{"type":"ScholarlyArticle","title":"Chasing Sets: How to Use Existential Rules for Expressive Reasoning","authors":[{"name":"David Carral","slug":"david-carral","given":"David","family":"Carral","affiliation":"Knowledge-Based Systems Group , TU Dresden , Dresden , Germany"},{"name":"Irina Dragoste","slug":"irina-dragoste","given":"Irina","family":"Dragoste","affiliation":"Knowledge-Based Systems Group , TU Dresden , Dresden , Germany"},{"name":"Markus Krötzsch","slug":"markus-krotzsch","given":"Markus","family":"Krötzsch","affiliation":"Knowledge-Based Systems Group , TU Dresden , Dresden , Germany"},{"name":"Christian Lewe","slug":"christian-lewe","given":"Christian","family":"Lewe","affiliation":"Knowledge-Based Systems Group , TU Dresden , Dresden , Germany"}],"abstract":"We propose that modern existential rule reasoners can enable fully declarative implementations of rule-based inference methods in knowledge representation, in the sense that a particular calculus is captured by a fixed set of rules that can be evaluated on varying inputs (encoded as facts). We introduce Datalog(S) -- Datalog with support for sets -- as a surface language for such translations, and show that it can be captured in a decidable fragment of existential rules. We then implement several known inference methods in Datalog(S), and empirically show that an existing existential rule reasoner can thus be used to solve practical reasoning problems.","doi":"10.24963/ijcai.2019/225","url":"https://ijcai.org/proceedings/2019/225","pdf":"https://ijcai.org/proceedings/2019/0225.pdf","markdown":"https://ijcai.org/proceedings/2019/225.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/225","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Knowledge Representation and Reasoning","track":"Main track","number":225,"pages":{"first":1624,"last":1631},"keywords":["Knowledge Representation and Reasoning: Computational Complexity of Reasoning","Knowledge Representation and Reasoning: Description Logics and Ontologies","Knowledge Representation and Reasoning: Logics for Knowledge Representation","Knowledge Representation and Reasoning: Knowledge Representation Languages"],"videos":[],"references":[{"position":1,"raw":"[Abiteboul et al., 1994] Serge Abiteboul, Richard Hull, and Victor Vianu. Foundations of Databases. Addison Wesley, 1994.","title":"Foundations of Databases","authors":"Serge Abiteboul, Richard Hull, Victor Vianu","year":"1994","venue":null,"doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Ahmetaj et al., 2018] Shqiponja Ahmetaj, Magdalena Or- tiz, and Mantas Simkus. Rewriting guarded existential rules into small datalog programs. In Proc. 21st Int. Conf. on Database Theory (ICDT'18), volume 98 of LIPIcs, pages 4:1-4:24. Schloss Dagstuhl -Leibniz-Zentrum fuer Informatik, 2018.","title":"Shqiponja Ahmetaj, Magdalena Ortiz, and Mantas Simkus. Rewriting guarded existential rules into small datalog programs","authors":"Ahmetaj","year":"2018","venue":"Proc. 21st Int. Conf. on Database Theory (ICDT'18)","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Aref et al., 2015] Molham Aref, Balder ten Cate, Todd J. Green, Benny Kimelfeld, Dan Olteanu, Emir Pasalic, Todd L. Veldhuizen, and Geoffrey Washburn. Design and implementation of the LogicBlox system. In Proc. 2015 ACM SIGMOD Int. Conf. on Management of Data, pages 1371-1382. ACM, 2015.","title":"Design and implementation of the LogicBlox system","authors":"Aref","year":"2015","venue":"Proc. 2015 ACM SIGMOD Int. Conf. on Management of Data","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Baader et al., 2007] Franz Baader, Diego Calvanese, Deb- orah McGuinness, Daniele Nardi, and Peter Patel- Schneider. The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, second edition, 2007.","title":"The Description Logic Handbook: Theory, Implementation, and Applications","authors":"Baader","year":"2007","venue":null,"doi":null,"url":null,"internal_url":null},{"position":5,"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. Artif. In- tell., 175(9-10):1620-1654, 2011.","title":"On rules with existential variables: Walking the decidability line","authors":"Baget","year":"2011","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Baget et al., 2015] Jean-Franc ¸ois Baget, Michel Leclère, Marie-Laure Mugnier, Swan Rocher, and Clément Sipi- eter. Graal: A toolkit for query answering with existential rules. In Proc. 9th Int. Web Rule Symposium (RuleML'15), volume 9202 of LNCS, pages 328-344. Springer, 2015.","title":"Graal: A toolkit for query answering with existential rules","authors":"Baget","year":"2015","venue":"Proc. 9th Int. Web Rule Symposium (RuleML'15)","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Benedikt et al., 2014] Michael Benedikt, Julien Leblay, and Efthymia Tsamoura. PDQ: proof-driven query answering over web-based data. PVLDB, 7(13):1553-1556, 2014.","title":"PDQ: proof-driven query answering over web-based data","authors":"Michael Benedikt, Julien Leblay, Efthymia Tsamoura","year":"2014","venue":"PVLDB","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Benedikt et al., 2017] Michael Benedikt, George Konstan- tinidis, Giansalvatore Mecca, Boris Motik, Paolo Papotti, Donatello Santoro, and Efthymia Tsamoura. Benchmark- ing the chase. In Proc. 36th Symposium on Principles of Database Systems (PODS'17), pages 37-52. ACM, 2017.","title":"Benchmarking the chase","authors":"Michael Benedikt, George Konstantinidis, Giansalvatore Mecca, Boris Motik, Paolo Papotti, Donatello Santoro, Efthymia Tsamoura","year":"2017","venue":"Proc. 36th Symposium on Principles of Database Systems (PODS'17)","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Carral et al., 2017] David Carral, Irina Dragoste, and Markus Krötzsch. Restricted chase (non)termination for existential rules with disjunctions. In Proc. 26th Int. Joint Conf. on Artif. Intell. (IJCAI'17), pages 922-928. ijcai.org, 2017.","title":"Restricted chase (non)termination for existential rules with disjunctions","authors":"David Carral, Irina Dragoste, Markus Krötzsch","year":"2017","venue":"Proc. 26th Int. Joint Conf. on Artif. Intell. (IJCAI'17)","doi":null,"url":null,"internal_url":"/proceedings/2017/128"},{"position":10,"raw":"[Carral et al., 2018] David Carral, Irina Dragoste, and Markus Krötzsch. The combined approach to query an- swering in Horn-ALCHOIQ. In Proc. 16th Int. Conf. on Principles of Knowledge Representation and Reason- ing (KR'18), pages 339-348. AAAI Press, 2018.","title":"The combined approach to query answering in Horn-ALCHOIQ","authors":"David Carral, Irina Dragoste, Markus Krötzsch","year":"2018","venue":"Proc. 16th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR'18)","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Carral et al., 2019] David Carral, Irina Dragoste, Markus Krötzsch, and Christian Lewe. Chasing sets: How to use existential rules for expressive reasoning (extended techni- cal report). Available at https://iccl.inf.tu-dresden.de/web/ Inproceedings3212/en, 2019.","title":"Chasing sets: How to use existential rules for expressive reasoning (extended technical report","authors":"David Carral, Irina Dragoste, Markus Krötzsch, Christian Lewe","year":"2019","venue":null,"doi":null,"url":"https://iccl.inf.tu-dresden.de/web/Inproceedings3212/en","internal_url":null},{"position":12,"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. Artif. Intell. Res., 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. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":13,"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":14,"raw":"[Deutsch et al., 2008] Alin Deutsch, Alan Nash, and Jef- frey B. Remmel. The chase revisited. In Proc. 27th Sympo- sium on Principles of Database Systems (PODS'08), pages 149-158. ACM, 2008.","title":"The chase revisited","authors":"Alin Deutsch, Alan Nash, Jeffrey B Remmel","year":"2008","venue":"Proc. 27th Symposium on Principles of Database Systems (PODS'08)","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Geerts et al., 2014] Floris Geerts, Giansalvatore Mecca, Paolo Papotti, and Donatello Santoro. That's all folks! LLUNATIC goes open source. PVLDB, 7(13):1565-1568, 2014.","title":"That's all folks! LLUNATIC goes open source","authors":"Floris Geerts, Giansalvatore Mecca, Paolo Papotti, Donatello Santoro","year":"2014","venue":"PVLDB","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Gottlob et al., 2014] Georg Gottlob, Sebastian Rudolph, and Mantas Simkus. Expressiveness of guarded existential rule languages. In Proc. 33rd ACM SIGMOD-SIGACT- SIGART Symposium on Principles of Database Systems (PODS'14), pages 27-38. ACM, June 2014.","title":"Expressiveness of guarded existential rule languages","authors":"Gottlob","year":"2014","venue":"Proc. 33rd ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems (PODS'14)","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Kazakov, 2009] Yevgeny Kazakov. Consequence-driven reasoning for Horn SHIQ ontologies. In Proc. 21st Int. Joint Conf. on Artif. Intell. (IJCAI'09), pages 2040-2045. IJCAI, 2009.","title":"Consequence-driven reasoning for Horn SHIQ ontologies","authors":"Yevgeny Kazakov","year":"2009","venue":"Proc. 21st Int. Joint Conf. on Artif. Intell. (IJCAI'09)","doi":null,"url":null,"internal_url":"/proceedings/2009/336"},{"position":18,"raw":"[Krötzsch et al., 2013] Markus