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When Is a Concept Algebra Boolean?

  • Léonard Kwuida
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2961)

Abstract

Concept algebras are concept lattices enriched by a weak negation and a weak opposition. The introduction of these two operations was motivated by the search of a negation on formal concepts. These weak operations form a weak dicomplementation. A weakly dicomplemented lattice is a bounded lattice equipped with a weak dicomplementation. (Weakly) dicomplemented lattices abstract (at least for finite distributive lattices) concept algebras. Distributive double p-algebras and Boolean algebras are some special subclasses of the class of weakly dicomplemented lattices. We investigate in the present work the connection between weak dicomplementations and complementation notions like semicomplementation, pseudocomplementation, complementation or orthocomplementation.

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References

  1. 1.
    Balbes, R., Dwinger, P.: Distributive lattices. University of Missouri Press (1974)Google Scholar
  2. 2.
    Boole, G.: An investigation of the laws of thought on which are founded the mathematical theories of logic and probabilities. Macmillan, Basingstoke (1854); Reprinted by Dover Publ., New york (1958)Google Scholar
  3. 3.
    Ganter, B., Kwuida, L.: Representing weak dicomplementations on finite distributive lattices. Preprint MATH-AL-10-2002Google Scholar
  4. 4.
    Grätzer, G.: Distributive Lattices. Springer, Heidelberg (1970)Google Scholar
  5. 5.
    Gramaglia, H., Vaggione, D.: A note on distributive double p-algebras. Czech. Math. J. 48(2), 321–327 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Ganter, B., Wille, R.: Formal Concept Analysis. Mathematical Foundations. Springer, Heidelberg (1999)zbMATHGoogle Scholar
  7. 7.
    Katriňák, T.: The structure of distributive double p-algebras. Regularity and congruences. Algebra Universalis 3(2), 238–246 (1973)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Wille, R.: Boolean Concept Logic. In: Ganter, B., Mineau, G.W. (eds.) ICCS 2000. LNCS, vol. 1867, Springer, Heidelberg (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Léonard Kwuida
    • 1
  1. 1.Institut für AlgebraTU DresdenDresden

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