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Tuple-Generating Dependencies Capture Complex Values

Authors Maximilian Marx , Markus Krötzsch

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Author Details

Maximilian Marx
  • Knowledge-Based Systems Group, TU Dresden, Germany
Markus Krötzsch
  • Knowledge-Based Systems Group, TU Dresden, Germany

Funding

This work is partly supported by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) in project number 389792660 (TRR 248, https://www.perspicuous-computing.science/), by the Bundesministerium für Bildung und Forschung (BMBF, Federal Ministry of Education and Research) in the https://www.scads.de (ScaDS.AI), and by the Center for Advancing Electronics Dresden (cfaed).

Acknowledgements

We would like to thank the anonymous reviewers for their detailed feedback that led to this revised version of the paper.

Cite As Get BibTex

Maximilian Marx and Markus Krötzsch. Tuple-Generating Dependencies Capture Complex Values. In 25th International Conference on Database Theory (ICDT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 220, pp. 13:1-13:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.ICDT.2022.13

Abstract

We formalise a variant of Datalog that allows complex values constructed by nesting elements of the input database in sets and tuples. We study its complexity and give a translation into sets of tuple-generating dependencies (TGDs) for which the standard chase terminates on any input database. We identify a fragment for which reasoning is tractable. As membership is undecidable for this fragment, we develop decidable sufficient conditions.

Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity theory and logic
  • Theory of computation → Constraint and logic programming
  • Theory of computation → Logic and databases
Keywords
  • terminating standard chase
  • existential rules
  • Datalog
  • complexity

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References

  1. Serge Abiteboul and Stéphane Grumbach. COL: A logic-based language for complex objects. In Joachim W. Schmidt, Stefano Ceri, and Michele Missikoff, editors, Proc. 1st Int. Conf. on Extending Database Technology (EDBT'88), volume 303 of LNCS, pages 271-293. Springer, 1988. Google Scholar
  2. Serge Abiteboul, Richard Hull, and Victor Vianu. Foundations of Databases. Addison Wesley, 1994. Google Scholar
  3. Serge Abiteboul and Paris C. Kanellakis. Object identity as a query language primitive. J. ACM, 45(5):798-842, 1998. Google Scholar
  4. Shqiponja Ahmetaj, Magdalena Ortiz, and Mantas Simkus. Rewriting guarded existential rules into small datalog programs. In Benny Kimelfeld and Yael Amsterdamer, editors, 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. Google Scholar
  5. Renzo Angles, Marcelo Arenas, Pablo Barceló, Peter A. Boncz, George H. L. Fletcher, Claudio Gutiérrez, Tobias Lindaaker, Marcus Paradies, Stefan Plantikow, Juan F. Sequeda, Oskar van Rest, and Hannes Voigt. G-CORE: A core for future graph query languages. In Gautam Das, Christopher M. Jermaine, and Philip A. Bernstein, editors, Proc. 2018 ACM SIGMOD Int. Conf. on Management of Data, pages 1421-1432. ACM, 2018. Google Scholar
  6. Catriel Beeri, Shamim A. Naqvi, Raghu Ramakrishnan, Oded Shmueli, and Shalom Tsur. Sets and negation in a logic database language (LDL1). In Moshe Y. Vardi, editor, Proc. 6th Symposium on Principles of Database Systems (PODS'87), pages 21-37. ACM, 1987. Google Scholar
  7. Catriel Beeri and Moshe Y. Vardi. A proof procedure for data dependencies. J. of the ACM, 31(4):718-741, 1984. Google Scholar
  8. Camille Bourgaux, David Carral, Markus Krötzsch, Sebastian Rudolph, and Michaël Thomazo. Capturing homomorphism-closed decidable queries with existential rules. In Meghyn Bienvenu, Gerhard Lakemeyer, and Esra Erdem, editors, Proc. 18th International Conference on Principles of Knowledge Representation and Reasoning (KR'21), pages 141-150, 2021. Google Scholar
  9. Pierre Bourhis, Juan L. Reutter, and Domagoj Vrgoc. JSON: data model and query languages. Inf. Syst., 89:101478, 2020. Google Scholar
  10. Francesco Calimeri, Susanna Cozza, Giovambattista Ianni, and Nicola Leone. Finitely recursive programs: Decidability and bottom-up computation. J. of AI Commun., 24(4):311-334, 2011. Google Scholar
  11. David Carral, Irina Dragoste, Larry González, Ceriel J. H. Jacobs, Markus Krötzsch, and Jacopo Urbani. Vlog: A rule engine for knowledge graphs. In Chiara Ghidini, Olaf Hartig, Maria Maleshkova, Vojtech Svátek, Isabel F. Cruz, Aidan Hogan, Jie Song, Maxime Lefrançois, and Fabien Gandon, editors, Proc. 18th Int. Semantic Web Conf. (ISWC'19), Part II, volume 11779 of Lecture Notes in Computer Science, pages 19-35. Springer, 2019. Google Scholar
  12. David Carral, Irina Dragoste, and Markus Krötzsch. Reasoner = logical calculus + rule engine. KI, 2020. Google Scholar
  13. David Carral, Irina Dragoste, Markus Krötzsch, and Christian Lewe. Chasing sets: How to use existential rules for expressive reasoning. In Sarit Kraus, editor, Proc. 28th Int. Joint Conf. on Artificial Intelligence (IJCAI'19). ijcai.org, 2019. Google Scholar
  14. Angelos Charalambidis, Christos Nomikos, and Panos Rondogiannis. The expressive power of higher-order datalog. Theory Pract. Log. Program., 19(5-6):925-940, 2019. 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. 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
  18. Alin Deutsch and Val Tannen. Reformulation of XML queries and constraints. In Diego Calvanese, Maurizio Lenzerini, and Rajeev Motwani, editors, Proc. 9th Int. Conf. on Database Theory (ICDT'03), volume 2572 of LNCS, pages 225-241. Springer, 2003. Google Scholar
  19. 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
  20. Georg Gottlob, Marco Manna, and Andreas Pieris. Polynomial rewritings for linear existential rules. In Qiang Yang and Michael Wooldridge, editors, Proc. 24th Int. Joint Conf. on Artificial Intelligence (IJCAI'15), pages 2992-2998. AAAI Press, 2015. Google Scholar
  21. Georg Gottlob and Christos H. Papadimitriou. On the complexity of single-rule datalog queries. Inf. Comput., 183(1):104-122, 2003. Google Scholar
  22. Marc Gyssens, Dan Suciu, and Dirk Van Gucht. Equivalence and normal forms for the restricted and bounded fixpoint in the nested algebra. Inf. Comput., 164(1):85-117, 2001. Google Scholar
  23. Jan Hidders, Jan Paredaens, and Jan Van den Bussche. J-logic: Logical foundations for JSON querying. In Emanuel Sallinger, Jan Van den Bussche, and Floris Geerts, editors, Proc. 36th Symposium on Principles of Database Systems (PODS'17), pages 137-149. ACM, 2017. Google Scholar
  24. Narendra Karmarkar. A new polynomial-time algorithm for linear programming. Combinatorica, 4(4):373-396, 1984. Google Scholar
  25. Michael Kifer and James Wu. A logic for programming with complex objects. J. of Comput. Syst. Sci., 47(1):77-120, 1993. Google Scholar
  26. Markus Krötzsch, Maximilian Marx, and Sebastian Rudolph. The power of the terminating 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. Google Scholar
  27. Gabriel M. Kuper. Logic programming with sets. J. of Comput. Syst. Sci., 41(1):44-64, 1990. Google Scholar
  28. Mengchi Liu. Relationlog: A typed extension to datalog with sets and tuples. J. of Log. Program., 36(3):271-299, 1998. Google Scholar
  29. David Martin and Peter F. Patel-Schneider. Wikidata constraints on MARS. In Lucie-Aimée Kaffee, Oana Tifrea-Marciuska, Elena Simperl, and Denny Vrandečić, editors, Proc. 1st Wikidata Workshop (Wikidata 2020), volume 2773 of CEUR Workshop Proceedings. CEUR-WS.org, 2020. Google Scholar
  30. Maximilian Marx, Markus Krötzsch, and Veronika Thost. Logic on MARS: Ontologies for generalised property graphs. In Carles Sierra, editor, Proc. 26th Int. Joint Conf. on Artificial Intelligence (IJCAI'17), pages 1188-1194. ijcai.org, 2017. Google Scholar
  31. Yavor Nenov, Robert Piro, Boris Motik, Ian Horrocks, Zhe Wu, and Jay Banerjee. Rdfox: A highly-scalable RDF store. In Marcelo Arenas, Óscar Corcho, Elena Simperl, Markus Strohmaier, Mathieu d'Aquin, Kavitha Srinivas, Paul Groth, Michel Dumontier, Jeff Heflin, Krishnaprasad Thirunarayan, and Steffen Staab, editors, Proc. 14th Int. Semantic Web Conf. (ISWC'15), Part II, volume 9367 of Lecture Notes in Computer Science, pages 3-20. Springer, 2015. Google Scholar
  32. Magdalena Ortiz, Sebastian Rudolph, and Mantas Simkus. Worst-case optimal reasoning for the Horn-DL fragments of OWL 1 and 2. In Fangzhen Lin, Ulrike Sattler, and Miroslaw Truszczynski, editors, Proc. 12th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR'10), pages 269-279. AAAI Press, 2010. Google Scholar
  33. Jan Paredaens and Dirk Van Gucht. Converting nested algebra expressions into flat algebra expressions. ACM Trans. Database Syst., 17(1):65-93, 1992. Google Scholar
  34. Marko A. Rodriguez and Peter Neubauer. Constructions from dots and lines. Bulletin of the American Society for Information Science and Technology, 36(6):35-41, 2010. Google Scholar
  35. Michael Rudolf, Marcus Paradies, Christof Bornhövd, and Wolfgang Lehner. The graph story of the SAP HANA database. In Datenbanksysteme für Business, Technologie und Web (BTW), 15. Fachtagung des GI-Fachbereichs "Datenbanken und Informationssysteme" (DBIS), 11.-15.3.2013 in Magdeburg, Germany. Proceedings, pages 403-420, 2013. Google Scholar
  36. Dan Suciu. Bounded fixpoints for complex objects. Theor. Comput. Sci., 176(1-2):283-328, 1997. Google Scholar
  37. Shalom Tsur and Carlo Zaniolo. LDL: A logic-based data language. In Wesley W. Chu, Georges Gardarin, Setsuo Ohsuga, and Yahiko Kambayashi, editors, Proc. 12th Int. Conf. on Very Large Data Bases (VLDB'86), pages 33-41. Morgan Kaufmann, 1986. Google Scholar
  38. Denny Vrandečić and Markus Krötzsch. Wikidata: A free collaborative knowledgebase. Commun. ACM, 57(10), 2014. Google Scholar
  39. Qing Zhou and Ligong Long. SEDatalog: A set extension of datalog. In Zhongzhi Shi and Qing He, editors, Proc. 2nd Int. Conf. on Intelligent Information Processing (IFIP'04), volume 163 of IFIP, pages 383-388. Springer, 2004. Google Scholar
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