{"type":"ScholarlyArticle","title":"Restricted Chase (Non)Termination for Existential Rules with Disjunctions","authors":[{"name":"David Carral","slug":"david-carral","given":"David","family":"Carral","affiliation":"Center for Advancing Electronics Dresden (cfaed) , TU Dresden , Germany"},{"name":"Irina Dragoste","slug":"irina-dragoste","given":"Irina","family":"Dragoste","affiliation":"Center for Advancing Electronics Dresden (cfaed) , TU Dresden , Germany"},{"name":"Markus Krötzsch","slug":"markus-krotzsch","given":"Markus","family":"Krötzsch","affiliation":"Center for Advancing Electronics Dresden (cfaed) , TU Dresden , Germany"}],"abstract":"The restricted chase is a sound and complete algorithm for conjunctive query answering over ontologies of disjunctive existential rules. We develop acyclicity conditions to ensure its termination. Our criteria cannot always detect termination (the problem is undecidable), and we develop the first cyclicity criteria to show non-termination of the restricted chase. Experiments on real-world ontologies show that our acyclicity notions improve significantly over known criteria.","doi":"10.24963/ijcai.2017/128","url":"https://ijcai.org/proceedings/2017/128","pdf":"https://ijcai.org/proceedings/2017/0128.pdf","markdown":"https://ijcai.org/proceedings/2017/128.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/128","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":128,"pages":{"first":922,"last":928},"keywords":["Knowledge Representation, Reasoning, and Logic: Description Logics and Ontologies","Knowledge Representation, Reasoning, and Logic: Logics for Knowledge Representation","Knowledge Representation, Reasoning, and Logic: Computational Complexity of Reasoning","Knowledge Representation, Reasoning, and Logic: Knowledge Representation Languages"],"videos":[],"references":[{"position":1,"raw":"[Baget et al., 2011] Jean-Franc ¸ois Baget, Michel Leclère, Marie-Laure Mugnier, and Eric Salvat. On rules with ex- istential variables: Walking the decidability line. Artificial Intelligence, 175(9-10):1620-1654, 2011.","title":"On rules with existential variables: Walking the decidability line","authors":"Baget","year":"2011","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Beeri and Vardi, 1981] Catriel Beeri and Moshe Y. Vardi. The implication problem for data dependencies. In Shi- mon Even and Oded Kariv, editors, Proc. 8th Colloquium on Automata, Languages and Programming (ICALP'81), volume 115 of LNCS, pages 73-85. Springer, 1981.","title":"The implication problem for data dependencies","authors":"Catriel Beeri, Moshe Y Vardi","year":"1981","venue":"Proc. 8th Colloquium on Automata, Languages and Programming (ICALP'81)","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Bienvenu et al., 2016] Meghyn Bienvenu, Peter Hansen, Carsten Lutz, and Frank Wolter. First order-rewritability and containment of conjunctive queries in Horn descrip- tion logics. In Subbarao Kambhampati, editor, Proc. 25th Int. Joint Conf. on Artificial Intelligence (IJCAI'16), pages 965-971. IJCAI/AAAI Press, 2016.","title":"First order-rewritability and containment of conjunctive queries in Horn description logics","authors":"Bienvenu","year":"2016","venue":"Proc. 25th Int. Joint Conf. on Artificial Intelligence (IJCAI'16)","doi":null,"url":null,"internal_url":"/proceedings/2016/141"},{"position":4,"raw":"[Bourhis et al., 2016] Pierre Bourhis, Marco Manna, Michael Morak, and Andreas Pieris. Guarded-based disjunctive tuple-generating dependencies. ACM Trans. Database Syst., 41(4):27:1-27:45, 2016.","title":"Guarded-based disjunctive tuple-generating dependencies","authors":"Pierre Bourhis, Marco Manna, Michael Morak, Andreas Pieris","year":"2016","venue":"ACM Trans. Database Syst","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Calì et al., 2010] Andrea Calì, Georg Gottlob, and Andreas Pieris. Query answering under non-guarded rules in Datalog+/-. In Pascal Hitzler and Thomas Lukasiewicz, editors, Proc. 4th Int. Conf. on Web Reasoning and Rule Systems (RR 2010), volume 6333 of LNCS, pages 1-17. Springer, 2010.","title":"Query answering under non-guarded rules in Datalog+","authors":"Andrea