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Inseparability and Conservative Extensions of Description Logic Ontologies: A Survey

  • Elena Botoeva
  • Boris Konev
  • Carsten Lutz
  • Vladislav Ryzhikov
  • Frank WolterEmail author
  • Michael Zakharyaschev
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9885)

Abstract

The question whether an ontology can safely be replaced by another, possibly simpler, one is fundamental for many ontology engineering and maintenance tasks. It underpins, for example, ontology versioning, ontology modularization, forgetting, and knowledge exchange. What ‘safe replacement’ means depends on the intended application of the ontology. If, for example, it is used to query data, then the answers to any relevant ontology-mediated query should be the same over any relevant data set; if, in contrast, the ontology is used for conceptual reasoning, then the entailed subsumptions between concept expressions should coincide. This gives rise to different notions of ontology inseparability such as query inseparability and concept inseparability, which generalize corresponding notions of conservative extensions. In this chapter, we survey results on various notions of inseparability in the context of description logic ontologies, discussing their applications, useful model-theoretic characterizations, algorithms for determining whether two ontologies are inseparable (and, sometimes, for computing the difference between them if they are not), and the computational complexity of this problem.

Notes

Acknowledgments

Elena Botoeva was supported by EU IP project Optique, grant n. FP7-318338. Carsten Lutz was supported by ERC grant 647289. Boris Konev, Frank Wolter and Michael Zakharyaschev were supported by the UK EPSRC grants EP/M012646, EP/M012670, EP/H043594, and EP/H05099X.

References

  1. 1.
    Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P.F., et al. (eds.): The Description Logic Handbook Theory Implementation and Applications. Cambridge University Press, Cambridge (2003)zbMATHGoogle Scholar
  2. 2.
    Baader, F., Brandt, S., Lutz, C.: Pushing the EL envelope. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI 2005), pp. 364–369 (2005)Google Scholar
  3. 3.
    Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Tractable reasoning and efficient query answering in description logics: the DL-Lite family. J. Autom. Reason. 39(3), 385–429 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Artale, A., Calvanese, D., Kontchakov, R., Zakharyaschev, M.: The DL-Lite family and relations. J. Artif. Intell. Res. (JAIR) 36, 1–69 (2009)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Hustadt, U., Motik, B., Sattler, U.: Reasoning in description logics by a reduction to disjunctive Datalog. J. Autom. Reason. 39(3), 351–384 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Kazakov, Y.: Consequence-driven reasoning for Horn-SHIQ ontologies. In: Proceedings of the 21st International Joint Conference on Artificial Intelligence (IJCAI 2009), pp. 2040–2045 (2009)Google Scholar
  7. 7.
    Glimm, B., Lutz, C., Horrocks, I., Sattler, U.: Answering conjunctive queries in the \(\cal{SHIQ}\) description logic. J. Artif. Intell. Res. (JAIR) 31, 150–197 (2008)zbMATHGoogle Scholar
  8. 8.
    Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Data complexity of query answering in description logics. In: Proceedings of the 10th International Conference on the Principles of Knowledge Representation and Reasoning (KR 2006), pp. 260–270 (2006)Google Scholar
  9. 9.
    Calvanese, D., Eiter, T., Ortiz, M.: Answering regular path queries in expressive description logics: an automata-theoretic approach. In: Proceedings of the 22nd National Conference on Artificial Intelligence (AAAI 2007), pp. 391–396 (2007)Google Scholar
  10. 10.
    Konev, B., Lutz, C., Walther, D., Wolter, F.: Formal properties of modularisation. In: Stuckenschmidt et al. [21], pp. 25–66. http://dx.doi.org/10.1007/978-3-642-01907-4_3
  11. 11.
    Konev, B., Ludwig, M., Walther, D., Wolter, F.: The logical difference for the lightweight description logic EL. J. Artif. Intell. Res. (JAIR) 44, 633–708 (2012)zbMATHGoogle Scholar
  12. 12.
