Entailment and symmetry in confirmation measures of interestingness

In a recent paper Greco et al. (2012) propose a number of properties for measures of rule interestingness. The most fundamental of these properties is that such measures should be Bayesian confirmation measures and this criterion provides the context for the current paper as well. They also propose a number of properties relating to entailment and symmetry in order to discriminate between various confirmation measures which have been proposed in the literature. Working within the same framework of confirmation measures, several limitations of their proposed properties are discussed and a motivation provided for alternative properties. Two new measures of interestingness are proposed and then compared with two other recently proposed measures which also satisfy these properties.