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Semiconcept and Protoconcept Algebras: The Basic Theorems

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Formal Concept Analysis

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3626))

Abstract

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.

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Vormbrock, B., Wille, R. (2005). Semiconcept and Protoconcept Algebras: The Basic Theorems. In: Ganter, B., Stumme, G., Wille, R. (eds) Formal Concept Analysis. Lecture Notes in Computer Science(), vol 3626. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11528784_2

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  • DOI: https://doi.org/10.1007/11528784_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-27891-7

  • Online ISBN: 978-3-540-31881-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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