  We investigate determining the exact bounds of the frequencies of
conjunctions based on frequent sets. Our scenario is an important special case
of some general probabilistic logic problems that are known to be intractable.
We show that despite the limitations our problems are also intractable, namely,
we show that checking whether the maximal consistent frequency of a query is
larger than a given threshold is NP-complete and that evaluating the Maximum
Entropy estimate of a query is PP-hard. We also prove that checking consistency
is NP-complete.
