{"type":"ScholarlyArticle","title":"Query Conservative Extensions in Horn Description Logics with Inverse Roles","authors":[{"name":"Jean Christoph Jung","slug":"jean-christoph-jung","given":"Jean Christoph","family":"Jung","affiliation":"Fachbereich Informatik , Universität Bremen , Germany"},{"name":"Carsten Lutz","slug":"carsten-lutz","given":"Carsten","family":"Lutz","affiliation":"Fachbereich Informatik , Universität Bremen , Germany"},{"name":"Mauricio Martel","slug":"mauricio-martel","given":"Mauricio","family":"Martel","affiliation":"Fachbereich Informatik , Universität Bremen , Germany"},{"name":"Thomas Schneider","slug":"thomas-schneider","given":"Thomas","family":"Schneider","affiliation":"Fachbereich Informatik , Universität Bremen , Germany"}],"abstract":"We investigate the decidability and computational complexity of query conservative extensions in Horn description logics (DLs) with inverse roles. This is more challenging than without inverse roles because characterizations in terms of unbounded homomorphisms between universal models fail, blocking the standard approach to establishing decidability. We resort to a combination of automata and mosaic techniques, proving that the problem is 2EXPTIME-complete in Horn-ALCHIF (and also in Horn-ALC and in ELI). We obtain the same upper bound for deductive conservative extensions, for which we also prove a coNEXPTIME lower bound.","doi":"10.24963/ijcai.2017/155","url":"https://ijcai.org/proceedings/2017/155","pdf":"https://ijcai.org/proceedings/2017/0155.pdf","markdown":"https://ijcai.org/proceedings/2017/155.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/155","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Knowledge Representation, Reasoning, and Logic","track":"Main track","number":155,"pages":{"first":1116,"last":1122},"keywords":["Knowledge Representation, Reasoning, and Logic: Computational Complexity of Reasoning","Knowledge Representation, Reasoning, and Logic: Automated Reasoning and Theorem Proving","Knowledge Representation, Reasoning, and Logic: Description Logics and Ontologies"],"videos":[],"references":[{"position":1,"raw":"[Arenas et al., 2016] Marcelo Arenas, Elena Botoeva, Diego Calvanese, and Vladislav Ryzhikov. Knowledge base ex- change: The case of OWL 2 QL. Artif. Intell., 238:11-62, 2016.","title":"Knowledge base exchange: The case of OWL 2 QL","authors":"Marcelo Arenas, Elena Botoeva, Diego Calvanese, Vladislav Ryzhikov","year":"2016","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Baader et al., 2017] Franz Baader, Ian Horrocks, Carsten Lutz, and Ulrike Sattler. An Introduction to Description Logics. Cambride University Press, 2017.","title":"An Introduction to Description Logics","authors":"Franz Baader, Ian Horrocks, Carsten Lutz, Ulrike Sattler","year":"2017","venue":null,"doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Bienvenu and Ortiz, 2015] Meghyn Bienvenu and Magdalena Ortiz. Ontology-mediated query answering with data-tractable description logics. In Proc. RW, pages 218-307, 2015.","title":"Ontology-mediated query answering with data-tractable description logics","authors":"Ortiz Bienvenu, Meghyn Bienvenu, Magdalena Ortiz","year":"2015","venue":"Proc. RW","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Bienvenu and Rosati, 2015] Meghyn Bienvenu and Riccardo Rosati. Query-based comparison of OBDA specifications. In Proc. DL, volume 1350. ceur-ws.org, 2015.","title":"Query-based comparison of OBDA specifications","authors":"Rosati Bienvenu, Meghyn Bienvenu, Riccardo Rosati","year":"2015","venue":"Proc. DL","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Bienvenu et al., 2013] Meghyn Bienvenu, Carsten Lutz, and Frank Wolter. First order-rewritability of atomic queries in Horn description logics. In Proc. IJCAI, pages 754-760, 2013.","title":"First order-rewritability of atomic queries in Horn description logics","authors":"Bienvenu","year":"2013","venue":"Proc. IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2013/118"},{"position":6,"raw":"[Bienvenu et al., 2016] Meghyn Bienvenu, Peter Hansen, Carsten Lutz, and Frank Wolter. First order-rewritability and containment of conjunctive queries in Horn description logics. In Proc. IJCAI, pages 965-971, 2016.","title":"First order-rewritability and containment of conjunctive queries in Horn description logics","authors":"Bienvenu","year":"2016","venue":"Proc. IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2016/141"},{"position":7,"raw":"[Botoeva et al., 2016a] Elena Botoeva, Boris Konev, Carsten Lutz, Vladislav Ryzhikov, Frank Wolter, and Michael Zakharyaschev. Inseparability and conservative extensions of description logic ontologies: A survey. In Proc. RW, 2016.","title":"Inseparability and conservative extensions of description logic ontologies: A survey","authors":"Botoeva","year":"2016","venue":"Proc. RW","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Botoeva et al., 2016b] Elena Botoeva, Roman Kontchakov, Vladislav Ryzhikov, Frank Wolter, and Michael Zakharyaschev. Games for query inseparability of de- scription logic knowledge bases. Artif. Intell., 234:78-119, 2016.","title":"Games for query inseparability of description logic knowledge bases","authors":"Botoeva","year":"2016","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Botoeva et al., 2016c] Elena Botoeva, Carsten Lutz, Vladislav Ryzhikov, Frank Wolter, and Michael Zakharyaschev. Query- based entailment and inseparability for ALC ontologies. In Proc. IJCAI, pages 1001-1007, 2016.","title":"Querybased entailment and inseparability for ALC ontologies","authors":"Botoeva","year":"2016","venue":"Proc. IJCAI","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Calvanese et al., 2007] Diego Calvanese, Giuseppe De Gia- como, Domenico Lembo, Maurizio Lenzerini, and Riccardo Rosati. Tractable reasoning and efficient query answering in description logics: The DL-Lite family. J. Autom. Reas., 39(3):385-429, 2007.","title":"Tractable reasoning and efficient query answering in description logics: The DL-Lite family","authors":"Calvanese","year":"2007","venue":"J. Autom. Reas","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Eiter et al., 2008] Thomas Eiter, Georg Gottlob, Magdalena Or- tiz, and Mantas Šimkus. Query answering in the description logic Horn-SHIQ. In Proc. JELIA, volume 5293 of LNCS, pages 166-179. Springer, 2008.","title":"Query answering in the description logic Horn-SHIQ","authors":"Thomas Eiter, Georg Gottlob, Magdalena Ortiz, Mantas Šimkus","year":"2008","venue":"Proc. JELIA","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Eiter et al., 2012] Thomas Eiter, Magdalena Ortiz, Mantas Šimkus, Trung-Kien Tran, and Guohui Xiao. Query rewriting for Horn-SHIQ plus rules. In Proc. AAAI, 2012.","title":"Query rewriting for Horn-SHIQ plus rules","authors":"Thomas Eiter, Magdalena Ortiz, Mantas Šimkus, Trung-Kien Tran, Guohui Xiao","year":"2012","venue":"Proc. AAAI","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Ghilardi et al., 2006] Silvio Ghilardi, Carsten Lutz, and Frank Wolter. Did I damage my ontology? A case for conservative extensions in description logics. In Proc. KR, pages 187-197, 2006.","title":"Did I damage my ontology? A case for conservative extensions in description logics","authors":"Silvio Ghilardi, Carsten Lutz, Frank Wolter","year":"2006","venue":"Proc. KR","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Grädel and Walukiewicz, 1999] Erich Grädel and Igor Walukiewicz. Guarded fixed point logic. In Proc. LICS, pages 45-54, 1999.","title":"Erich Grädel and Igor Walukiewicz. Guarded fixed point logic","authors":"Walukiewicz