Skip to main content

Concept Lattice Orbifolds – First Steps

  • Conference paper
Formal Concept Analysis (ICFCA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5548))

Included in the following conference series:

Abstract

Concept lattices with symmetries may be simplified by “folding” them along the orbits of their automorphism group. The resulting diagram is often more intuitive than the full lattice diagram, but well defined annotations are required to make the folded diagram as informative as the original one. The folding procedure can be extended to formal contexts.

A typical situation where such lattice foldings are useful is when hierarchies of structures are considered “up to isomorphisms”.

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Behrisch, M.: Personal communication (2006)

    Google Scholar 

  2. Caspard, N., Monjardet, B.: The lattices of closure systems, closure operators, and implicational systems on a finite set: a survey. Discrete Applied Mathematics 127(2), 241–269 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  3. Habib, M., Nourine, L.: The number of Moore families on n = 6. Discrete Mathematics 294, 291–296 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.4.12 (2008), http://www.gap-system.org

  5. Ganter, B., Reuter, K.: Finding closed sets: a general approach. Order 8, 283–290 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ganter, B., Wille, R.: Formal Concept Analysis – Mathematical Foundations. Springer, Heidelberg (1999)

    Book  MATH  Google Scholar 

  7. Sloane, N.J.A.: The On-Line Encyclopedia of Integer Sequences. Sequences A102896 and A108799, http://www.research.att.com/~njas/sequences/A108799

  8. Zickwolff, M.: Rule Exploration: First Order Logic in Formal Concept Analysis. Dissertation, Darmstadt (1991)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Borchmann, D., Ganter, B. (2009). Concept Lattice Orbifolds – First Steps. In: Ferré, S., Rudolph, S. (eds) Formal Concept Analysis. ICFCA 2009. Lecture Notes in Computer Science(), vol 5548. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01815-2_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-01815-2_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01814-5

  • Online ISBN: 978-3-642-01815-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics