Skip to main content
SpringerLink
Log in

“Properties of Finite Lattices” by S. Reeg and W. Weiß, Revisited

In Memoriam Peter Burmeister (1941–2019)

  • 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

We review an attribute exploration form 1990, which was never published, although the results are impressive. We suggest a method for making implication lists better readable and demonstrate its effect on the canonical basis obtained from that exploration by Reeg and Weiß.

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

Access this chapter

Log in via an institution
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

Notes

  1. 1.

    \(x\wedge y=x\wedge z\) and \(x\vee z=y\vee z\) together imply \(x\le z\).

  2. 2.

    I recently learnt from A. Hotho and G. Stumme that my construction is very similar to that of the canonical cover for functional dependencies [10].

  3. 3.

    Note that in our example we have sometimes split such implications in two, one of which is contained in Fig. 2, the other in Fig. 5.

References

  1. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1998). https://doi.org/10.1007/978-3-642-59830-2

    Book  MATH  Google Scholar 

  2. Burmeister, P.: ConImp: Ein Programm zur Formalen Begriffsanalyse. In: [11], pp. 25–56

    Google Scholar 

  3. Reeg, S., Weiß, W.: Properties of finite lattices. Master’s thesis, Technische Universität Darmstadt (1990) (Diplomarbeit)

    Google Scholar 

  4. Stern, M.: Semimodular Lattices. Teubner, Stuttgart (1991)

    Book  Google Scholar 

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

    Book  MATH  Google Scholar 

  6. Birkhoff, G.: Lattice Theory, 3rd edn. Volume 25 of Colloquium Publications. American Mathematical Society, Providence (1967)

    Google Scholar 

  7. Crawley, P., Dilworth, R.: Algebraic Theory of Lattices. Prentice-Hall, Englewood Cliffs (1973)

    MATH  Google Scholar 

  8. Grätzer, G.: General Lattice Theory. Birkhäuser Verlag, Basel (2003)

    MATH  Google Scholar 

  9. Wille, R.: Halbkomplementäre Verbände. Math. Zeitschrift 94, 1–31 (1966)

    Article  MathSciNet  Google Scholar 

  10. Kemper, A., Eickler, A.: Datenbanksysteme: Eine Einführung. Oldenbourg (2009)

    Google Scholar 

  11. Stumme, G., Wille, R. (eds.): Begriffliche Wissensverarbeitung – Methoden und Anwendungen. Springer, Heidelberg (2000)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Algebra, Technische Universität Dresden, Dresden, Germany

    Bernhard Ganter

Authors
  1. Bernhard Ganter
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bernhard Ganter .

Editor information

Editors and Affiliations

  1. Babeș-Bolyai University, Cluj-Napoca, Romania

    Diana Cristea

  2. University of Strasbourg, ENGEES, Strasbourg, France

    Florence Le Ber

  3. Frankfurt University of Applied Sciences, Frankfurt, Germany

    Baris Sertkaya

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

Ganter, B. (2019). “Properties of Finite Lattices” by S. Reeg and W. Weiß, Revisited. 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_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-21462-3_8

  • 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

Search

Navigation