Krötzsch, Sebastian Rudolph, and Pascal Hitzler. Complexities of Horn description logics. ACM Trans. Comput. Logic, 14(1):2:1- 2:36, 2013.","title":"Complexities of Horn description logics","authors":"Markus Krötzsch, Sebastian Rudolph, Pascal Hitzler","year":"2013","venue":"ACM Trans. Comput. Logic","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Krötzsch, 2011] Markus Krötzsch. Efficient rule-based in- ferencing for OWL EL. In Proc. 22nd Int. Joint Conf. on Artif. Intell. (IJCAI'11), pages 2668-2673. AAAI Press/IJCAI, 2011.","title":"Efficient rule-based inferencing for OWL EL","authors":"Markus Krötzsch","year":"2011","venue":"Proc. 22nd Int. Joint Conf. on Artif. Intell. (IJCAI'11)","doi":null,"url":null,"internal_url":"/proceedings/2011/444"},{"position":20,"raw":"[Krötzsch et al., 2019] Markus Krötzsch, Maximilian Marx, and Sebastian Rudolph. The power of the terminat- ing chase. In Proc. 22nd Int. Conf. on Database Theory (ICDT'19), volume 127 of LIPIcs, pages 3:1- 3:17. Schloss Dagstuhl -Leibniz-Zentrum fuer Informatik, 2019.","title":"The power of the terminating chase","authors":"Krötzsch","year":"2019","venue":"Proc. 22nd Int. Conf. on Database Theory (ICDT'19)","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Nenov et al., 2015] Yavor Nenov, Robert Piro, Boris Motik, Ian Horrocks, Zhe Wu, and Jay Banerjee. RDFox: A highly-scalable RDF store. In Proc. 14th Int. Semantic Web Conf. (ISWC'15), Part II, volume 9367 of LNCS, pages 3-20. Springer, 2015.","title":"RDFox: A highly-scalable RDF store","authors":"Yavor Nenov, Robert Piro, Boris Motik, Ian Horrocks, Zhe Wu, Jay Banerjee","year":"2015","venue":"Proc. 14th Int. Semantic Web Conf. (ISWC'15), Part II","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Ortiz et al., 2010] Magdalena Ortiz, Sebastian Rudolph, and Mantas Simkus. Worst-case optimal reasoning for the Horn-DL fragments of OWL 1 and 2. In Proc. 12th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR'10), pages 269-279. AAAI Press, 2010.","title":"Worst-case optimal reasoning for the Horn-DL fragments of OWL 1 and 2","authors":"Magdalena Ortiz, Sebastian Rudolph, Mantas Simkus","year":"2010","venue":"Proc. 12th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR'10)","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Simančík et al., 2011] František Simančík, Yevgeny Kaza- kov, and Ian Horrocks. Consequence-based reasoning be- yond Horn ontologies. In Proc. 22nd Int. Joint Conf. on Artif. Intell. (IJCAI'11), pages 1093-1098. AAAI Press/IJCAI, 2011.","title":"Consequence-based reasoning beyond Horn ontologies","authors":"Simančík","year":"2011","venue":"Proc. 22nd Int. Joint Conf. on Artif. Intell. (IJCAI'11)","doi":null,"url":null,"internal_url":"/proceedings/2011/187"},{"position":24,"raw":"[Steigmiller et al., 2014] Andreas Steigmiller, Thorsten Liebig, and Birte Glimm. Konclude: System description. J. Web Semant., 27-28:78-85, 2014.","title":"Konclude: System description","authors":"Andreas Steigmiller, Thorsten Liebig, Birte Glimm","year":"2014","venue":"J. Web Semant","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Urbani et al., 2016] Jacopo Urbani, Ceriel Jacobs, and Markus Krötzsch. Column-oriented Datalog materializa- tion for large knowledge graphs. In Proc. 30th AAAI Conf. on Artif. Intell. (AAAI'16), pages 258-264. AAAI Press, 2016.","title":"Column-oriented Datalog materialization for large knowledge graphs","authors":"Urbani","year":"2016","venue":"Proc. 30th AAAI Conf. on Artif. Intell. (AAAI'16)","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Urbani et al., 2018] Jacopo Urbani, Markus Krötzsch, Ceriel J. H. Jacobs, Irina Dragoste, and David Carral. Efficient model construction for Horn logic with VLog: System description. In Proc. 9th Int. Joint Conf. on Automated Reasoning (IJCAR'18), volume 10900 of LNCS, pages 680-688. Springer, 2018.","title":"Efficient model construction for Horn logic with VLog: System description","authors":"Jacopo Urbani, Markus Krötzsch, J H Ceriel, Irina Jacobs, David Dragoste, Carral","year":"2018","venue":"Proc. 9th Int. Joint Conf. on Automated Reasoning (IJCAR'18)","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Zhou et al., 2015] Yujiao Zhou, Bernardo Cuenca Grau, Ya- vor Nenov, Mark Kaminski, and Ian Horrocks. PAGOdA: Pay-as-you-go ontology query answering using a Datalog reasoner. J. of Artif. Intell. Res., 54:309-367, 2015.","title":"PAGOdA: Pay-as-you-go ontology query answering using a Datalog reasoner","authors":"Yujiao Zhou, Bernardo Cuenca Grau, Yavor Nenov, Mark Kaminski, Ian Horrocks","year":"2015","venue":"J. of Artif. Intell. Res","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}