Abstract
Concept algebras are concept lattices enriched by a weak negation and a weak opposition. In Ganter and Kwuida (Contrib. Gen. Algebra, 14:63–72, 2004) we gave a contextual description of the lattice of weak negations on a finite lattice. In this contribution1 we use this description to give a characterization of finite distributive concept algebras.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, New York, Second Edition (2002)
Ganter, B.: Congruence of finite distributive concept algebras. In: Lecture Notes in Computer Science, vol. 2961, pp. 128–141. Springer, Berlin Heidelberg New York (2004)
Ganter, B., Kwuida, L.: Representable weak dicomplementations on finite lattices. Contrib. Gen. Algebra 14, 63–72 (2004) (J. Heyn Klagenfurt)
Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Berlin Heidelberg New York (1999)
Kwuida, L.: Dicomplemented lattices. A contextual generalization of Boolean algebras. Shaker Verlag, Aachen (2004)
Wille, R.: Boolean concept logic. In: Lecture Notes in Computer Scince, vol. 1867, pp. 317–331. Springer, Berlin Heidelberg New York (2000)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ganter, B., Kwuida, L. Finite Distributive Concept Algebras. Order 23, 235–248 (2006). https://doi.org/10.1007/s11083-006-9045-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11083-006-9045-x
Key words
- formal concept analysis
- negation
- concept algebras
- weakly dicomplemented lattices
- superalgebraic lattices