper/view/8231.
  5. Computing and Explaining Query Answers over Inconsistent DL-Lite Knowledge Bases. J. Artif. Intell. Res., 64:563–644, 2019. doi:10.1613/jair.1.11395.
  6. Nuel D Belnap. How a computer should think. In New Essays on Belnap-Dunn Logic, pages 35–53. Springer, 2019.
  7. Belief based on inconsistent information. In Manuel A. Martins and Igor Sedlár, editors, DaLí 2020, volume 12569 of LNCS, pages 68–86. Springer, 2020. doi:10.1007/978-3-030-65840-3_5.
  8. Relative inconsistency measures. Artif. Intell., 280:103231, 2020. doi:10.1016/j.artint.2019.103231.
  9. Classifying inconsistency measures using graphs. J. Artif. Intell. Res., 66:937–987, 2019. doi:10.1613/jair.1.11852.
  10. Description logics. In Frank van Harmelen, Vladimir Lifschitz, and Bruce Porter, editors, Handbook of Knowledge Representation, chapter 3, pages 135–179. Elsevier Amsterdam, 2008.
  11. Handling conflicts in uncertain ontologies using deductive argumentation. In Amit P. Sheth, Axel Ngonga, Yin Wang, Elizabeth Chang, Dominik Slezak, Bogdan Franczyk, Rainer Alt, Xiaohui Tao, and Rainer Unland, editors, Proceedings of the International Conference on Web Intelligence, Leipzig, Germany, August 23-26, 2017, pages 65–72. ACM Press, 2017. doi:10.1145/3106426.3106454.
  12. Computing optimal repairs of quantified ABoxes wrt static EL TBoxes. In CADE 2021, 2021.
  13. F. Baader and R. Peñaloza. Automata-based axiom pinpointing. J. Autom. Reasoning, 45(2):91–129, 2010.
  14. F. Baader and R. Peñaloza. Axiom pinpointing in general tableaux. J. Logic Comput., 20(1):5–34, 2010.
  15. Tractable approximations of consistent query answering for robust ontology-based data access. In Francesca Rossi, editor, IJCAI 2013, pages 775–781. AAAI Press/IJCAI, 2013. URL: http://www.aaai.org/ocs/index.php/IJCAI/IJCAI13/paper/view/6904.
  16. On probabilistic inference by weighted model counting. Artif. Intell., 172(6-7):772–799, 2008.
  17. A tutorial on query answering and reasoning over probabilistic knowledge bases. In Claudia d’Amato and Martin Theobald, editors, RW 2018, volume 11078 of LNCS, pages 35–77. Springer, 2018. doi:10.1007/978-3-030-00338-8_3.
  18. Complexity results for probabilistic datalog±plus-or-minus{}^{\mbox{{$\pm$}}}start_FLOATSUPERSCRIPT ± end_FLOATSUPERSCRIPT. In Gal A. Kaminka, Maria Fox, Paolo Bouquet, Eyke Hüllermeier, Virginia Dignum, Frank Dignum, and Frank van Harmelen, editors, ECAI 2016, volume 285 of Frontiers in Artificial Intelligence and Applications, pages 1414–1422. IOS Press, 2016. doi:10.3233/978-1-61499-672-9-1414.
  19. The bayesian ontology reasoner is born! In Michel Dumontier, Birte Glimm, Rafael S. Gonçalves, Matthew Horridge, Ernesto Jiménez-Ruiz, Nicolas Matentzoglu, Bijan Parsia, Giorgos B. Stamou, and Giorgos Stoilos, editors, ORE-2015, volume 1387 of CEUR-WS, pages 8–14. CEUR-WS.org, 2015.
  20. Bayesian description logics. In Meghyn Bienvenu, Magdalena Ortiz, Riccardo Rosati, and Mantas Simkus, editors, DL 2014, volume 1193 of CEUR-WS, pages 447–458, Aachen, 2014. Sun SITE Central Europe.
  21. Probabilistic query answering in the bayesian description logic BEl. In Christoph Beierle and Alex Dekhtyar, editors, SUM 2015, volume 9310 of LNCS, pages 21–35. Springer, 2015.
