Complete Subalgebras of Semiconcept Algebras and Protoconcept Algebras

  • Björn Vormbrock
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3403)


In order to define a negation on formal concepts in Formal Concept Analysis, the more general notions of semiconcepts and protoconcepts were introduced. The theory of the resulting protoconcept and semiconcept algebras is developed in Boolean Concept Logic as a part of Contextual Logic. In this paper it is shown that each complete subalgebra of a semiconcept algebra is itself the semiconcept algebra of an appropriate context. An analogous result holds for the complete subalgebras of protoconcept algebras. These contexts can be obtained from the original context through partitions of the object and the attribute set satisfying certain conditions. Characterizations of the complete subalgebras of semiconcept and protoconcept algebras in terms of contexts, in terms of subsets, and through closed subrelations are given.


Formal Concept Concept Lattice Formal Context Formal Concept Analysis Basic Theorem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Björn Vormbrock
    • 1
  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtD

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