Document Open Access Logo

Querying the Unary Negation Fragment with Regular Path Expressions

Authors Jean Christoph Jung, Carsten Lutz, Mauricio Martel, Thomas Schneider

PDF
Thumbnail PDF

File

LIPIcs.ICDT.2018.15.pdf
  • Filesize: 492 kB
  • 18 pages

Document Identifiers

Author Details

Jean Christoph Jung
Carsten Lutz
Mauricio Martel
Thomas Schneider

Cite AsGet BibTex

Jean Christoph Jung, Carsten Lutz, Mauricio Martel, and Thomas Schneider. Querying the Unary Negation Fragment with Regular Path Expressions. In 21st International Conference on Database Theory (ICDT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 98, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.ICDT.2018.15

Abstract

The unary negation fragment of first-order logic (UNFO) has recently been proposed as a generalization of modal logic that shares many of its good computational and model-theoretic properties. It is attractive from the perspective of database theory because it can express conjunctive queries (CQs) and ontologies formulated in many description logics (DLs). Both are relevant for ontology-mediated querying and, in fact, CQ evaluation under UNFO ontologies (and thus also under DL ontologies) can be `expressed' in UNFO as a satisfiability problem. In this paper, we consider the natural extension of UNFO with regular expressions on binary relations. The resulting logic UNFOreg can express (unions of) conjunctive two-way regular path queries (C2RPQs) and ontologies formulated in DLs that include transitive roles and regular expressions on roles. Our main results are that evaluating C2RPQs under UNFOreg ontologies is decidable, 2ExpTime-complete in combined complexity, and coNP-complete in data complexity, and that satisfiability in UNFOreg is 2ExpTime-complete, thus not harder than in UNFO.
Keywords
  • Query Answering
  • Regular Path Queries
  • Decidable Fragments of First-Order Logic
  • Computational Complexity

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Antoine Amarilli, Michael Benedikt, Pierre Bourhis, and Michael Vanden Boom. Query answering with transitive and linear-ordered data. In Proc. IJCAI, pages 893-899, 2016. Google Scholar
  2. Renzo Angles and Claudio Gutiérrez. Survey of graph database models. ACM Comput. Surv., 40(1):1:1-1:39, 2008. Google Scholar
  3. Franz Baader. Augmenting concept languages by transitive closure of roles: An alternative to terminological cycles. In Proc. IJCAI, pages 446-451, 1991. Google Scholar
  4. Franz Baader, Diego Calvanese, Deborah L. McGuinness, Daniele Nardi, and Peter F. Patel-Schneider. The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge Univ. Press, 2nd edition, 2007. Google Scholar
  5. Franz Baader, Ian Horrocks, Carsten Lutz, and Ulrike Sattler. An Introduction to Description Logic. Cambride University Press, 2017. Google Scholar
  6. Jean-François Baget, Michel Leclère, Marie-Laure Mugnier, and Eric Salvat. On rules with existential variables: Walking the decidability line. Artif. Intell., 175(9-10):1620-1654, 2011. Google Scholar
  7. Jean-François Baget, Marie-Laure Mugnier, Sebastian Rudolph, and Michaël Thomazo. Walking the complexity lines for generalized guarded existential rules. In Proc. IJCAI, pages 712-717, 2011. Google Scholar
  8. Vince Bárány, Georg Gottlob, and Martin Otto. Querying the guarded fragment. Logical Methods in Computer Science, 10(2), 2014. Google Scholar
  9. Vince Bárány, Balder ten Cate, and Luc Segoufin. Guarded negation. J. ACM, 62(3):22:1-22:26, 2015. Google Scholar
  10. Pablo Barceló. Querying graph databases. In Proc. PODS, pages 175-188, 2013. Google Scholar
  11. Pablo Barceló, Gerald Berger, and Andreas Pieris. Containment for rule-based ontology-mediated queries. In Proc. PODS, 2018. Google Scholar
  12. Meghyn Bienvenu, Diego Calvanese, Magdalena Ortiz, and Mantas Šimkus. Nested regular path queries in description logics. In Proc. KR, 2014. Google Scholar
  13. 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. IJCAI/AAAI Press, 2016. Google Scholar
  14. Meghyn Bienvenu, Carsten Lutz, and Frank Wolter. Query containment in description logics reconsidered. In Proc. KR. AAAI Press, 2012. Google Scholar
  15. Meghyn Bienvenu and Magdalena Ortiz. Ontology-mediated query answering with data-tractable description logics. In Proc. Reasoning Web, volume 9203 of LNCS, pages 218-307. Springer, 2015. Google Scholar
  16. Meghyn Bienvenu, Magdalena Ortiz, and Mantas Šimkus. Conjunctive regular path queries in lightweight description logics. In Proc. IJCAI, pages 761-767. IJCAI/AAAI, 2013. Google Scholar
  17. Meghyn Bienvenu, Magdalena Ortiz, and Mantas Šimkus. Navigational queries based on frontier-guarded datalog: Preliminary results. In Proc. AMW, volume 1378 of CEUR Workshop Proceedings, 2015. Google Scholar
  18. Meghyn Bienvenu, Magdalena Ortiz, and Mantas Šimkus. Regular path queries in lightweight description logics: Complexity and algorithms. J. Artif. Intell. Res., 53:315-374, 2015. Google Scholar
  19. Meghyn Bienvenu, Balder ten Cate, Carsten Lutz, and Frank Wolter. Ontology-based data access: A study through disjunctive datalog, CSP, and MMSNP. ACM Trans. Database Syst., 39(4):33:1-33:44, 2014. Google Scholar
  20. Pierre Bourhis, Markus Krötzsch, and Sebastian Rudolph. How to best nest regular path queries. In Proc. DL, volume 1193 of CEUR Workshop Proceedings, pages 404-415, 2014. Google Scholar
  21. Pierre Bourhis and Carsten Lutz. Containment in monadic disjunctive datalog, MMSNP, and expressive description logics. In Proc. KR, pages 207-216. AAAI Press, 2016. Google Scholar
  22. Andrea Calì, Georg Gottlob, and Michael Kifer. Taming the infinite chase: Query answering under expressive relational constraints. In Proc. KR, pages 70-80, 2008. Google Scholar
  23. Diego Calvanese, Giuseppe De Giacomo, Domenico Lembo, Maurizio Lenzerini, and Riccardo Rosati. Data complexity of query answering in description logics. Artif. Intell., 195:335-360, 2013. Google Scholar
  24. Diego Calvanese, Giuseppe De Giacomo, Maurizio Lenzerini, and Daniele Nardi. Reasoning in expressive description logics. In Handbook of Automated Reasoning, pages 1581-1634. Elsevier and MIT Press, 2001. Google Scholar
  25. Diego Calvanese, Giuseppe De Giacomo, Maurizio Lenzerini, and Moshe Y. Vardi. Containment of conjunctive regular path queries with inverse. In Proc. KR, pages 176-185, 2000. Google Scholar
  26. Diego Calvanese, Thomas Eiter, and Magdalena Ortiz. Answering regular path queries in expressive description logics: An automata-theoretic approach. In Proc. AAAI, pages 391-396, 2007. Google Scholar
  27. Diego Calvanese, Thomas Eiter, and Magdalena Ortiz. Regular path queries in expressive description logics with nominals. In Proc. IJCAI, pages 714-720, 2009. Google Scholar
  28. Diego Calvanese, Thomas Eiter, and Magdalena Ortiz. Answering regular path queries in expressive description logics via alternating tree-automata. Inf. Comput., 237:12-55, 2014. Google Scholar
  29. Isabel F. Cruz, Alberto O. Mendelzon, and Peter T. Wood. A graphical query language supporting recursion. In Proc. SIGMOD, pages 323-330, 1987. Google Scholar
  30. Michael J. Fischer and Richard E. Ladner. Propositional dynamic logic of regular programs. J. Comput. Syst. Sci., 18(2):194-211, 1979. Google Scholar
  31. Stefan Göller, Markus Lohrey, and Carsten Lutz. PDL with intersection and converse: satisfiability and infinite-state model checking. J. Symb. Log., 74(1):279-314, 2009. Google Scholar
  32. Georg Gottlob, Christoph Koch, and Reinhard Pichler. Efficient algorithms for processing XPath queries. In Proc. VLDB, pages 95-106, 2002. Google Scholar
  33. Georg Gottlob, Giorgio Orsi, Andreas Pieris, and Mantas Šimkus. Datalog and its extensions for semantic web databases. In Proc. Reasoning Web, volume 7487 of LNCS, pages 54-77. Springer, 2012. Google Scholar
  34. Georg Gottlob, Andreas Pieris, and Lidia Tendera. Querying the guarded fragment with transitivity. In Proc. ICALP II, volume 7966 of LNCS, pages 287-298. Springer, 2013. Google Scholar
  35. Erich Grädel. On the restraining power of guards. J. Symb. Log., 64(4):1719-1742, 1999. Google Scholar
  36. Erich Grädel and Igor Walukiewicz. Guarded fixed point logic. In Proc. LICS-99, pages 45-54, 1999. Google Scholar
  37. Roman Kontchakov and Michael Zakharyaschev. An introduction to description logics and query rewriting. In Proc. Reasoning Web, volume 8714 of LNCS, pages 195-244. Springer, 2014. Google Scholar
  38. Adila Krisnadhi and Carsten Lutz. Data complexity in the E:L family of description logics. In Proc. LPAR, volume 4790 of LNCS, pages 333-347. Springer, 2007. Google Scholar
  39. Carsten Lutz. The complexity of conjunctive query answering in expressive description logics. In Proc. IJCAR, volume 5195 of LNCS, pages 179-193. Springer, 2008. Google Scholar
  40. Magdalena Ortiz, Sebastian Rudolph, and Mantas Šimkus. Query answering in the Horn fragments of the description logics SHOIQ and SROIQ. In Proc. IJCAI, pages 1039-1044, 2011. Google Scholar
  41. Antonella Poggi, Domenico Lembo, Diego Calvanese, Giuseppe De Giacomo, Maurizio Lenzerini, and Riccardo Rosati. Linking data to ontologies. J. Data Semantics, 10:133-173, 2008. Google Scholar
  42. Juan L. Reutter, Miguel Romero, and Moshe Y. Vardi. Regular queries on graph databases. Theory Comput. Syst., 61(1):31-83, 2017. Google Scholar
  43. Sebastian Rudolph and Markus Krötzsch. Flag & check: data access with monadically defined queries. In Proc. PODS, pages 151-162, 2013. Google Scholar
  44. Klaus Schild. A correspondence theory for terminological logics: Preliminary report. In Proc. IJCAI, pages 466-471, 1991. Google Scholar
  45. Wiesław Szwast and Lidia Tendera. The guarded fragment with transitive guards. Ann. Pure Appl. Logic, 128(1-3):227-276, 2004. Google Scholar
  46. Balder ten Cate and Luc Segoufin. Unary negation. Logical Methods in Computer Science, 9(3), 2013. Google Scholar
  47. Moshe Y. Vardi. Reasoning about the past with two-way automata. In Proc. ICALP-98, pages 628-641, 1998. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact