James Buckley, Jennifer Seitzer, Yongzhi Zhang, and Yi Pan
Data mining is the process of extracting implicit, previously unknown, and potentially useful information from data in databases. It is widely recognized as a useful tool for decision making and knowledge discovery. Rule mining, however, is computationally expensive. Moreover, certain mathematical properties of mined rules have been given little attention. This paper applies logical identities to mined rules thereby producing additional rules that are much more efficiently acquired. We use simple properties of set theory to present a set of theorems applicable to association rules, and by using the support and confidence of mined association rules, we produce new association rules, each with its own support and confidence.