Why concept lattices are large: extremal theory for generators, concepts, and VC-dimension
Alexandre Albano, Bogdan Chornomaz · International Journal of General Systems · 2017
A unique type of subcontexts is always present in formal contexts with many concepts: the contranominal scales. We make this precise by giving an upper bound for the number of minimal generators (and thereby for the number of concepts) of contexts without contranominal scales larger than a given size. We give an interpretation of this bound in terms of the Vapnik–Chervonenkis dimension of the concept lattice. Extremal contexts are constructed which meet this bound exactly. They are completely classified.