Galois connection between sets of objects from a subject domain and their ordered descriptions define a closure operator and respective closed sets of objects and closed descriptions, which make two antitone lattices. When descriptions are sets of attributes, these two lattices make a concept (Galois) lattice, studied in Formal Concept Analysis (FCA). On the one hand, the lattice of closed descriptions gives a taxonomy of a subject domain, where each class of objects is given by its specific closed description. On the other hand, the closure operator gives a natural definition of implicative dependencies related to functional dependencies and Horn formulas. The lattice diagram gives a natural concise representation of all association rules that hold in the domain. We consider relationships between various knowledge discovery models naturally described in terms of lattices of closed descriptions and present respective results on algorithmic complexity.