    Conradi, R., Westfechtel, B.: Version models for software configuration management. ACM Comput. Surv. (CSUR) 30(2), 232–282 (1998)CrossRefGoogle Scholar
  13. 13.
    Noy, N.F., Musen, M.A.: PromptDiff: a fixed-point algorithm for comparing ontology versions. In: Proceedings of the 18th National Conference on Artificial Intelligence (AAAI 2002), pp. 744–750. AAAI Press, Menlo Park (2002)Google Scholar
  14. 14.
    Klein, M., Fensel, D., Kiryakov, A., Ognyanov, D.: Ontology versioning and change detection on the web. In: Gómez-Pérez, A., Benjamins, V.R. (eds.) EKAW 2002. LNCS (LNAI), vol. 2473, pp. 197–212. Springer, Heidelberg (2002). doi: 10.1007/3-540-45810-7_20 CrossRefGoogle Scholar
  15. 15.
    Redmond, T., Smith, M., Drummond, N., Tudorache, T.: Managing change: an ontology version control system. In: Proceedings of the 5th International Workshop on OWL: Experiences and Directions (OWLED 2008). CEUR Workshop Proceedings, vol. 432, CEUR-WS.org (2008)Google Scholar
  16. 16.
    Jimenez-Ruiz, E., Cuenca Grau, B., Horrocks, I., Llavori, R.B.: Supporting concurrent ontology development: framework, algorithms and tool. Data Knowl. Eng. 70(1), 146–164 (2011)CrossRefGoogle Scholar
  17. 17.
    Konev, B., Walther, D., Wolter, F.: The logical difference problem for description logic terminologies. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 259–274. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-71070-7_21 CrossRefGoogle Scholar
  18. 18.
    Kontchakov, R., Wolter, F., Zakharyaschev, M.: Can you tell the difference between DL-Lite ontologies. In: Proceedings of the 11th International Conference on the Principles of Knowledge Representation and Reasoning (KR 2008), pp. 285–295 (2008)Google Scholar
  19. 19.
    Ghilardi, S., Lutz, C., Wolter, F.: Did I damage my ontology? A case for conservative extensions in description logic. In: Proceedings of the 10th International Conference on the Principles of Knowledge Representation and Reasoning (KR 2006), pp. 187–197. AAAI Press (2006)Google Scholar
  20. 20.
    Cuenca-Grau, B., Horrocks, I., Kazakov, Y., Sattler, U.: Modular reuse of ontologies: theory and practice. J. Artif. Intell. Res. (JAIR) 31, 273–318 (2008)MathSciNetzbMATHGoogle Scholar
  21. 21.
    Stuckenschmidt, H., Parent, C., Spaccapietra, S. (eds.): Modular Ontologies: Concepts, Theories and Techniques for Knowledge Modularization. LNCS, vol. 5445. Springer, Heidelberg (2009)zbMATHGoogle Scholar
  22. 22.
    Kutz, O., Mossakowski, T., Lücke, D.: Carnap, Goguen, and the hyperontologies: logical pluralism and heterogeneous structuring in ontology design. Log. Univers. 4(2), 255–333 (2010). doi: 10.1007/s11787-010-0020-3 MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Kontchakov, R., Wolter, F., Zakharyaschev, M.: Logic-based ontology comparison and module extraction, with an application to DL-Lite. Artif. Intell. 174, 1093–1141 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Shvaiko, P., Euzenat, J.: Ontology matching: state of the art and future challenges. IEEE Trans. Knowl. Data Eng. 25(1), 158–176 (2013). doi: 10.1109/TKDE.2011.253 CrossRefGoogle Scholar
  25. 25.
    Solimando, A., Jiménez-Ruiz, E., Guerrini, G.: Detecting and correcting conservativity principle violations in ontology-to-ontology mappings. In: Mika, P., et al. (eds.) ISWC 2014. LNCS, vol. 8797, pp. 1–16. Springer, Heidelberg (2014). doi: 10.1007/978-3-319-11915-1_1 Google Scholar
  26. 26.