  22. The bayesian ontology language ℬ⁢ℰ⁢ℒℬℰℒ\mathcal{BEL}caligraphic_B caligraphic_E caligraphic_L. J. Autom. Reasoning, 58(1):67–95, 2017. URL: https://doi.org/10.1007/s10817-016-9386-0, doi:10.1007/S10817-016-9386-0.
  23. A modular inference system for probabilistic description logics. In Davide Ciucci, Gabriella Pasi, and Barbara Vantaggi, editors, SUM 2018, volume 11142 of LNCS, pages 78–92, Heidelberg, Germany, 2018. Springer. URL: http://mcs.unife.it/~friguzzi/Papers/CotRigZes-SUM18.pdf, doi:10.1007/978-3-030-00461-3_6.
  24. Learning probabilistic ontologies with distributed parameter learning. In Elena Bellodi and Alessio Bonfietti, editors, AI*IA DC-2015, volume 1485 of CEUR Workshop Proceedings, pages 7–12, Aachen, Germany, 2015.
  25. Distributed parameter learning for probabilistic ontologies. In Katsumi Inoue, Hayato Ohwada, and Akihiro Yamamoto, editors, 25th International Conference on Inductive Logic Programming, 2015.
  26. ProbLog: A probabilistic Prolog and its application in link discovery. In Manuela M. Veloso, editor, IJCAI 2007, volume 7, pages 2462–2467. AAAI Press, 2007.
  27. Towards tractable and practical abox abduction over inconsistent description logic ontologies. In Blai Bonet and Sven Koenig, editors, AAAI 2015, pages 1489–1495. AAAI Press, 2015. URL: http://www.aaai.org/ocs/index.php/AAAI/AAAI15/paper/view/9389.
  28. Generalized consistent query answering under existential rules. In KR-2016, KR’16, pages 359–368, 2016. doi:10.5555/3032027.3032070.
  29. ACQUA: approximate consistent query answering over inconsistent knowledge bases. In 2nd IEEE International Conference on Artificial Intelligence and Knowledge Engineering, AIKE 2019, Sardinia, Italy, June 3-5, 2019, pages 107–110. IEEE Press, 2019. doi:10.1109/AIKE.2019.00027.
  30. Reasoning with inconsistent ontologies. Tsinghua Science and Technology, 15(6):687–691, 2010.
  31. Reasoning with inconsistent ontologies through argumentation. Appl. Artif. Intell., 24(1&2):102–148, 2010. doi:10.1080/08839510903448692.
  32. Measuring the good and the bad in inconsistent information. In Toby Walsh, editor, IJCAI-2011, pages 2632–2637. AAAI Press/IJCAI, 2011. URL: https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-438.
  33. Distance-based measures of inconsistency. In Linda C. van der Gaag, editor, ECSQARU 2013, volume 7958 of LNCS, pages 230–241. Springer, 2013. doi:10.1007/978-3-642-39091-3_20.
  34. LUBM: A benchmark for OWL knowledge base systems. J. Web Semant., 3(2-3):158–182, 2005. doi:10.1016/j.websem.2005.06.005.
  35. John Grant. Classifications for inconsistent theories. Notre Dame J. Formal Log., 19(3):435–444, 1978. doi:10.1305/ndjfl/1093888404.
  36. Measuring inconsistency through minimal inconsistent sets. In Gerhard Brewka and Jérôme Lang, editors, KR-2008, pages 358–366. AAAI Press, 2008. URL: http://www.aaai.org/Library/KR/2008/kr08-035.php.
  37. The even more irresistible SROIQ. In Patrick Doherty, John Mylopoulos, and Christopher A. Welty, editors, KR-2006, pages 57–67. AAAI Press, 2006. URL: http://dl.acm.org/citation.cfm?id=3029947.3029959.
