One of the more well-studied problems in data mining is the search for
association rules in market basket data.  Association rules are
intended to identify patterns of the type: ``A customer purchasing
item A often also purchases item B.''  Motivated partly by the goal of
generalizing beyond market basket data and partly by the goal of
ironing out some problems in the definition of association rules, we
develop the notion of *dependence rules* that identify statistical
dependence in both the presence and absence of items in itemsets.  We
propose measuring significance of dependence via the chi-squared test
for independence 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 dependent and
independent itemsets in the lattice.  We develop pruning strategies
based on the closure property and thereby devise an efficient
algorithm for discovering dependence rules.  We demonstrate our
algorithm's effectiveness by testing it on census data, text data
(wherein we seek term dependence), and synthetic data.