Calì, Georg Gottlob, Andreas Pieris","year":"2010","venue":"Proc. 4th Int. Conf. on Web Reasoning and Rule Systems (RR 2010)","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Calì et al., 2013] Andrea Calì, Georg Gottlob, and Michael Kifer. Taming the infinite chase: Query answering un- der expressive relational constraints. J. Artif. Intell. Res. (JAIR), 48:115-174, 2013.","title":"Taming the infinite chase: Query answering under expressive relational constraints","authors":"Andrea Calì, Georg Gottlob, Michael Kifer","year":"2013","venue":"J. Artif. Intell. Res. (JAIR)","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Calvanese et al., 2007] Diego Calvanese, Guiseppe De Gi- acomo, Domenico Lembo, Maurizio Lenzerini, and Ric- cardo Rosati. Tractable reasoning and efficient query an- swering in description logics: The DL-Lite family. J. of Automated Reasoning, 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. of Automated Reasoning","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Calvanese et al., 2014] Diego Calvanese, Thomas Eiter, and Magdalena Ortiz. Answering regular path queries in ex- pressive description logics via alternating tree-automata. Inf. Comput., 237:12-55, 2014.","title":"Answering regular path queries in expressive description logics via alternating tree-automata","authors":"Calvanese","year":"2014","venue":"Inf. Comput","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Carral et al., 2016] David Carral, Cristina Feier, and Pas- cal Hitzler. A practical acyclicity notion for query an- swering over Horn-SRIQ ontologies. In Paul T. Groth, Elena Simperl, Alasdair J. G. Gray, Marta Sabou, Markus Krötzsch, Freddy Lécué, Fabian Flöck, and Yolanda Gil, editors, Proc. 15th Int. Semantic Web Conf. (ISWC'16), volume 9981 of LNCS, pages 70-85. Springer, 2016.","title":"A practical acyclicity notion for query answering over Horn-SRIQ ontologies","authors":"David Carral, Cristina Feier, Pascal Hitzler","year":"2016","venue":"Proc. 15th Int. Semantic Web Conf. (ISWC'16)","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Carral et al., 2017] David Carral, Irina Dragoste, and Markus Krötzsch. Detecting chase (non)termination for existential rules with disjunctions: Extended tech- nical report. Available at https://iccl.inf. tu-dresden.de/web/Inproceedings3140/en, 2017.","title":"Detecting chase (non)termination for existential rules with disjunctions: Extended technical report","authors":"David Carral, Irina Dragoste, Markus Krötzsch","year":"2017","venue":null,"doi":null,"url":"https://iccl.inf.tu-dresden.de/web/Inproceedings3140/en","internal_url":null},{"position":11,"raw":"[Cuenca Grau et al., 2013] Bernardo Cuenca Grau, Ian Hor- rocks, Markus Krötzsch, Clemens Kupke, Despoina Magka, Boris Motik, and Zhe Wang. Acyclicity notions for existential rules and their application to query answer- ing in ontologies. J. of Art. Int. Research, 47:741-808, 2013.","title":"Acyclicity notions for existential rules and their application to query answering in ontologies","authors":"Cuenca Bernardo, Ian Grau, Markus Horrocks, Clemens Krötzsch, Despoina Kupke, Boris Magka, Zhe Motik, Wang","year":"2013","venue":"J. of Art. Int. Research","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Dantsin et al., 2001] Evgeny Dantsin, Thomas Eiter, Georg Gottlob, and Andrei Voronkov. Complexity and expressive power of logic programming. ACM Computing Surveys, 33(3):374-425, 2001.","title":"Complexity and expressive power of logic programming","authors":"Evgeny Dantsin, Thomas Eiter, Georg Gottlob, Andrei Voronkov","year":"2001","venue":"ACM Computing Surveys","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Deutsch and Tannen, 2002] Alin Deutsch and Val Tannen. Optimization properties for classes of conjunctive regular path queries. In Giorgio Ghelli and Gösta Grahne, edi- tors, Proc. 21st Int. Workshop on Database Programming Languages (DBPL 2001), volume 2397 of LNCS, pages 21-39. Springer, 2002.","title":"Optimization properties for classes of conjunctive regular path queries","authors":"Alin Deutsch, Val Tannen","year":"2002","venue":"editors, Proc. 21st Int. Workshop on Database Programming Languages (DBPL 2001)","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Krötzsch and Rudolph, 2011] Markus Krötzsch and Sebas- tian Rudolph. Extending decidable existential rules by joining acyclicity and guardedness. In Toby Walsh, edi- tor, Proc. 22nd Int. Joint Conf. on Artificial Intelligence (IJCAI'11), pages 963-968. AAAI Press/IJCAI, 2011.","title":"Extending decidable existential rules by joining acyclicity and guardedness","authors":"Rudolph ; Krötzsch, Markus Krötzsch, Sebastian Rudolph","year":"2011","venue":"Proc. 22nd Int. Joint Conf. on Artificial Intelligence (IJCAI'11)","doi":null,"url":null,"internal_url":"/proceedings/2011/166"},{"position":15,"raw":"[Marnette, 2009] Bruno Marnette. Generalized schema- mappings: from termination to tractability. In J. Paredaens and J. Su, editors, Proc. 28th Symp. on Principles of Database Systems (PODS'09), pages 13-22. ACM, 2009.","title":"Generalized schemamappings: from termination to tractability","authors":"Bruno Marnette","year":"2009","venue":"Proc. 28th Symp. on Principles of Database Systems (PODS'09)","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Matentzoglu and Parsia, 2014] Nicolas Matentzoglu and Bijan Parsia. The Manchester OWL Corpus (MOWL- Corp), original serialisation, July 2014. https://doi. org/10.5281/zenodo.10851.","title":"The Manchester OWL Corpus (MOWL-Corp), original serialisation","authors":"Parsia Matentzoglu","year":"2014","venue":null,"doi":"10.5281/zenodo.10851","url":"https://doi.org/10.5281/zenodo.10851","internal_url":null},{"position":17,"raw":"[Matentzoglu et al., 2013] Nicolas Matentzoglu, Samantha Bail, and Bijan Parsia. A snapshot of the OWL Web. In Harith Alani, Lalana Kagal, Achille Fokoue, Paul T. Groth, Chris Biemann, Josiane Xavier Parreira, Lora Aroyo, Natasha F. Noy, Chris Welty, and Krzysztof Janowicz, ed- itors, Proc. 12th Int. Semantic Web Conf. (ISWC'13), vol- ume 8218 of LNCS, pages 331-346. Springer, 2013.","title":"A snapshot of the OWL Web","authors":"Nicolas Matentzoglu, Samantha Bail, Bijan Parsia","year":"2013","venue":"Proc. 12th Int. Semantic Web Conf. (ISWC'13)","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Motik et al., 2009] Boris Motik, Rob Shearer, and Ian Hor- rocks. Hypertableau reasoning for description logics. J. of Artificial Intelligence Research, 36:165-228, 2009.","title":"Hypertableau reasoning for description logics","authors":"Boris Motik, Rob Shearer, Ian Horrocks","year":"2009","venue":"J. of Artificial Intelligence Research","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Motik et al., 2014] Boris Motik, Yavor Nenov, Robert Piro, Ian Horrocks, and Dan Olteanu. Parallel materialisa- tion of Datalog programs in centralised, main-memory RDF systems. In Carla E. Brodley and Peter Stone, editors, Proc. 28th AAAI Conf. on Artificial Intelligence (AAAI'14), pages 129-137. AAAI Press, 2014.","title":"Parallel materialisation of Datalog programs in centralised, main-memory RDF systems","authors":"Boris Motik, Yavor Nenov, Robert Piro, Ian Horrocks, Dan Olteanu","year":"2014","venue":"Proc. 28th AAAI Conf. on Artificial Intelligence (AAAI'14)","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Rudolph and Glimm, 2010] Sebastian Rudolph and Birte Glimm. Nominals, inverses, counting, and conjunctive queries or: Why infinity is your friend! J. of Artificial In- telligence Research, 39:429-481, 2010.","title":"Sebastian Rudolph and Birte Glimm. Nominals, inverses, counting, and conjunctive queries or: Why infinity is your friend!","authors":"Glimm Rudolph","year":"2010","venue":"J. of Artificial Intelligence Research","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Stefanoni et al., 2014] Giorgio Stefanoni, Boris Motik, Markus Krötzsch, and Sebastian Rudolph. The complex- ity of answering conjunctive and navigational queries over OWL 2 EL knowledge bases. J. of Art. Int. Research, 51:645-705, 2014.","title":"The complexity of answering conjunctive and navigational queries over OWL 2 EL knowledge bases","authors":"Giorgio Stefanoni, Boris Motik, Markus Krötzsch, Sebastian Rudolph","year":"2014","venue":"J. of Art. Int. Research","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}