    Kharlamov, E., et al.: Ontology based access to exploration data at Statoil. In: Arenas, M., et al. (eds.) ISWC 2015. LNCS, vol. 9367, pp. 93–112. Springer, Heidelberg (2015). doi: 10.1007/978-3-319-25010-6_6 CrossRefGoogle Scholar
  27. 27.
    Jiménez-Ruiz, E., Payne, T.R., Solimando, A., Tamma, V.A.M.: Limiting logical violations in ontology alignnment through negotiation. In: Proceedings of the 15th International Conference on the Principles of Knowledge Representation and Reasoning (KR 2016), pp. 217–226 (2016)Google Scholar
  28. 28.
    Fagin, R., Kolaitis, P.G., Miller, R.J., Popa, L.: Data exchange: semantics and query answering. Theor. Comput. Sci. 336(1), 89–124 (2005). doi: 10.1016/j.tcs.2004.10.033 MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Arenas, M., Botoeva, E., Calvanese, D., Ryzhikov, V.: Knowledge base exchange: the case of OWL 2 QL. Artif. Intell. 238, 11–62 (2016). ISSN 0004-3702MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Cuenca-Grau, B., Motik, B.: Reasoning over ontologies with hidden content: the import-by-query approach. J. Artif. Intell. Res. (JAIR) 45, 197–255 (2012)MathSciNetzbMATHGoogle Scholar
  31. 31.
    Reiter, R., Lin, F.: Forget it! In: Proceedings of AAAI Fall Symposium on Relevance, pp. 154–159 (1994)Google Scholar
  32. 32.
    Pitts, A.: On an interpretation of second-order quantification in first-order intuitionistic propositional logic. J. Symb. Logic 57, 33–52 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    D’Agostino, G., Hollenberg, M.: Uniform interpolation, automata, and the modal \(\mu \)-calculus. In: Advances in Modal Logic, vol. 1 (1998)Google Scholar
  34. 34.
    Visser, A.: Uniform interpolation and layered bisimulation. In: Hájek, P. (ed.) Gödel ’96 (Brno, 1996). Lecture Notes Logic, vol. 6. Springer, Berlin (1996)Google Scholar
  35. 35.
    Ghilardi, S., Zawadowski, M.: Undefinability of propositional quantifiers in the modal system S4. Stud. Logica 55, 259–271 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    French, T.: Bisimulation quantifiers for modal logics. Ph.D. thesis, University of Western Australia (2006)Google Scholar
  37. 37.
    Su, K., Sattar, A., Lv, G., Zhang, Y.: Variable forgetting in reasoning about knowledge. J. Artif. Intell. Res. (JAIR) 35, 677–716 (2009). doi: 10.1613/jair.2750 MathSciNetzbMATHGoogle Scholar
  38. 38.
    Konev, B., Walther, D., Wolter, F.: Forgetting and uniform interpolation in large-scale description logic terminologies. In: Proceedings of the 21st International Joint Conference on Artificial Intelligence (IJCAI 2009), pp. 830–835 (2009). http://ijcai.org/papers09/Papers/IJCAI09-142.pdf
  39. 39.
    Wang, Z., Wang, K., Topor, R.W., Pan, J.Z.: Forgetting for knowledge bases in DL-Lite. Ann. Math. Artif. Intell. 58(1–2), 117–151 (2010). doi: 10.1007/s10472-010-9187-9 MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Lutz, C., Wolter, F.: Foundations for uniform interpolation and forgetting in expressive description logics. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI 2011), pp. 989–995. IJCAI/AAAI (2011)Google Scholar
  41. 41.
    Wang, K., Wang, Z., Topor, R.W., Pan, J.Z., Antoniou, G.: Eliminating concepts and roles from ontologies in expressive descriptive logics. Comput. Intell. 30(2), 205–232 (2014). doi: 10.1111/j.1467-8640.2012.00442.x MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Koopmann, P., Schmidt, R.A.: Count and forget: uniform interpolation of \(\cal{SHQ}\)-ontologies. In: Demri, S., Kapur, D., Weidenbach, C. (eds.) IJCAR 2014. LNCS (LNAI), vol. 8562, pp. 434–448. Springer, Heidelberg (2014). doi: 10.1007/978-3-319-08587-6_34 Google Scholar
  43. 43.
    Nikitina, N., Rudolph, S.: (Non-)succinctness of uniform interpolants of general terminologies in the description logic EL. Artif. Intell. 215, 120–140 (2014). doi: 10.1016/j.artint.2014.06.005 MathSciNetCrossRefzbMATHGoogle Scholar
  44. 44.
    Koopmann, P., Schmidt, R.A.: Uniform interpolation and forgetting for \(\cal{ALC}\) ontologies with ABoxes. In: Proceedings of the 29th National Conference on Artificial Intelligence (AAAI 2015), pp. 175–181 (2015). http://www.aaai.org/ocs/index.php/AAAI/AAAI15/paper/view/9981
  45. 45.
    Goranko, V., Otto, M.: Model theory of modal logic. In: Blackburn, P., van Benthem, J., Wolter, F. (eds.) Handbook of Modal Logic, pp. 249–330. Elsevier, Amsterdam (2006)Google Scholar
  46. 46.
    Lutz, C., Piro, R., Wolter, F.: Description logic TBoxes: model-theoretic characterizations and rewritability. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI 2011), pp. 983–988. AAAI Press, Menlo Park (2011)Google Scholar
  47. 47.
    Lutz, C., Walther, D., Wolter, F.: Conservative extensions in expressive description logics. In: Proceedings of the 20th Internatioanl Joint Conference on Artificial Intelligence (IJCAI), pp. 453–458. AAAI Press, Menlo Park (2007)Google Scholar
  48. 48.
    Wilke, T.: Alternating tree automata, parity games, and modal \(\mu \)-calculus. Bull. Belgian Math. Soc. 8(2), 359–391 (2001)MathSciNetzbMATHGoogle Scholar
  49. 49.
    Konev, B., Lutz, C., Wolter, F., Zakharyaschev, M.: Conservative rewritability of description logic TBoxes. In: Proceedings of the 25th International Joint Conference on Artificial Intelligence (IJCAI 2016) (2016)Google Scholar
  50. 50.
    Horrocks, I., Sattler, U.: A description logic with transitive and inverse roles and role hierarchies. J. Log. Comput. 9(3), 385–410 (1999). doi: 10.1093/logcom/9.3.385 MathSciNetCrossRefzbMATHGoogle Scholar
  51. 51.
    Ghilardi, S., Lutz, C., Wolter, F., Zakharyaschev, M.: Conservative extensions in modal logics. In: Proceedings of the AiML, vol. 6, pp. 187–207 (2006)Google Scholar
  52. 52.
    Lutz, C., Wolter, F.: Deciding inseparability and conservative extensions in the description logic EL. J. Symb. Comput. 45(2), 194–228 (2010)CrossRefzbMATHGoogle Scholar
  53. 53.
    Lutz, C., Seylan, I., Wolter, F.: An automata-theoretic approach to uniform interpolation and approximation in the description logic EL. In: Proceedings of the 13th International Conference on the Principles of Knowledge Representation and Reasoning (KR 2012), pp. 286–296. AAAI Press (2012)Google Scholar
  54. 54.
    Nikitina, N., Rudolph, S.: ExpExpExplosion: uniform interpolation in general EL terminologies. In: Proceedings of the 20th European Conference on Artificial Intelligence (ECAI 2012), pp. 618–623 (2012). doi: 10.3233/978-1-61499-098-7-618
  55. 55.
    Clarke, E., Schlingloff, H.: Model checking. In: Handbook of Automated Reasoning, vol. II, chap. 24, pp. 1635–1790. Elsevier (2001)Google Scholar
  56. 56.
    Ludwig, M., Walther, D.: The logical difference for \(\cal{ELH}^r\)-terminologies using hypergraphs. In: Proceedings of the 21st European Conference on Artificial Intelligence (ECAI 2014). Frontiers in Artificial Intelligence and Applications, vol. 263, pp. 555–560. IOS Press (2014)Google Scholar
  57. 57.
    Feng, S., Ludwig, M., Walther, D.: Foundations for the logical difference of EL-TBoxes. In: Global Conference on Artificial Intelligence (GCAI 2015). EPiC Series in Computing, vol. 36, pp. 93–112. EasyChair (2015). ISSN 2040-557XGoogle Scholar
  58. 58.
    Byers, P., Pitt, D.: Conservative extensions: a cautionary note. EATCS-Bull. 41, 196–201 (1990)zbMATHGoogle Scholar
  59. 59.
    Veloso, P.: Yet another cautionary note on conservative extensions: a simple case with a computing flavour. EATCS-Bull. 46, 188–193 (1992)zbMATHGoogle Scholar
  60. 60.
    Veloso, P., Veloso, S.: Some remarks on conservative extensions. A socratic dialog. EATCS-Bull. 43, 189–198 (1991)zbMATHGoogle Scholar
  61. 61.
    Diaconescu, J.G.R., Stefaneas, P.: Logical support for modularisation. In: Huet, G., Plotkin, G. (eds.) Logical Environments (1993)Google Scholar
  62. 62.
    Maibaum, T.S.E.: Conservative extensions, interpretations between theories and all that!. In: Bidoit, M., Dauchet, M. (eds.) CAAP 1997. LNCS, vol. 1214, pp. 40–66. Springer, Heidelberg (1997). doi: 10.1007/BFb0030588 CrossRefGoogle Scholar
  63. 63.
    Konev, B., Lutz, C., Walther, D., Wolter, F.: Model-theoretic inseparability and modularity of description logic ontologies. Artif. Intell. 203, 66–103 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  64. 64.
    Berger, R.: The Undecidability of the Domino Problem. Memoirs of the AMS, issue 66. American Mathematical Society, Providence (1966)Google Scholar
  65. 65.
    Robinson, R.: Undecidability and nonperiodicity for tilings of the plane. Inventiones Math. 12, 177–209 (1971)MathSciNetCrossRefzbMATHGoogle Scholar
  66. 66.
    Börger, E., Grädel, E., Gurevich, Y.: The Classical Decision Problem. Perspectives in Mathematical Logic. Springer, Heidelberg (1997)CrossRefzbMATHGoogle Scholar
  67. 67.
    Feferman, S., Vaught, R.L.: The first-order properties of algebraic systems. Fundamenta Math. 47, 57–103 (1959)MathSciNetzbMATHGoogle Scholar
  68. 68.
    Bonatti, P., Faella, M., Lutz, C., Sauro, L., Wolter, F.: Decidability of circumscribed description logics revisited. In: Eiter, T., Strass, H., Truszczyński, M., Woltran, S. (eds.) Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation. LNCS (LNAI), vol. 9060, pp. 112–124. Springer, Heidelberg (2015). doi: 10.1007/978-3-319-14726-0_8 CrossRefGoogle Scholar
  69. 69.
    Maher, M.J.: Equivalences of logic programs. In: Foundations of Deductive Databases and Logic Programming, pp. 627–658. Morgan Kaufmann (1988)Google Scholar
  70. 70.
    Lifschitz, V., Pearce, D., Valverde, A.: Strongly equivalent logic programs. ACM Trans. Comput. Logic 2(4), 526–541 (2001). doi: 10.1145/502166.502170 MathSciNetCrossRefGoogle Scholar
  71. 71.
