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Logic"],"published-print":{"date-parts":[[2013,6]]},"abstract":"<jats:p>Hybrid MKNF knowledge bases are one of the most prominent tightly integrated combinations of open-world ontology languages with closed-world (nonmonotonic) rule paradigms. Based on the logic of minimal knowledge and negation as failure (MKNF), the definition of Hybrid MKNF is parametric on the description logic (DL) underlying the ontology language, in the sense that nonmonotonic rules can extend any decidable DL language. Two related semantics have been defined for Hybrid MKNF: one that is based on the Stable Model Semantics for logic programs and one on the Well-Founded Semantics (WFS). Under WFS, the definition of Hybrid MKNF relies on a bottom-up computation that has polynomial data complexity whenever the DL language is tractable. Here we define a general query-driven procedure for Hybrid MKNF that is sound with respect to the stable model-based semantics, and sound and complete with respect to its WFS variant. This procedure is able to answer a slightly restricted form of conjunctive queries, and is based on tabled rule evaluation extended with an external oracle that captures reasoning within the ontology. Such an (abstract) oracle receives as input a query along with knowledge already derived, and replies with a (possibly empty) set of atoms, defined in the rules, whose truth would suffice to prove the initial query. With appropriate assumptions on the complexity of the abstract oracle, the general procedure maintains the data complexity of the WFS for Hybrid MKNF knowledge bases.<\/jats:p>\n          <jats:p>\n            To illustrate this approach, we provide a concrete oracle for\n            <jats:italic>EL<\/jats:italic>\n            <jats:sup>+<\/jats:sup>\n            , a fragment of the lightweight DL\n            <jats:italic>EL<\/jats:italic>\n            <jats:sup>++<\/jats:sup>\n            . Such an oracle has practical use, as\n            <jats:italic>EL<\/jats:italic>\n            <jats:sup>++<\/jats:sup>\n            is the language underlying OWL 2 EL, which is part of the W3C recommendations for the Semantic Web, and is tractable for reasoning tasks such as subsumption. We show that query-driven Hybrid MKNF preserves polynomial data complexity when using the\n            <jats:italic>EL<\/jats:italic>\n            <jats:sup>+<\/jats:sup>\n            oracle and WFS.\n          <\/jats:p>","DOI":"10.1145\/2480759.2480768","type":"journal-article","created":{"date-parts":[[2013,6,18]],"date-time":"2013-06-18T12:36:08Z","timestamp":1371558968000},"page":"1-43","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":13,"title":["Query-Driven Procedures for Hybrid MKNF Knowledge Bases"],"prefix":"10.1145","volume":"14","author":[{"given":"Jos\u00e9 J\u00falio","family":"Alferes","sequence":"first","affiliation":[{"name":"CENTRIA, Departamento de Inform\u00e1tica, Faculdade de Ci\u00eancias e Tecnologia, Universidade Nova de Lisboa, Portugal"}]},{"given":"Matthias","family":"Knorr","sequence":"additional","affiliation":[{"name":"CENTRIA, Departamento de Inform\u00e1tica, Faculdade de Ci\u00eancias e Tecnologia, Universidade Nova de Lisboa, Portugal"}]},{"given":"Terrance","family":"Swift","sequence":"additional","affiliation":[{"name":"CENTRIA, Departamento de Inform\u00e1tica, Faculdade de Ci\u00eancias e Tecnologia, Universidade Nova de Lisboa, Portugal"}]}],"member":"320","published-online":{"date-parts":[[2013,6]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-04930-9_1"},{"key":"e_1_2_1_2_1","volume-title":"Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI\u201905)","author":"Baader F.","unstructured":"Baader , F. , Brandt , S. , and Lutz , C . 2005. Pushing the EL envelope . In Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI\u201905) . L. P. Kaelbing and A. Saffiotti Eds., Morgan Kaufmann, 364--369. Baader, F., Brandt, S., and Lutz, C. 2005. Pushing the EL envelope. In Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI\u201905). L. P. Kaelbing and A. Saffiotti Eds., Morgan Kaufmann, 364--369."