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Closure systems, implicational systems, overhanging relations and the case of hierarchical classification. (English) Zbl 1059.93007

The authors investigate Moore families and closure operators, especially those appearing in hierarchical classification, from the point of view of their related implicational systems and overhanging relations. They establish which properties distinguish hierarchies among Moore families and give a new proof of a theorem of Adams. They also characterize canonical implication bases of hierarchies and obtain a similar results for overhangings.

MSC:

93A13 Hierarchical systems
06A15 Galois correspondences, closure operators (in relation to ordered sets)
68T30 Knowledge representation
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