    Eiter, T., Fink, M.: Uniform equivalence of logic programs under the stable model semantics. In: Palamidessi, C. (ed.) ICLP 2003. LNCS, vol. 2916, pp. 224–238. Springer, Heidelberg (2003). doi: 10.1007/978-3-540-24599-5_16 CrossRefGoogle Scholar
  72. 72.
    Cuenca Grau, B., Horrocks, I., Kazakov, Y., Sattler, U.: Extracting modules from ontologies: a logic-based approach. In: Stuckenschmidt, H., Parent, C., Spaccapietra, S. (eds.) Modular Ontologies. LNCS, vol. 5445, pp. 159–186. Springer, Heidelberg (2009). doi: 10.1007/978-3-642-01907-4_8 CrossRefGoogle Scholar
  73. 73.
    Grau, B.C., Horrocks, I., Kazakov, Y., Sattler, U.: Just the right amount: extracting modules from ontologies. In: Proceedings of the 16th International World Wide Web Conference (WWW 2007), pp. 717–726. ACM (2007)Google Scholar
  74. 74.
    Grau, B.C., Horrocks, I., Kazakov, Y., Sattler, U.: A logical framework for modularity of ontologies. In: Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI 2007), pp. 298–303 (2007)Google Scholar
  75. 75.
    Sattler, U., Schneider, T., Zakharyaschev, M.: Which kind of module should I extract? In: Proceedings of the 22th International Workshop on Description Logics (DL 2009). CEUR Workshop Proceedings, vol. 477. CEUR-WS.org (2009)Google Scholar
  76. 76.
    Romero, A.A., Grau, B.C., Horrocks, I., Jiménez-Ruiz, E.: MORe: a modular OWL reasoner for ontology classification. In: ORE. CEUR Workshop Proceedings, vol. 1015, pp. 61–67. CEUR-WS.org (2013)Google Scholar
  77. 77.
    Romero, A.A., Grau, B.C., Horrocks, I.: Modular combination of reasoners for ontology classification. In: Proceedings of the 25th International Workshop on Description Logics (DL 2012). CEUR Workshop Proceedings, vol. 846. CEUR-WS.org (2012)Google Scholar
  78. 78.
    Romero, A.A., Kaminski, M., Grau, B.C., Horrocks, I.: Module extraction in expressive ontology languages via Datalog reasoning. J. Artif. Intell. Res. (JAIR) 55, 499–564 (2016)MathSciNetzbMATHGoogle Scholar
  79. 79.
    Bienvenu, M., ten Cate, B., Lutz, C., Wolter, F.: Ontology-based data access a study through Disjunctive Datalog, CSP, and MMSNP. ACM Trans. Database Syst. 39(4), 33:1–33:44 (2014)MathSciNetCrossRefGoogle Scholar
  80. 80.
    Poggi, A., Lembo, D., Calvanese, D., De Giacomo, G., Lenzerini, M., Rosati, R.: Linking data to ontologies. J. Data Semant. 10, 133–173 (2008)zbMATHGoogle Scholar
  81. 81.
    Botoeva, E., Kontchakov, R., Ryzhikov, V., Wolter, F., Zakharyaschev, M.: Games for query inseparability of description logic knowledge bases. Artif. Intell. 234, 78–119 (2016). doi: 10.1016/j.artint.2016.01.010. http://www.sciencedirect.com/science/article/pii/S0004370216300017, ISSN 0004-3702MathSciNetCrossRefzbMATHGoogle Scholar
  82. 82.
    Lutz, C., Wolter, F.: Non-uniform data complexity of query answering in description logics. In: Proceedings of KR. AAAI Press (2012)Google Scholar
  83. 83.
    Chang, C.C., Keisler, H.J.: Model Theory. Studies in Logic and the Foundations of Mathematics, vol. 73. Elsevier, Amsterdam (1990)Google Scholar
  84. 84.
    Botoeva, E., Lutz, C., Ryzhikov, V., Wolter, F., Zakharyaschev, M.: Query-based entailment and inseparability for ALC ontologies (Full Version). CoRR Technical report abs/1604.04164, arXiv.org e-Print archive (2016). http://arxiv.org/abs/1604.04164
  85. 85.
