Complete subalgebras of semiconcept algebras and protoconcept algebras

Authors:
Björn Vormbrock
Affiliations:
Fachbereich Mathematik, Technische Universität Darmstadt, Darmstadt, D
Venue:
ICFCA'05 Proceedings of the Third international conference on Formal Concept Analysis
Year:
2005

Citing 4
Cited 0

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Abstract

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.