Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

Data Graphs with Incomplete Information (and a Way to Complete Them)

  • Conference paper
  • First Online:
Logics in Artificial Intelligence (JELIA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14281))

Included in the following conference series:

  • 494 Accesses

Abstract

We introduce a modal language for reasoning about data graphs with incomplete information. Such data graphs are formally represented as models in which data value functions are partial—to capture what is unknown. In this setting, we also allow for unknown data values to be learned. Our main result is a sound and strongly complete axiomatization for the logic.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Abriola, S., Barceló, P., Figueira, D., Figueira, S.: Bisimulations on data graphs. J. Artif. Intell. Res. 61, 171–213 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  2. Abriola, S., Cifuentes, S., Martinez, M., Pardal, N., Pin, E.: An epistemic approach to model uncertainty in data-graphs. Int. J. Approximate Reason. 160, 108948 (2023)

    Article  MathSciNet  MATH  Google Scholar 

  3. Abriola, S., Descotte, M.E., Fervari, R., Figueira, S.: Axiomatizations for downward XPath on data trees. J. Comput. Syst. Sci. 89, 209–245 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  4. Angles, R., Gutiérrez, C.: Survey of graph database models. ACM Comput. Surv. 40(1), 1:1-1:39 (2008)

    Article  Google Scholar 

  5. Areces, C., ten Cate, B.: Hybrid logics. In: Handbook of Modal Logic, pp. 821–868. Elsevier (2006)

    Google Scholar 

  6. Areces, C., Fervari, R.: Axiomatizing hybrid XPath with data. Log. Methods Comput. Sci. 17(3) (2021)

    Google Scholar 

  7. Areces, C., Fervari, R., Hoffmann, G.: Relation-changing modal operators. Logic J. IGPL 23(4), 601–627 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  8. Areces, C., Fervari, R., Seiler, N.: Tableaux for hybrid XPath with data. In: Oliveira, E., Gama, J., Vale, Z., Lopes Cardoso, H. (eds.) EPIA 2017. LNCS (LNAI), vol. 10423, pp. 611–623. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-65340-2_50

    Chapter  Google Scholar 

  9. Arenas, M., Fan, W., Libkin, L.: On verifying consistency of XML specifications. In: 21st ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems (PODS 2002), pp. 259–270. ACM (2002)

    Google Scholar 

  10. Aucher, G., van Benthem, J., Grossi, D.: Modal logics of sabotage revisited. J. Logic Comput. 28(2), 269–303 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  11. Baelde, D., Lunel, S., Schmitz, S.: A sequent calculus for a modal logic on finite data trees. In: 25th EACSL Annual Conference on Computer Science Logic (CSL 2016), LIPIcs, vol. 62, pp. 32:1–32:16. Schloss Dagstuhl (2016)

    Google Scholar 

  12. Barceló, P., Libkin, L., Reutter, J.L.: Querying regular graph patterns. J. ACM 61(1), 81–854 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  13. Blackburn, P., van Benthem, J., Wolter, F.: Handbook of Modal Logic. Elsevier, Amsterdam (2006)

    MATH  Google Scholar 

  14. Blackburn, P., ten Cate, B.: Pure extensions, proof rules, and hybrid axiomatics. Stud. Logica. 84(2), 277–322 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  15. Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic, Cambridge Tracts in Theoretical Computer Science, vol. 53. Cambridge University Press (2001)

    Google Scholar 

  16. Bojańczyk, M., Muscholl, A., Schwentick, T., Segoufin, L.: Two-variable logic on data trees and XML reasoning. J. ACM 56(3) (2009)

    Google Scholar 

  17. Braüner, T.: Hybrid Logics and its Proof-Theory, Applied Logics Series, vol. 37. Springer, Cham (2011). https://doi.org/10.1007/978-94-007-0002-4

  18. ten Cate, B., Fontaine, G., Litak, T.: Some modal aspects of XPath. J. Appl. Non-Class. Logics 20(3), 139–171 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  19. ten Cate, B., Litak, T., Marx, M.: Complete axiomatizations for XPath fragments. J. Appl. Logic 8(2), 153–172 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  20. Clark, J., DeRose, S.: XML path language (XPath). Website (1999). W3C Recommendation. http://www.w3.org/TR/xpath

  21. van Dalen, D.: Logic and Structure, 5th edn. Springer, Berlin (2013). https://doi.org/10.1007/978-3-540-85108-0

    Book  MATH  Google Scholar 

  22. Figueira, D.: Reasoning on Words and Trees with Data. PhD thesis, Laboratoire Spécification et Vérification, ENS Cachan, France (2010)

    Google Scholar 

  23. Figueira, D.: Decidability of downward XPath. ACM Trans. Comput. Logic 13(4), 34 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  24. Goldblatt, R.: An abstract setting for Henkin proofs. Topoi 3(1), 37–41 (1984)

    Article  MathSciNet  Google Scholar 

  25. Gottlob, G., Koch, C., Pichler, R.: Efficient algorithms for processing XPath queries. ACM Trans. Database Syst. 30(2), 444–491 (2005)

    Article  Google Scholar 

  26. Grabon, M., Michaliszyn, J., Otop, J., Wieczorek, P.: Querying data graphs with arithmetical regular expressions. In: 25th International Joint Conference on Artificial Intelligence (IJCAI 2016), pp. 1088–1094. IJCAI/AAAI Press (2016)

    Google Scholar 

  27. Libkin, L., Martens, W., Vrgoč, D.: Querying graphs with data. J. ACM 63(2), 14:1-14:53 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  28. Libkin, L., Vrgoč, D.: Regular path queries on graphs with data. In: International Conference on Database Theory (ICDT 2012), pp. 74–85. ACM (2012)

    Google Scholar 

  29. Plaza, J.: Logics of public communications. Synthese 158(2), 165–179 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  30. Robinson, I., Webber, J., Eifrem, E.: Graph Databases. O’Reilly Media Inc., Newton (2013)

    Google Scholar 

  31. Schinner, A.: The Voynich manuscript: evidence of the hoax hypothesis. Cryptologia 31(2), 95–107 (2007)

    Article  MATH  Google Scholar 

Download references

Acknowledgments

We thank the reviewers for their valuable comments. Our work is supported by the Laboratoire International Associé SINFIN, the EU Grant Agreement 101008233 (MISSION), the ANPCyT projects PICT-2020-3780, PICT-2021-00400, PICT-2021-00675, and PICTO-2022-CBA-00088, and the CONICET projects PIBAA-28720210100428CO, PIBAA-28720210100165CO, and PIP-11220200100812CO.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Valentin Cassano .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Areces, C., Cassano, V., Dutto, D., Fervari, R. (2023). Data Graphs with Incomplete Information (and a Way to Complete Them). In: Gaggl, S., Martinez, M.V., Ortiz, M. (eds) Logics in Artificial Intelligence. JELIA 2023. Lecture Notes in Computer Science(), vol 14281. Springer, Cham. https://doi.org/10.1007/978-3-031-43619-2_49

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-43619-2_49

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-43618-5

  • Online ISBN: 978-3-031-43619-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics