On the size of ∃ -generalized concept lattices

Formal Concept Analysis (FCA) offers several tools for qualitative data analysis. One
possibility is to group objects that share common attributes together and get a concept
lattice that describes the data. Quite often the size of this concept lattice is very large.
Many authors have investigated methods to reduce the size of this lattice. In Kwuida
et al. (2014) the authors consider putting together some attributes to reduce the size of
the attribute sets. But this reduction does not always carry over to the set of concepts.
They provided some counter examples where the size of the concept lattice increases
by one after putting two attributes together, and asked the following question: ‘‘How
many new concepts can be generated by an ∃-generalization on just two attributes?’’
The present paper provides a family of contexts for which the size increases on more
than one concept after putting solely two attributes together.