?Mining association rules on large data sets has received considerable attention in recent years. Association rules are useful for determining correlations between attributes of a relation and have applications in marketing, financial, and retail sectors. Furthermore, optimized association rules are an effective way to focus on the most interesting characteristics involving certain attributes. Optimized association rules are permitted to contain uninstantiated attributes and the problem is to determine instantiations such that either the support or confidence of the rule is maximized. In this paper, we generalize the optimized association rules problem in three ways: 1) association rules are allowed to contain disjunctions over uninstantiated attributes, 2) association rules are permitted to contain an arbitrary number of uninstantiated attributes, and 3) uninstantiated attributes can be either categorical or numeric. Our generalized association rules enable us to extract more useful i...