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Erschienen in:
2005 | OriginalPaper | Buchkapitel
Semiconcept and Protoconcept Algebras: The Basic Theorems
verfasst von : Björn Vormbrock, Rudolf Wille
Erschienen in: Formal Concept Analysis
Verlag: Springer Berlin Heidelberg
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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.