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The Power of the Terminating Chase (Invited Talk)

Authors Markus Krötzsch , Maximilian Marx , Sebastian Rudolph



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Markus Krötzsch
  • TU Dresden, Germany
Maximilian Marx
  • TU Dresden, Germany
Sebastian Rudolph
  • TU Dresden, Germany

Acknowledgements

We thank David Carral for his comments on an earlier version of this paper.

Cite AsGet BibTex

Markus Krötzsch, Maximilian Marx, and Sebastian Rudolph. The Power of the Terminating Chase (Invited Talk). In 22nd International Conference on Database Theory (ICDT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 127, pp. 3:1-3:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.ICDT.2019.3

Abstract

The chase has become a staple of modern database theory with applications in data integration, query optimisation, data exchange, ontology-based query answering, and many other areas. Most application scenarios and implementations require the chase to terminate and produce a finite universal model, and a large arsenal of sufficient termination criteria is available to guarantee this (generally undecidable) condition. In this invited tutorial, we therefore ask about the expressive power of logical theories for which the chase terminates. Specifically, which database properties can be recognised by such theories, i.e., which Boolean queries can they realise? For the skolem (semi-oblivious) chase, and almost any known termination criterion, this expressivity is just that of plain Datalog. Surprisingly, this limitation of most prior research does not apply to the chase in general. Indeed, we show that standard - chase terminating theories can realise queries with data complexities ranging from PTime to non-elementary that are out of reach for the terminating skolem chase. A "Datalog-first" standard chase that prioritises applications of rules without existential quantifiers makes modelling simpler - and we conjecture: computationally more efficient. This is one of the many open questions raised by our insights, and we conclude with an outlook on the research opportunities in this area.

Subject Classification

ACM Subject Classification
  • Theory of computation → Database query languages (principles)
  • Theory of computation → Complexity theory and logic
  • Theory of computation → Database constraints theory
  • Theory of computation → Logic and databases
Keywords
  • Existential rules
  • Tuple-generating dependencies
  • all-instances chase termination
  • expressive power
  • data complexity

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References

  1. Serge Abiteboul, Richard Hull, and Victor Vianu. Foundations of Databases. Addison Wesley, 1994. Google Scholar
  2. Alfred V. Aho, Catriel Beeri, and Jeffrey D. Ullman. The Theory of Joins in Relational Databases. ACM Trans. Database Syst., 4(3):297-314, 1979. Google Scholar
  3. Jean-François Baget, Michel Leclère, Marie-Laure Mugnier, and Eric Salvat. On rules with existential variables: Walking the decidability line. Artificial Intelligence, 175(9-10):1620-1654, 2011. Google Scholar
  4. Jean-François Baget, Michel Leclère, Marie-Laure Mugnier, Swan Rocher, and Clément Sipieter. Graal: A Toolkit for Query Answering with Existential Rules. In Nick Bassiliades, Georg Gottlob, Fariba Sadri, Adrian Paschke, and Dumitru Roman, editors, Proc. 9th Int. Web Rule Symposium (RuleML'15), volume 9202 of LNCS, pages 328-344. Springer, 2015. Google Scholar
  5. Bruce L. Bauslaugh. Core-like properties of infinite graphs and structures. Discrete Math., 138(1):101-111, 1995. Google Scholar
  6. Catriel Beeri and Moshe Y. Vardi. The Implication Problem for Data Dependencies. In Shimon Even and Oded Kariv, editors, Proc. 8th Colloquium on Automata, Languages and Programming (ICALP'81), volume 115 of LNCS, pages 73-85. Springer, 1981. Google Scholar
  7. Catriel Beeri and Moshe Y. Vardi. A Proof Procedure for Data Dependencies. J. ACM, 31(4):718-741, 1984. Google Scholar
  8. Michael Benedikt, George Konstantinidis, Giansalvatore Mecca, Boris Motik, Paolo Papotti, Donatello Santoro, and Efthymia Tsamoura. Benchmarking the Chase. In Proc. 36th Symposium on Principles of Database Systems (PODS'17), pages 37-52. ACM, 2017. Google Scholar
  9. Angela Bonifati, Ioana Ileana, and Michele Linardi. Functional Dependencies Unleashed for Scalable Data Exchange. In Peter Baumann, Ioana Manolescu-Goujot, Luca Trani, Yannis E. Ioannidis, Gergely Gábor Barnaföldi, László Dobos, and Evelin Bányai, editors, Proc. 28th Int. Conf. on Scientific and Statistical Database Management (SSDBM'16), pages 2:1-2:12. ACM, 2016. Google Scholar
  10. Marco Calautti and Andreas Pieris. Oblivious Chase Termination: The Sticky Case. In Proc. 22nd Int. Conf. on Database Theory (ICDT'19). Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2019. Google Scholar
  11. 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. Google Scholar
  12. David Carral, Irina Dragoste, and Markus Krötzsch. Restricted Chase (Non)Termination for Existential Rules with Disjunctions. In Carles Sierra, editor, Proc. 26th Int. Joint Conf. on Artificial Intelligence (IJCAI'17), pages 922-928. ijcai.org, 2017. Google Scholar
  13. David Carral, Markus Krötzsch, Maximilian Marx, Ana Ozaki, and Sebastian Rudolph. Preserving Constraints with the Stable Chase. In Benny Kimelfeld and Yael Amsterdamer, editors, Proc. 21st Int. Conf. on Database Theory (ICDT'18), volume 98 of LIPIcs, pages 12:1-12:19. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2018. Google Scholar
  14. Stefano Ceri, Georg Gottlob, and Letizia Tanca. Logic Programming and Databases. Springer, 1990. Google Scholar
  15. Bernardo Cuenca Grau, Ian Horrocks, Markus Krötzsch, Clemens Kupke, Despoina Magka, Boris Motik, and Zhe Wang. Acyclicity Notions for Existential Rules and Their Application to Query Answering in Ontologies. J. of Artificial Intelligence Research, 47:741-808, 2013. Google Scholar
  16. Evgeny Dantsin, Thomas Eiter, Georg Gottlob, and Andrei Voronkov. Complexity and Expressive Power of Logic Programming. ACM Computing Surveys, 33(3):374-425, 2001. Google Scholar
  17. Anuj Dawar and Stephan Kreutzer. On Datalog vs. LFP. In Luca Aceto, Ivan Damgård, Leslie Ann Goldberg, Magnús M. Halldórsson, Anna Ingólfsdóttir, and Igor Walukiewicz, editors, Proc. 35th Int. Colloquium on Automata, Languages, and Programming (ICALP'08); Part II, volume 5126 of LNCS, pages 160-171. Springer, 2008. Google Scholar
  18. Stathis Delivorias, Michel Leclère, Marie-Laure Mugnier, and Federico Ulliana. On the k-Boundedness for Existential Rules. In Christoph Benzmüller, Francesco Ricca, Xavier Parent, and Dumitru Roman, editors, Proc. 2nd Int. Joint Conf. on Rules and Reasoning (RuleML+RR'18), volume 11092 of LNCS, pages 48-64. Springer, 2018. Google Scholar