  38. A tableau decision procedure for 𝒮⁢ℋ⁢𝒪⁢ℐ⁢𝒬𝒮ℋ𝒪ℐ𝒬\mathcal{SHOIQ}caligraphic_S caligraphic_H caligraphic_O caligraphic_I caligraphic_Q. J. Autom. Reasoning, 39(3):249–276, 2007.
  39. Extending tableau tracing for ABox updates. Technical report, University of Maryland, 2006.
  40. Aditya Kalyanpur. Debugging and Repair of OWL Ontologies. PhD thesis, The Graduate School of the University of Maryland, 2006.
  41. On the implementation of the probabilistic logic programming language ProbLog. Theor. Pract. Log. Prog., 11(2-3):235–262, 2011.
  42. Quantifying information and contradiction in propositional logic through test actions. In Georg Gottlob and Toby Walsh, editors, IJCAI-2003, pages 106–111. Morgan Kaufmann, 2003. URL: http://ijcai.org/Proceedings/03/Papers/015.pdf.
  43. Conditioning probabilistic databases. Proc. VLDB Endow., 1(1):313–325, 2008. URL: http://www.vldb.org/pvldb/vol1/1453894.pdf, doi:10.14778/1453856.1453894.
  44. Finding all justifications of owl dl entailments. In K. Aberer, K. Choi, N. Fridman Noy, D. Allemang, K. Lee, L. J. B. Nixon, J. Golbeck, P. Mika, D. Maynard, R. Mizoguchi, G. Schreiber, and P. Cudré-Mauroux, editors, The Semantic Web, 6th International Semantic Web Conference, 2nd Asian Semantic Web Conference, ISWC 2007 + ASWC 2007, Busan, Korea, November 11-15, 2007, volume 4825 of Lecture Notes in Computer Science (LNCS), pages 267–280, Berlin, 2007. Springer.
  45. Efficient knowledge compilation beyond weighted model counting. Theor. Pract. Log. Prog., 22(4):505–522, 2022. doi:10.1017/S147106842200014X.
  46. Inconsistency-tolerant semantics for description logics. In Pascal Hitzler and Thomas Lukasiewicz, editors, RR 2010, volume 6333 of LNCS, pages 103–117. Springer, 2010. doi:10.1007/978-3-642-15918-3_9.
  47. Error-tolerant reasoning in the description logic ℰ⁢ℒℰℒ\mathcal{EL}caligraphic_E caligraphic_L. In Eduardo Fermé and João Leite, editors, JELIA 2014, volume 8761 of LNCS, pages 107–121. Springer, 2014. doi:10.1007/978-3-319-11558-0_8.
  48. Thomas Lukasiewicz. Probabilistic deduction with conditional constraints over basic events. J. Artif. Intell. Res., 10:199–241, 1999. doi:10.1613/jair.577.
  49. Paraconsistent reasoning for expressive and tractable description logics. In Franz Baader, Carsten Lutz, and Boris Motik, editors, DL-2008, volume 353 of CEUR-WS. CEUR-WS.org, 2008. URL: http://ceur-ws.org/Vol-353/MaHitzlerLin.pdf.
  50. N. J. Nilsson. Probabilistic logic. Artif. Intell., 28(1):71–87, 1986.
  51. Graham Priest. The logic of paradox. J. Philos. Logic, 8(1):219–241, 1979. doi:10.1007/BF00258428.
  52. Axiom pinpointing is hard. In Bernardo Cuenca Grau, Ian Horrocks, Boris Motik, and Ulrike Sattler, editors, DL 2009, volume 477 of CEUR-WS. CEUR-WS.org, 2009. URL: http://ceur-ws.org/Vol-477/paper_39.pdf.
  53. Complexity of axiom pinpointing in the dl-lite family. In Volker Haarslev, David Toman, and Grant E. Weddell, editors, DL 2010, volume 573 of CEUR-WS. CEUR-WS.org, 2010. URL: http://ceur-ws.org/Vol-573/paper_24.pdf.
  54. Complexity of axiom pinpointing in the dl-lite family of description logics. In Helder Coelho, Rudi Studer, and Michael J. Wooldridge, editors, ECAI-2010, volume 215 of FRONTIERS, pages 29–34. IOS Press, 2010. URL: http://www.booksonline.iospress.nl/Content/View.aspx?piid=17709.
