Skip to main content

Structural and Computational Properties of Possibilistic Armstrong Databases

  • Conference paper
  • First Online:
Conceptual Modeling (ER 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12400))

Included in the following conference series:

  • 2105 Accesses

Abstract

We investigate structural and computational properties of Armstrong databases for a new class of possibilistic functional dependencies. We establish sufficient and necessary conditions for a given possibilistic relation to be Armstrong for a given set of possibilistic functional dependencies. We then use the characterization to compute Armstrong databases for any given set of these dependencies. The problem of finding an Armstrong database is precisely exponential in the input, but our algorithm computes an output whose size is always guaranteed to be at most quadratic in a minimum-sized output. Extensive experiments indicate that our algorithm shows good computational behavior on average. As our possibilistic functional dependencies have important applications in database design, our results indicate that Armstrong databases can effectively support business analysts during the acquisition of functional dependencies that are meaningful in a given application domain.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Notes

  1. 1.

    https://www.dropbox.com/s/fciy01597tgxnfu/Possibilistic-Armstrong-Calculator.exe.

References

  1. Arenas, M.: Normalization theory for XML. SIGMOD Rec. 35(4), 57–64 (2006)

    Article  Google Scholar 

  2. Balamuralikrishna, N., Jiang, Y., Koehler, H., Leck, U., Link, S., Prade, H.: Possibilistic keys. Fuzzy Sets Syst. 376, 1–36 (2019)

    Article  MathSciNet  Google Scholar 

  3. Beeri, C., Dowd, M., Fagin, R., Statman, R.: On the structure of Armstrong relations for functional dependencies. J. ACM 31(1), 30–46 (1984)

    Article  MathSciNet  Google Scholar 

  4. Brown, P., Link, S.: Probabilistic keys. IEEE Trans. Knowl. Data Eng. 29(3), 670–682 (2017)

    Article  Google Scholar 

  5. Calì, A., Calvanese, D., Lenzerini, M.: Data integration under integrity constraints. In: Seminal Contributions to Information Systems Engineering, 25 Years of CAiSE, pp. 335–352 (2013)

    Google Scholar 

  6. Codd, E.F.: A relational model of data for large shared data banks. Commun. ACM 13(6), 377–387 (1970)

    Article  Google Scholar 

  7. Dubois, D., Prade, H.: Possibility theory and its applications: where do we stand? In: Kacprzyk, J., Pedrycz, W. (eds.) Springer Handbook of Computational Intelligence, pp. 31–60. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-43505-2_3

    Chapter  MATH  Google Scholar 

  8. Fagin, R.: Horn clauses and database dependencies. J. ACM 29(4), 952–985 (1982)

    Article  MathSciNet  Google Scholar 

  9. Johnson, D.S., Klug, A.C.: Testing containment of conjunctive queries under functional and inclusion dependencies. J. Comput. Syst. Sci. 28(1), 167–189 (1984)

    Article  MathSciNet  Google Scholar 

  10. Köhler, H., Link, S.: SQL schema design: foundations, normal forms, and normalization. Inf. Syst. 76, 88–113 (2018)

    Article  Google Scholar 

  11. Langeveldt, W.D., Link, S.: Empirical evidence for the usefulness of Armstrong relations in the acquisition of meaningful functional dependencies. Inf. Syst. 35(3), 352–374 (2010)

    Article  Google Scholar 

  12. Link, S., Prade, H.: Possibilistic functional dependencies and their relationship to possibility theory. IEEE Trans. Fuzzy Syst. 24, 1–7 (2016)

    Article  Google Scholar 

  13. Link, S., Prade, H.: Relational database schema design for uncertain data. Inf. Syst. 84, 88–110 (2019)

    Article  Google Scholar 

  14. Mannila, H., Räihä, K.J.: Design by example: an application of Armstrong relations. J. Comput. Syst. Sci. 33(2), 126–141 (1986)

    Article  MathSciNet  Google Scholar 

  15. Marnette, B., Mecca, G., Papotti, P.: Scalable data exchange with functional dependencies. Proc. VLDB Endow. 3(1), 105–116 (2010)

    Article  Google Scholar 

  16. Prokoshyna, N., Szlichta, J., Chiang, F., Miller, R.J., Srivastava, D.: Combining quantitative and logical data cleaning. Proc. VLDB Endow. 9(4), 300–311 (2015)

    Article  Google Scholar 

  17. Ram, S.: Deriving functional dependencies from the entity-relationship model. Commun. ACM 38(9), 95–107 (1995)

    Article  Google Scholar 

  18. Roblot, T., Hannula, M., Link, S.: Probabilistic cardinality constraints - validation, reasoning, and semantic summaries. VLDB J. 27(6), 771–795 (2018)

    Article  Google Scholar 

  19. Roblot, T., Link, S.: Cardinality constraints and functional dependencies over possibilistic data. Data Knowl. Eng. 117, 339–358 (2018)

    Article  Google Scholar 

  20. Selman, B., Kautz, H.A.: Knowledge compilation and theory approximation. J. ACM 43(2), 193–224 (1996)

    Article  MathSciNet  Google Scholar 

  21. Tan, H.B.K., Zhao, Y.: Automated elicitation of functional dependencies from source codes of database transactions. Inf. Software Technol. 46(2), 109–117 (2004)

    Article  Google Scholar 

  22. Vincent, M.: Semantic foundations of 4NF in relational database design. Acta Inf. 36(3), 173–213 (1999)

    Article  MathSciNet  Google Scholar 

  23. Wei, Z., Hartmann, S., Link, S.: Discovery algorithms for embedded functional dependencies. In: Maier, D., Pottinger, R., Doan, A., Tan, W., Alawini, A., Ngo, H.Q. (eds.) Proceedings of the 2020 International Conference on Management of Data, SIGMOD Conference 2020, Online Conference [Portland, OR, USA], June 14–19, 2020. pp. 833–843. ACM (2020)

    Google Scholar 

  24. Wei, Z., Leck, U., Link, S.: Discovery and ranking of embedded uniqueness constraints. Proc. VLDB Endow. 12(13), 2339–2352 (2019)

    Article  Google Scholar 

  25. Wei, Z., Link, S.: Embedded functional dependencies and data-completeness tailored database design. Proc. VLDB Endow. 12(11), 1458–1470 (2019)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sebastian Link .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Jeong, S., Ma, H., Wei, Z., Link, S. (2020). Structural and Computational Properties of Possibilistic Armstrong Databases. In: Dobbie, G., Frank, U., Kappel, G., Liddle, S.W., Mayr, H.C. (eds) Conceptual Modeling. ER 2020. Lecture Notes in Computer Science(), vol 12400. Springer, Cham. https://doi.org/10.1007/978-3-030-62522-1_43

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-62522-1_43

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-62521-4

  • Online ISBN: 978-3-030-62522-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics