Upper Bound for the Number of Concepts of Contranominal-Scale Free Contexts

We show an improvement of Prisner’s upper bound for the number of concepts of a formal context. The improvement factor is of the order ( max {|G|,|M|}) c , where c is the size of the biggest contranominal scale that can be found as a subcontext. We also prove that the c ∈ O(1) condition is necessary to establish that an arbitrary sequence of contexts has a polynomial number of concepts, by constructing a lower bound. Complexity aspects of calculating c are discussed.