Advertisement

Which Concept Lattices Are Pseudocomplemented?

  • Bernhard Ganter
  • Léonard Kwuida
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3403)

Abstract

We give a contextual characterization of pseudocomplementation by means of the arrow relations.

AMS Subject Classification: 06D15

Keywords

lattices pseudocomplement closure operator Formal Concept Analysis arrow-relation complete homomorphism 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BD74]
    Balbes, R., Dwinger, P.: Distributive lattices. University of Missouri Press (1974)Google Scholar
  2. [CG00]
    Chajda, I., Glazek, K.: A basic course on general algebra. Technical University Press, Zielona Góra (2000)Google Scholar
  3. [CM93]
    Chameni Nembua, C., Monjardet, B.: Finite pseudocomplemented lattices and “permutoedre”. Discrete Math. 111(1-3), 105–112 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  4. [GW99]
    Ganter, B., Wille, R.: Formal Concept Analysis – Mathematical Foundations. Springer, Heidelberg (1999)zbMATHGoogle Scholar
  5. [Gr71]
    Grätzer, G.: Lattice Theory. First concepts and distributive lattices. W.H. Freeman and Company, New York (1971)zbMATHGoogle Scholar
  6. [Ka80]
    Katrinak, T.: P-algebras. Contributions to lattice theory, Szeged/Hung (1980), Colloq. Math. Soc. Janos Bolyai 33, 549–573 (1983)Google Scholar
  7. [Kw04]
    Kwuida, L.: Dicomplemented lattices. A contextual generalization of Boolean algebras. Dissertation, TU Dresden (2004)Google Scholar
  8. [Lee70]
    Lee, K.B.: Equational classes of distributive pseudo-complemented lattices. Can. J. Math. 22, 881–891 (1970)zbMATHCrossRefGoogle Scholar
  9. [Sc88]
    Schmid, J.: Lee classes and sentences for pseudo-complemented semilattices. Algebra Univers. 25(2), 223–232 (1988)zbMATHCrossRefGoogle Scholar
  10. [So98]
    Sofronie-Stokkermans, V.: Representation theorems and automated theorem proving in certain classes of non-classical logics. In: Proceedings of the ECAI 1998, workshop on many-valued Logic for AI applications (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Bernhard Ganter
    • 1
  • Léonard Kwuida
    • 1
  1. 1.Institut für AlgebraTU DresdenDresdenGermany

Personalised recommendations