Skip to main content

Learning Implications from Data and from Queries

  • Conference paper
  • First Online:
Formal Concept Analysis (ICFCA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11511))

Included in the following conference series:

Abstract

In this paper, we consider computational problems related to finding implications in an explicitly given formal context or via queries to an oracle. We are concerned with two types of problems: enumerating implications (or association rules) and finding a single implication satisfying certain conditions. We present complexity results for some of these problems and leave others open. The paper is not meant as a comprehensive survey, but rather as a subjective selection of interesting problems.

Supported by the Russian Science Foundation (grant 17-11-01294).

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 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 74.99
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

References

  1. Adaricheva, K., Nation, J.: Discovery of the D-basis in binary tables based on hypergraph dualization. Theor. Comput. Sci. 658, 307–315 (2017)

    Article  MathSciNet  Google Scholar 

  2. Angluin, D.: Queries and concept learning. Mach. Learn. 2(4), 319–342 (1988)

    MathSciNet  Google Scholar 

  3. Angluin, D., Frazier, M., Pitt, L.: Learning conjunctions of Horn clauses. Mach. Learn. 9(2–3), 147–164 (1992)

    MATH  Google Scholar 

  4. Angluin, D., Kriis, M., Sloan, R.H., Turán, G.: Malicious omissions and errors in answers to membership queries. Mach. Learn. 28(2), 211–255 (1997)

    Article  Google Scholar 

  5. Angluin, D., Slonim, D.K.: Randomly fallible teachers: learning monotone DNF with an incomplete membership oracle. Mach. Learn. 14(1), 7–26 (1994)

    MATH  Google Scholar 

  6. Arias, M., Balcázar, J.L.: Construction and learnability of canonical Horn formulas. Mach. Learn. 85(3), 273–297 (2011)

    Article  MathSciNet  Google Scholar 

  7. Arias, M., Balcázar, J.L., Tîrnăucă, C.: Learning definite Horn formulas from closure queries. Theor. Comput. Sci. 658(Part B), 346–356 (2017)

    Article  MathSciNet  Google Scholar 

  8. Baader, F., Ganter, B., Sertkaya, B., Sattler, U.: Completing description logic knowledge bases using formal concept analysis. In: Veloso, M.M. (ed.) Proceedings IJCAI 2007, pp. 230–235. AAAI Press (2007)

    Google Scholar 

  9. Babin, M.A., Kuznetsov, S.O.: Computing premises of a minimal cover of functional dependencies is intractable. Discrete Appl. Math. 161(6), 742–749 (2013)

    Article  MathSciNet  Google Scholar 

  10. Bertet, K., Monjardet, B.: The multiple facets of the canonical direct unit implicational basis. Theor. Comput. Sci. 411(22), 2155–2166 (2010)

    Article  MathSciNet  Google Scholar 

  11. Borchmann, D., Hanika, T., Obiedkov, S.: On the usability of probably approximately correct implication bases. In: Bertet, K., Borchmann, D., Cellier, P., Ferré, S. (eds.) ICFCA 2017. LNCS (LNAI), vol. 10308, pp. 72–88. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59271-8_5

    Chapter  Google Scholar 

  12. Borchmann, D., Hanika, T., Obiedkov, S.: Probably approximately correct learning of Horn envelopes from queries. Discrete Appl. Math. (2019, in press)

    Google Scholar 

  13. Distel, F.: Hardness of enumerating pseudo-intents in the lectic order. In: Kwuida and Sertkaya [25], pp. 124–137

    Chapter  Google Scholar 

  14. Distel, F., Sertkaya, B.: On the complexity of enumerating pseudo-intents. Discrete Appl. Math. 159(6), 450–466 (2011)

    Article  MathSciNet  Google Scholar 

  15. Ganter, B.: Two basic algorithms in concept analysis. In: Kwuida and Sertkaya [25], pp. 312–340

    Chapter  Google Scholar 

  16. Ganter, B., Obiedkov, S.: Conceptual Exploration. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49291-8

    Book  MATH  Google Scholar 

  17. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999). https://doi.org/10.1007/978-3-642-59830-2

    Book  MATH  Google Scholar 

  18. Guigues, J.L., Duquenne, V.: Famille minimale d’implications informatives résultant d’un tableau de données binaires. Mathématiques et Sciences Humaines 24(95), 5–18 (1986)

    Google Scholar 

  19. Hanika, T., Zumbrägel, J.: Towards collaborative conceptual exploration. In: Chapman, P., Endres, D., Pernelle, N. (eds.) ICCS 2018. LNCS (LNAI), vol. 10872, pp. 120–134. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-91379-7_10

    Chapter  Google Scholar 

  20. Jäschke, R., Rudolph, S.: Attribute exploration on the web. Preprint (2013). www.qucosa.de

  21. Kautz, H., Kearns, M., Selman, B.: Horn approximations of empirical data. Artif. Intell. 74(1), 129–145 (1995)

    Article  MathSciNet  Google Scholar 

  22. Khardon, R.: Translating between Horn representations and their characteristic models. J. Artif. Intell. Res. (JAIR) 3, 349–372 (1995)

    Article  Google Scholar 

  23. Kryszkiewicz, M.: Concise representations of association rules. In: Hand, D.J., Adams, N.M., Bolton, R.J. (eds.) Pattern Detection and Discovery. LNCS (LNAI), vol. 2447, pp. 92–109. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45728-3_8. ISBN 978-3-540-45728-2

    Chapter  Google Scholar 

  24. Kuznetsov, S.O.: Fitting pattern structures to knowledge discovery in big data. In: Cellier, P., Distel, F., Ganter, B. (eds.) ICFCA 2013. LNCS (LNAI), vol. 7880, pp. 254–266. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38317-5_17

    Chapter  Google Scholar 

  25. Kwuida, L., Sertkaya, B. (eds.): ICFCA 2010. LNCS (LNAI), vol. 5986. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-11928-6

    Book  MATH  Google Scholar 

  26. Obiedkov, S., Romashkin, N.: Collaborative conceptual exploration as a tool for crowdsourcing domain ontologies. In: Proceedings of Russian and South African Workshop on Knowledge Discovery Techniques Based on Formal Concept Analysis, CEUR Workshop Proceedings, vol. 1552, pp. 58–70 (2015)

    Google Scholar 

  27. Wild, M.: The joy of implications, aka pure Horn formulas: mainly a survey. Theoretical Computer Science 658, 264–292 (2017)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sergei Obiedkov .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Obiedkov, S. (2019). Learning Implications from Data and from Queries. In: Cristea, D., Le Ber, F., Sertkaya, B. (eds) Formal Concept Analysis. ICFCA 2019. Lecture Notes in Computer Science(), vol 11511. Springer, Cham. https://doi.org/10.1007/978-3-030-21462-3_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-21462-3_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-21461-6

  • Online ISBN: 978-3-030-21462-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics