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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 Ex1 concerning the behavior of measures in case of entailment or refutation of the conclusion by the rule's premise. We demonstrate that property Ex1, even though created for confirmation measures, does not fully reflect the concept of confirmation. We propose a modification of this property, called weak Ex1, that deploys the concept of confirmation in its larger sense and allows to escape paradoxes that might appear when using measures satisfying the original Ex1 property.