},{"key":"e_1_2_1_3_1","volume-title":"2007. The Description Logic Handbook: Theory, Implementation, and Applications","author":"Baader F.","unstructured":"Baader , F. , Calvanese , D. , McGuinness , D. L. , Nardi , D. , and Patel-Schneider , P. F. , Eds. 2007. The Description Logic Handbook: Theory, Implementation, and Applications 2 nd Ed. Cambridge University Press . Baader, F., Calvanese, D., McGuinness, D. L., Nardi, D., and Patel-Schneider, P. F., Eds. 2007. The Description Logic Handbook: Theory, Implementation, and Applications 2nd Ed. 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W3C Candidate Recommendation. http:\/\/www.w3.org\/TR\/rif-overview\/."},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/227595.227597"},{"key":"e_1_2_1_7_1","volume-title":"Proceedings of the 1st International Conference on Web Reasoning and Rule Systems (RR\u201907)","author":"Drabent W.","unstructured":"Drabent , W. and Ma\u0142uszy\u0144ski , J . 2007. Well-Founded semantics for hybrid rules . In Proceedings of the 1st International Conference on Web Reasoning and Rule Systems (RR\u201907) . M. M. Marchiori, J. Z. Pan, and C. de Sainte Marie Eds., Springer, 1--15. Drabent, W. and Ma\u0142uszy\u0144ski, J. 2007. Well-Founded semantics for hybrid rules. In Proceedings of the 1st International Conference on Web Reasoning and Rule Systems (RR\u201907). M. M. Marchiori, J. Z. 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Hitzler, P., Kr\u00f6tzsch, M., Parsia, B., Patel-Schneider, P. F., and Rudolph, S., Eds. 2009. OWL 2 Web Ontology Language: Primer. W3C Recommendation. http:\/\/www.w3.org\/TR\/owl2-primer\/."},{"key":"e_1_2_1_16_1","volume-title":"Proceedings of the 19th European Conference on Artificial Intelligence (ECAI\u201910)","author":"Knorr M.","unstructured":"Knorr , M. and Alferes , J. J . 2010. Querying in EL&thinsp;+ with nonmonotonic rules . In Proceedings of the 19th European Conference on Artificial Intelligence (ECAI\u201910) . H. Coelho, R. Studer, and M. Wooldridge Eds., IOS Press, 1079--1080. Knorr, M. and Alferes, J. J. 2010. Querying in EL&thinsp;+ with nonmonotonic rules. In Proceedings of the 19th European Conference on Artificial Intelligence (ECAI\u201910). H. Coelho, R. Studer, and M. 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Wooldridge Eds., Frontiers in Artificial Intelligence and Applications, vol. 215, IOS Press, 957--962."},{"key":"e_1_2_1_36_1","doi-asserted-by":"publisher","DOI":"10.1017\/S147106841000027X"},{"key":"e_1_2_1_37_1","doi-asserted-by":"crossref","unstructured":"Slota M.\n     and \n      Leite J\n  . \n  2011\n  . Back and forth between rules and SE-models. In Proceedings of the 11th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR\u201911). J. P. Delgrande and W. Faber Eds. Lecture Notes in Computer Science vol. \n  6645 Springer Vancouver Canada 174--186.   Slota M. and Leite J. 2011. Back and forth between rules and SE-models. In Proceedings of the 11th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR\u201911) . J. P. Delgrande and W. Faber Eds. Lecture Notes in Computer Science vol. 6645 Springer Vancouver Canada 174--186.","DOI":"10.1007\/978-3-642-20895-9_16"},{"key":"e_1_2_1_38_1","first-page":"4","article-title":"Splitting and updating hybrid knowledge bases","volume":"11","author":"Slota M.","year":"2011","unstructured":"Slota , M. , Leite , J. , and Swift , T. 2011 . Splitting and updating hybrid knowledge bases . Theory Pract. Logic Program. 11 , 4 -- 5 , 801--819. Slota, M., Leite, J., and Swift, T. 2011. Splitting and updating hybrid knowledge bases. Theory Pract. Logic Program. 11, 4--5, 801--819.","journal-title":"Theory Pract. Logic Program."},{"key":"e_1_2_1_39_1","series-title":"Lecture Notes in Artificial Intelligence","volume-title":"Recent Advances in Artifiial Intelligence","author":"Swift T.","unstructured":"Swift , T. 1999. A new formulation of tabled resolution with delay . In Recent Advances in Artifiial Intelligence , Lecture Notes in Artificial Intelligence , vol. 1695 , Springer , 163--177. 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