Generating complete sublattices by methods of formal concept analysis

We present a solution to the problem of finding the complete sublattice of a given concept lattice generated by a given set of elements. We construct the closed subrelation of the corresponding incidence relation whose concept lattice is equal to the desired complete sublattice. The construction does not require the presence of the original concept lattice. We introduce an efficient algorithm for the construction and give an example and experiments. We also study a related problem of characterizing complete sublattices of a given concept lattice that are given by a general subrelation of the incidence relation.