Association Rules Discovery is an increasing subdomain of Datamining. Many works have focused on the extraction and the evaluation of the association rules, leading to many technical improvments on the algorithms, and many different measures. But few number of them have tried to merge the both. We introduce here a formal framework for the study of association rules and interestingness measures that allows an analytic study of these objects. This framework is based on the contingency table of a rule and let us make a link between analytic properties of the measures and algorithmic properties. We give as example the case of three algorithmic properties for the extraction of association rules that were generalized and applied with the help of this framework. These properties allow a pruning of the search space based on a large number of measures and without any support constraint.