Grädel","year":"1999","venue":"Proc. LICS","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Hustadt et al., 2007] Ullrich Hustadt, Boris Motik, and Ulrike Sattler. Reasoning in description logics by a reduction to dis- junctive datalog. J. Autom. Reasoning, 39(3), 2007.","title":"Reasoning in description logics by a reduction to disjunctive datalog","authors":"Ullrich Hustadt, Boris Motik, Ulrike Sattler","year":"2007","venue":"J. Autom. Reasoning","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Ibáñez-García et al., 2014] Yazmín Ibáñez-García, Carsten Lutz, and Thomas Schneider. Finite model reasoning in Horn description logics. In Proc. KR, 2014.","title":"Finite model reasoning in Horn description logics","authors":"Ibáñez-García","year":"2014","venue":"Proc. KR","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Kazakov, 2009] Yevgeny Kazakov. Consequence-driven reason- ing for Horn-SHIQ ontologies. In Proc. IJCAI, pages 2040- 2045, 2009.","title":"Consequence-driven reasoning for Horn-SHIQ ontologies","authors":"Yevgeny Kazakov, Kazakov","year":"2009","venue":"Proc. IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2009/336"},{"position":18,"raw":"[Kollia and Glimm, 2013] Ilianna Kollia and Birte Glimm. Op- timizing SPARQL query answering over OWL ontologies. J. Artif. Intell. Res., 48:253-303, 2013.","title":"Ilianna Kollia and Birte Glimm. Optimizing SPARQL query answering over OWL ontologies","authors":"Glimm Kollia","year":"2013","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Konev et al., 2009] Boris Konev, Carsten Lutz, Dirk Walther, and Frank Wolter. Formal properties of modularisation. In H. Stuckenschmidt, S. Spacciapietra, and C. Parent, editors, Modular Ontologies, volume 5445 of LNCS, pages 25-66. Springer, 2009.","title":"Formal properties of modularisation","authors":"Boris Konev, Carsten Lutz, Dirk Walther, Frank Wolter","year":"2009","venue":"Modular Ontologies","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Konev et al., 2012] Boris Konev, Michel Ludwig, Dirk Walther, and Frank Wolter. The logical difference for the lightweight description logic EL. J. Artif. Intell. Res., 44:633-708, 2012.","title":"The logical difference for the lightweight description logic EL","authors":"Boris Konev, Michel Ludwig, Dirk Walther, Frank Wolter","year":"2012","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Kontchakov et al., 2009] Roman Kontchakov, Luca Pulina, Ul- rike Sattler, Thomas Schneider, P. Selmer, Frank Wolter, and Michael Zakharyaschev. Minimal module extraction from DL- Lite ontologies using QBF solvers. In Proc. IJCAI, pages 836- 840, 2009.","title":"Minimal module extraction from DL-Lite ontologies using QBF solvers","authors":"Kontchakov","year":"2009","venue":"Proc. IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2009/143"},{"position":22,"raw":"[Kontchakov et al., 2010] Roman Kontchakov, Frank Wolter, and Michaek Zakharyaschev. Logic-based ontology compar- ison and module extraction, with an application to DL-Lite. Artif. Intell., 174:1093-1141, 2010.","title":"Roman Kontchakov, Frank Wolter, and Michaek Zakharyaschev. Logic-based ontology comparison and module extraction, with an application to DL-Lite","authors":"Kontchakov","year":"2010","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Krötzsch et al., 2007] Markus Krötzsch, Sebastian Rudolph, and Pascal Hitzler. Complexity boundaries for Horn descrip- tion logics. In Proc. AAAI, pages 452-457, 2007.","title":"Complexity boundaries for Horn description logics","authors":"Krötzsch","year":"2007","venue":"Proc. AAAI","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Lutz and Wolter, 2010] Carsten Lutz and Frank Wolter. Decid- ing inseparability and conservative extensions in the descrip- tion logic EL. J. Symb. Comput., 45(2):194-228, 