Axiomatization of frequent sets

In data mining association rules are very popular. Most of the algorithms in the literature for finding association rules start by searching for frequent itemsets. The itemset mining algorithms typically interleave brute force counting of frequencies with a meta-phase for pruning parts of the search space. The knowledge acquired in the counting phases can be represented by frequent set expressions. A frequent set expression is a pair containing an itemset and a frequency indicating that the frequency of that itemset is greater than or equal to the given fre-quency. A system of frequent sets is a collection of such expressions. We give an axiomatization for these systems. This axiomatization characterizes complete systems. A system is complete when it explicitly contains all information that it logically implies. Every system of frequent sets has a unique completion. The completion of a system actually represents the knowledge that maximally can be derived in the meta-phase