    Botoeva, E., Lutz, C., Ryzhikov, V., Wolter, F., Zakharyaschev, M.: Query-based entailment and inseparability for ALC ontologies. In: Proceedings of the 25th International Joint Conference on Artificial Intelligence (IJCAI 2016), pp. 1001–1007 (2016)Google Scholar
  86. 86.
    Schaerf, A.: Query answering in concept-based knowledge representation systems: algorithms, complexity, and semantic issues. Ph.D. thesis, Dipartimento di Informatica e Sistemistica, Università di Roma La Sapienza (1994)Google Scholar
  87. 87.
    Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Boston (1995)zbMATHGoogle Scholar
  88. 88.
    Mazala, R.: Infinite games. In: Grädel, E., Thomas, W., Wilke, T. (eds.) Automata Logics, and Infinite Games. LNCS, vol. 2500, pp. 23–38. Springer, Heidelberg (2002). doi: 10.1007/3-540-36387-4_2 CrossRefGoogle Scholar
  89. 89.
    Chatterjee, K., Henzinger, M.: An O(\(n^2\)) time algorithm for alternating Büchi games. In: Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1386–1399. SIAM (2012)Google Scholar
  90. 90.
    Baader, F., Bienvenu, M., Lutz, C., Wolter, F.: Query and predicate emptiness in ontology-based data access. J. Artif. Intell. Res. (JAIR) 56, 1–59 (2016)MathSciNetzbMATHGoogle Scholar
  91. 91.
    Konev, B., Ludwig, M., Wolter, F.: Logical Difference Computation with CEX2.5. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS (LNAI), vol. 7364, pp. 371–377. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-31365-3_29 CrossRefGoogle Scholar
  92. 92.
    Bienvenu, M., Hansen, P., Lutz, C., Wolter, F.: First order-rewritability and containment of conjunctive queries in Horn description logics. In: Proceedings of the 25th International Joint Conference on Artificial Intelligence (IJCAI 2016), pp. 965–971 (2016)Google Scholar
  93. 93.
    Bienvenu, M., Rosati, R.: Query-based comparison of mappings in ontology-based data access. In: Proceedings of the 15th International Conference on the Principles of Knowledge Representation and Reasoning (KR 2016), pp. 197–206 (2016). http://www.aaai.org/ocs/index.php/KR/KR16/paper/view/12902
  94. 94.
    Arenas, M., Gottlob, G., Pieris, A.: Expressive languages for querying the semantic web. In: Proceedings of the 33rd ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, PODS 2014, Snowbird, UT, USA, 22–27 June 2014, pp. 14–26 (2014). doi: 10.1145/2594538.2594555
  95. 95.
    Fagin, R., Kolaitis, P.G., Nash, A., Popa, L.: Towards a theory of schema-mapping optimization. In: Proceedings of the 27th ACM SIGACT SIGMOD SIGART Symp. on Principles of Database Systems (PODS 2008), pp. 33–42 (2008). doi: 10.1145/1376916.1376922
  96. 96.
    Pichler, R., Sallinger, E., Savenkov, V.: Relaxed notions of schema mapping equivalence revisited. Theory Comput. Syst. 52(3), 483–541 (2013). doi: 10.1007/s00224-012-9397-0 MathSciNetCrossRefzbMATHGoogle Scholar
  97. 97.
    Konev, B., Kontchakov, R., Ludwig, M., Schneider, T., Wolter, F., Zakharyaschev, M.: Conjunctive query inseparability of OWL 2 QL TBoxes. In: Proceedings of the 25th National Conference on Artificial Intelligence (AAAI 2011), pp. 221–226. AAAI Press (2011)Google Scholar
  98. 98.