  55. Inconsistency-tolerant reasoning over linear probabilistic knowledge bases. Int. J. Approx. Reason., 88:209–236, 2017. doi:10.1016/j.ijar.2017.06.002.
  56. Reasoning with uncertain and inconsistent OWL ontologies. In Thomas Eiter and Thomas Krennwallner, editors, RW 2012, volume 7487 of LNCS, pages 211–244. Springer, 2012. doi:10.1007/978-3-642-33158-9_6.
  57. Extending description logics with uncertainty reasoning in possibilistic logic. Int. J. Intell. Syst., 26(4):353–381, 2011. doi:10.1002/int.20470.
  58. Learning probabilistic description logics. In Fernando Bobillo, Rommel N. Carvalho, Paulo C.G. Costa, Claudia d’Amato, Nicola Fanizzi, Kathryn B. Laskey, Kenneth J. Laskey, Thomas Lukasiewicz, Matthias Nickles, and Michael Pool, editors, Uncertainty Reasoning for the Semantic Web III, volume 8816 of LNCS, pages 63–78. Springer, Berlin, Heidelberg, 2014. doi:10.1007/978-3-319-13413-0_4.
  59. Parameter Learning for Probabilistic Ontologies. In Wolfgang Faber and Domenico Lembo, editors, RR 2013, volume 7994 of LNCS, pages 265–270. Springer, 2013. doi:10.1007/978-3-642-39666-3_26.
  60. Probabilistic description logics under the distribution semantics. Semant. Web, 6(5):447–501, 2015. doi:10.3233/SW-140154.
  61. A practical comparison of methods to assess sum-of-products. Reliability Engineering and System Safety, 79(1):33–42, 2003.
  62. Fabrizio Riguzzi. A top down interpreter for LPAD and CP-logic. In AI*IA-2007, volume 4733 of LNAI, pages 109–120. Springer, 2007. doi:10.1007/978-3-540-74782-6_11.
  63. Fabrizio Riguzzi. Extended semantics and inference for the independent choice logic. Logic Journal of the IGPL, 17(6):589–629, 2009. doi:10.1093/jigpal/jzp025.
  64. BUNDLE: A reasoner for probabilistic ontologies. In Wolfgang Faber and Domenico Lembo, editors, RR 2013, volume 7994 of LNCS, pages 183–197. Springer, 2013. doi:10.1007/978-3-642-39666-3_14.
  65. Tabling and answer subsumption for reasoning on logic programs with annotated disjunctions. In ICLP TC 2010, volume 7 of LIPIcs, pages 162–171. Schloss Dagstuhl, 2010. doi:10.4230/LIPIcs.ICLP.2010.162.
  66. The PITA system: Tabling and answer subsumption for reasoning under uncertainty. Theor. Pract. Log. Prog., 11(4–5):433–449, 2011. doi:10.1017/S147106841100010X.
  67. Taisuke Sato. A statistical learning method for logic programs with distribution semantics. In Leon Sterling, editor, ICLP 1995, pages 715–729. MIT Press, 1995. doi:10.7551/mitpress/4298.003.0069.
  68. Performing bayesian inference by weighted model counting. In AAAI-2005, pages 475–482, Palo Alto, California USA, 2005. AAAI Press.
  69. S. Schlobach and R. Cornet. Non-standard reasoning services for the debugging of description logic terminologies. In G. Gottlob and T. Walsh, editors, IJCAI-03, Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence, Acapulco, Mexico, August 9-15, 2003, pages 355–362, San Francisco, CA, USA, 2003. Morgan Kaufmann Publishers Inc.