2010.","title":"Deciding inseparability and conservative extensions in the description logic EL","authors":"Wolter Lutz, Carsten Lutz, Frank Wolter","year":"2010","venue":"J. Symb. Comput","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Lutz and Wolter, 2012] Carsten Lutz and Frank Wolter. Non- uniform data complexity of query answering in description logics. In Proc. KR, 2012.","title":"Nonuniform data complexity of query answering in description logics","authors":"Wolter Lutz, Carsten Lutz, Frank Wolter","year":"2012","venue":"Proc. KR","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Lutz et al., 2007] Carsten Lutz, Dirk Walther, and Frank Wolter. Conservative extensions in expressive description logics. In Proc. IJCAI, pages 453-458, 2007.","title":"Conservative extensions in expressive description logics","authors":"Carsten Lutz, Dirk Walther, Frank Wolter","year":"2007","venue":"Proc. IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2007/71"},{"position":27,"raw":"[Matentzoglu and Parsia, 2017] Nico Matentzoglu and Bijan Parsia. BioPortal Snapshot 30 March 2017 (data set), 2017. http://doi.org/10.5281/zenodo.439510.","title":"Nico Matentzoglu and Bijan Parsia","authors":"Parsia Matentzoglu","year":"2017","venue":"BioPortal Snapshot","doi":"10.5281/zenodo.439510","url":"http://doi.org/10.5281/zenodo.439510","internal_url":null},{"position":28,"raw":"[Poggi et al., 2008] Antonella Poggi, Domenico Lembo, Diego Calvanese, Giuseppe De Giacomo, Maurizio Lenzerini, and Riccardo Rosati. Linking data to ontologies. 10:133-173, 2008.","title":"Linking data to ontologies","authors":"Antonella Poggi, Domenico Lembo, Diego Calvanese, Giuseppe De Giacomo, Maurizio Lenzerini, Riccardo Rosati","year":"2008","venue":null,"doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Tobies, 2001] Stephan Tobies. Complexity Results and Practi- cal Algorithms for Logics in Knowledge Representation. PhD thesis, RWTH Aachen, 2001.","title":"Complexity Results and Practical Algorithms for Logics in Knowledge Representation","authors":"Stephan Tobies","year":"2001","venue":null,"doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Trivela et al., 2015] Despoina Trivela, Giorgos Stoilos, Alexan- dros Chortaras, and Giorgos B. Stamou. Optimising resolution-based rewriting algorithms for OWL ontologies. J. Web Sem., 33:30-49, 2015.","title":"Optimising resolution-based rewriting algorithms for OWL ontologies","authors":"Despoina Trivela, Giorgos Stoilos, Alexandros Chortaras, Giorgos B Stamou","year":"2015","venue":"J. Web Sem","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Vardi, 1998] Moshe Y. Vardi. Reasoning about the past with two-way automata. In Proc. ICALP, pages 628-641, 1998.","title":"Reasoning about the past with two-way automata","authors":"Moshe Y Vardi","year":"1998","venue":"Proc. ICALP","doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Wang et al., 2014] Kewen Wang, Zhe Wang, Rodney W. Topor, Jeff Z. Pan, and Grigoris Antoniou. Eliminating concepts and roles from ontologies in expressive descriptive logics. Comput. Intell., 30(2):205-232, 2014.","title":"Eliminating concepts and roles from ontologies in expressive descriptive logics","authors":"Kewen Wang, Zhe Wang, Rodney W Topor, Jeff Z Pan, Grigoris Antoniou","year":"2014","venue":"Comput. Intell","doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Zhou et al., 2015] Yujiao Zhou, Bernardo Cuenca Grau, Yavor Nenov, Mark Kaminski, and Ian Horrocks. PAGOdA: Pay-as- you-go ontology query answering using a Datalog reasoner. J. Artif. Intell. Res., 54:309-367, 2015.","title":"PAGOdA: Pay-asyou-go ontology query answering using a Datalog reasoner","authors":"Yujiao Zhou, Bernardo Cuenca Grau, Yavor Nenov, Mark Kaminski, Ian Horrocks","year":"2015","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}