    Vescovo, C., Klinov, P., Parsia, B., Sattler, U., Schneider, T., Tsarkov, D.: Empirical study of logic-based modules: cheap is cheerful. In: Alani, H., et al. (eds.) ISWC 2013. LNCS, vol. 8218, pp. 84–100. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-41335-3_6 CrossRefGoogle Scholar
  99. 99.
    Gatens, W., Konev, B., Wolter, F.: Lower and upper approximations for depleting modules of description logic ontologies. In: Proceedings of the 21st European Conference on Artificial Intelligence (ECAI 2014), vol. 263, pp. 345–350. IOS Press (2014)Google Scholar
  100. 100.
    Nortje, R., Britz, A., Meyer, T.: Module-theoretic properties of reachability modules for SRIQ. In: Proceedings of the 26th International Workshop on Description Logics (DL 2013). CEUR Workshop Proceedings, vol. 1014, pp. 868–884. CEUR-WS.org (2013)Google Scholar
  101. 101.
    Nortje, R., Britz, K., Meyer, T.: Reachability modules for the description logic \(\cal{SRIQ}\). In: McMillan, K., Middeldorp, A., Voronkov, A. (eds.) LPAR 2013. LNCS, vol. 8312, pp. 636–652. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-45221-5_42 CrossRefGoogle Scholar
  102. 102.
    Gonçalves, R.S., Parsia, B., Sattler, U.: Concept-based semantic difference in expressive description logics. In: Cudré-Mauroux, P., et al. (eds.) ISWC 2012. LNCS, vol. 7649, pp. 99–115. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-35176-1_7 CrossRefGoogle Scholar
  103. 103.
    Wang, K., Wang, Z., Topor, R., Pan, J.Z., Antoniou, G.: Concept and role forgetting in \({\cal{ALC}}\) ontologies. In: Bernstein, A., Karger, D.R., Heath, T., Feigenbaum, L., Maynard, D., Motta, E., Thirunarayan, K. (eds.) ISWC 2009. LNCS, vol. 5823, pp. 666–681. Springer, Heidelberg (2009). doi: 10.1007/978-3-642-04930-9_42 CrossRefGoogle Scholar
  104. 104.
    Zhou, Y., Zhang, Y.: Bounded forgetting. In: Burgard, W., Roth, D. (eds.) Proceedings of the 25th National Conference on Artificial Intelligence (AAAI 2011). AAAI Press (2011)Google Scholar
  105. 105.
    Ludwig, M., Konev, B.: Practical uniform interpolation and forgetting for \(\cal{ALC}\) tboxes with applications to logical difference. In: Proceedings of the 14th International Conference on the Principles of Knowledge Representation and Reasoning (KR 2014). AAAI Press (2014)Google Scholar
  106. 106.
    Gabbay, D.M., Schmidt, R.A., Szałas, A.: Second-Order Quantifier Elimination: Foundations, Computational Aspects and Applications. Studies in Logic: Mathematical Logic and Foundations, vol. 12. College Publications (2008). ISBN 978-1-904987-56-7Google Scholar
  107. 107.
    Zhao, Y., Schmidt, R.A.: Concept forgetting in \(\cal{ALCOI}\)-ontologies using an ackermann approach. In: Arenas, M., et al. (eds.) ISWC 2015. LNCS, vol. 9366, pp. 587–602. Springer, Heidelberg (2015). doi: 10.1007/978-3-319-25007-6_34 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Elena Botoeva
    • 1
  • Boris Konev
    • 2
  • Carsten Lutz
    • 3
  • Vladislav Ryzhikov
    • 1
  • Frank Wolter
    • 2
    Email author
  • Michael Zakharyaschev
    • 4
  1. 1.Faculty of Computer ScienceFree University of Bozen-BolzanoBolzanoItaly
  2. 2.Department of Computer ScienceUniversity of LiverpoolLiverpoolUK
  3. 3.Faculty of InformaticsUniversity of BremenBremenGermany
  4. 4.Department of Computer Science and Information SystemsBirkbeck University of LondonLondonUK

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