  70. HermiT: A highly-efficient OWL reasoner. In Catherine Dolbear, Alan Ruttenberg, and Ulrike Sattler, editors, OWLED-2008, volume 432 of CEUR-WS, pages 1–10. Sun SITE Central Europe, 2008.
  71. Pellet: A practical OWL-DL reasoner. J. Web Semant., 5(2):51–53, 2007.
  72. A modularization-based approach to finding all justifications for OWL DL entailments. In John Domingue and Chutiporn Anutariya, editors, ASWC-2008, volume 5367 of LNCS, pages 1–15. Springer, 2008. doi:10.1007/978-3-540-89704-0_1.
  73. Axiom pinpointing in lightweight description logics via horn-sat encoding and conflict analysis. In Renate A. Schmidt, editor, CADE 2009, volume 5663 of LNCS, pages 84–99. Springer, 2009. doi:10.1007/978-3-642-02959-2_6.
  74. Confidences for commonsense reasoning. In André Platzer and Geoff Sutcliffe, editors, CADE 2021, volume 12699 of Lecture Notes in Computer Science, pages 507–524. Springer, 2021. doi:10.1007/978-3-030-79876-5_29.
  75. FaCT++ description logic reasoner: System description. In Ulrich Furbach and Natarajan Shankar, editors, IJCAR-2006, volume 4130 of LNCS, pages 292–297. Springer, 2006. doi:10.1007/11814771_26.
  76. Matthias Thimm. On the evaluation of inconsistency measures. Measuring inconsistency in information, 73:19–60, 2018.
  77. Seinosuke Toda. On the computational power of PP and +p. In 30th Annual Symposium on Foundations of Computer Science, Research Triangle Park, North Carolina, USA, 30 October - 1 November 1989, pages 514–519. IEEE, 1989. doi:10.1109/SFCS.1989.63527.
  78. Leslie G. Valiant. The complexity of enumeration and reliability problems. SIAM J. Comput., 8(3):410–421, 1979.
  79. Inconsistency measurement based on variables in minimal unsatisfiable subsets. In Luc De Raedt, Christian Bessiere, Didier Dubois, Patrick Doherty, Paolo Frasconi, Fredrik Heintz, and Peter J. F. Lucas, editors, ECAI-2012, volume 242 of FRONTIERS, pages 864–869. IOS Press, 2012. doi:10.3233/978-1-61499-098-7-864.
  80. Tableau reasoning for description logics and its extension to probabilities. Ann. Math. Artif. Intell., 82(1–3):101–130, 2018. doi:10.1007/s10472-016-9529-3.
  81. Optimizing a tableau reasoner and its implementation in prolog. J. Web Semant., 71:100677, 2021. doi:10.1016/j.websem.2021.100677.
  82. Probabilistic DL reasoning with pinpointing formulas: A prolog-based approach. Theor. Pract. Log. Prog., 19(3):449–476, 2019. doi:10.1017/S1471068418000480.
  83. Riccardo Zese. Probabilistic Semantic Web: Reasoning and Learning, volume 28 of Studies on the Semantic Web. IOS Press, Amsterdam, 2017. URL: http://ebooks.iospress.nl/volume/probabilistic-semantic-web-reasoning-and-learning, doi:10.3233/978-1-61499-734-4-i.
  84. Inconsistency- with OWL DL. Int. J. Approx. Reason., 55(2):557–584, 2014. doi:10.1016/j.ijar.2013.09.005.

Summary

No one has generated a summary of this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Sign Up to Summarize

Paper to Video (Beta)

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

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

Continue Learning

We haven't generated follow-up questions for this paper yet.

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

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up