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Some decision and counting problems of the Duquenne-Guigues basis of implications. (English) Zbl 1160.68031

Summary: Implications of a formal context obey Armstrong rules, which allows one to define a minimal (in the number of implications) implication basis, called Duquenne-Guigues basis or stem base in the literature. In this paper we show how implications are reduced to functional dependencies and prove that the problem of determining the size of the stem base is a #P-complete problem.

MSC:

68T30 Knowledge representation
06A15 Galois correspondences, closure operators (in relation to ordered sets)
68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
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