One of the most well-studied problems in data mining is mining for
association rules in market basket data.  Association rules, whose
significance is measured via support and confidence, are intended to
identify rules of the type, ``A customer purchasing item A often
also purchases item B.''  Motivated by the goal of generalizing
beyond market baskets and the association rules used with them, we
develop the notion of mining rules that identify correlations
(generalizing associations), and we consider both the absence and
presence of items as a basis for generating rules.  We propose
measuring significance of associations via the chi-squared test for
correlation from classical statistics.  This leads to a measure that
is upward closed in the itemset lattice, enabling us to reduce the
mining problem to the search for a border between correlated and
uncorrelated itemsets in the lattice. We develop pruning strategies 
and devise an efficient algorithm for the resulting
problem. We demonstrate its effectiveness by testing it on census data
and finding term dependence in a corpus of text documents, as well as
on synthetic data.