Studying Interest Measures for Association Rules through a Logical Model

Many papers have addressed the task of proposing a set of convenient axioms that a good rule interestingness measure should fulfil. We provide a new study of the principles proposed until now by means of the logic model proposed by Hajek et al.14 In this model association rules can be viewed as general relations of two itemsets quantified by means of a convenient quantifier.28 Moreover, we propose and justify the addition of two new principles to the three proposed by Piatetsky-Shapiro.27 We also use the logic approach for studying the relation between the different classes of quantifiers and these axioms. We define new classes of quantifiers according to the notions of strong and very strong rules, and we present a quantifier based on the certainty factor measure,317 studying its most salient features.