New property for rule interestingness measures

The paper considers interestingness measures for evaluation of rules induced from data with respect to two properties: property of Bayesian confirmation and property Ex
1
concerning the behavior of measures in case of entailment or refutation of the conclusion by the rule's premise. We demonstrate that property Ex
1
, even though created for confirmation measures, does not fully reflect the concept of confirmation. We propose a modification of this property, called weak Ex
1
, that deploys the concept of confirmation in its larger sense and allows to escape paradoxes that might appear when using measures satisfying the original Ex
1
property.