  19. Alin Deutsch, Alan Nash, and Jeffrey B. Remmel. The Chase Revisited. In Maurizio Lenzerini and Domenico Lembo, editors, Proc. 27th Symposium on Principles of Database Systems (PODS'08), pages 149-158. ACM, 2008. Google Scholar
  20. Ronald Fagin, Phokion G. Kolaitis, Renée J. Miller, and Lucian Popa. Data exchange: semantics and query answering. Theoretical Computer Science, 336(1):89-124, 2005. Google Scholar
  21. Floris Geerts, Giansalvatore Mecca, Paolo Papotti, and Donatello Santoro. That’s All Folks! LLUNATIC Goes Open Source. PVLDB, 7(13):1565-1568, 2014. Google Scholar
  22. Tomasz Gogacz and Jerzy Marcinkowski. All-Instances Termination of Chase is Undecidable. In Javier Esparza, Pierre Fraigniaud, Thore Husfeldt, and Elias Koutsoupias, editors, Proc. 41st Int. Colloquium on Automata, Languages, and Programming (ICALP'14); Part II, volume 8573 of LNCS, pages 293-304. Springer, 2014. Google Scholar
  23. Gösta Grahne and Adrian Onet. Anatomy of the Chase. Fundam. Inform., 157(3):221-270, 2018. Google Scholar
  24. Pavol Hell and Jaroslav Nešetřil. The core of a graph. Discrete Math., 109:117-126, 1992. Google Scholar
  25. Markus Krötzsch and Sebastian Rudolph. Extending Decidable Existential Rules by Joining Acyclicity and Guardedness. In Toby Walsh, editor, Proc. 22nd Int. Joint Conf. on Artificial Intelligence (IJCAI'11), pages 963-968. AAAI Press/IJCAI, 2011. Google Scholar
  26. David Maier, Alberto O. Mendelzon, and Yehoshua Sagiv. Testing implications of data dependencies. ACM Transactions on Database Systems, 4:455-469, 1979. Google Scholar
  27. Bruno Marnette. Generalized Schema-Mappings: from Termination to Tractability. In Jan Paredaens and Jianwen Su, editors, Proc. 28th Symposium on Principles of Database Systems (PODS'09), pages 13-22. ACM, 2009. Google Scholar
  28. Michael Meier, Michael Schmidt, and Georg Lausen. On Chase Termination Beyond Stratification. PVLDB, 2(1):970-981, 2009. Google Scholar
  29. Michaël Thomazo Michel Leclére, Marie-Laure Mugnier and Federico Ulliana. A Single Approach to Decide Chase Termination on Linear Existential Rules. CoRR, abs/1810.02132, 2018. URL: http://arxiv.org/abs/1810.02132.
  30. Boris Motik, Yavor Nenov, Robert Piro, Ian Horrocks, and Dan Olteanu. Parallel Materialisation of Datalog Programs in Centralised, Main-Memory RDF Systems. In Proc. 28th AAAI Conf. on Artif. Intell. (AAAI'14), pages 129-137. AAAI Press, 2014. Google Scholar
  31. Sebastian Rudolph. The Two Views on Ontological Query Answering. In Georg Gottlob and Jorge Pérez, editors, Proc. 8th Alberto Mendelzon Workshop on Foundations of Data Management (AMW'14), volume 1189 of CEUR Workshop Proceedings. CEUR-WS.org, 2014. Google Scholar
  32. Sebastian Rudolph and Michaël Thomazo. Characterization of the Expressivity of Existential Rule Queries. In Qiang Yang and Michael Wooldridge, editors, Proc. 24th Int. Joint Conf. on Artificial Intelligence (IJCAI'15), pages 3193-3199. AAAI Press, 2015. Google Scholar
  33. Sebastian Rudolph and Michaël Thomazo. Expressivity of Datalog Variants - Completing the Picture. In Subbarao Kambhampati, editor, Proc. 25th Int. Joint Conf. on Artificial Intelligence (IJCAI'15), pages 1230-1236. AAAI Press, 2016. Google Scholar
  34. Andreas Pieris Tomasz Gogacz, Jerzy Marcinkowski. All-Instances Restricted Chase Termination: The Guarded Case. CoRR, abs/1901.03897, 2019. URL: http://arxiv.org/abs/1901.03897.
  35. Jacopo Urbani, Markus Krötzsch, Ceriel J. H. Jacobs, Irina Dragoste, and David Carral. Efficient Model Construction for Horn Logic with VLog: System description. In Didier Galmiche, Stephan Schulz, and Roberto Sebastiani, editors, Proc. 9th Int. Joint Conf. on Automated Reasoning (IJCAR'18), volume 10900 of LNCS, pages 680-688. Springer, 2018. Google Scholar
  36. Heng Zhang, Yan Zhang, and Jia-Huai You. Existential Rule Languages with Finite Chase: Complexity and Expressiveness. In Blai Bonet and Sven Koenig, editors, Proc. 29th AAAI Conf. on Artificial Intelligence (AAAI'15). AAAI Press, 2015. Google Scholar
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