Semiconcept and Protoconcept Algebras: The Basic Theorems

  • Björn Vormbrock
  • Rudolf Wille
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3626)


The concern of this paper is to elaborate a basic understanding of semiconcepts and protoconcepts as notions of Formal Concept Analysis. First, semiconcepts and protoconcepts are motivated by their use for effectively describing formal concepts. It is shown that one can naturally operate with those units of description, namely with operations which constitute algebras of semiconcepts and algebras of protoconcepts as so-called double Boolean algebras. The main results of this paper are the two basic theorems which characterize semiconcept resp. protoconcept algebras as pure resp. fully contextual double Boolean algebras whose related Boolean algebras are complete and atomic. Those theorems may, for instance, be applied to check whether line diagram representations of semiconcept and protoconcept algebras are correct.


Boolean Algebra Formal Concept Conceptual Structure Concept Lattice Formal Context 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Björn Vormbrock
    • 1
  • Rudolf Wille
    • 1
  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadt

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