Assessing rules with interestingness measures is the cornerstone of successful applications of association rule discovery. However, there exists no information-theoretic measure which is adapted to the semantics of association rules. In this article, we present the Directed Information Ratio (DIR), a new rule interestingness measure which is based on information theory. DIR is specially designed for association rules, and in particular it differentiates two opposite rules a --> b and a --> non(b). Moreover, to our knowledge, DIR is the only rule interestingness measure which rejects both independence and (what we call) equilibrium, i.e. it discards both the rules whose antecedent and consequent are negatively correlated, and the rules which have more counter-examples than examples. Experimental studies show that DIR is a very filtering measure, which is useful for association rule post-processing.