Overdiagnosis is a phenomenon in which screening identities cancer which may not go on to cause symptoms or death. Women over 65 who develop breast cancer bear the heaviest burden of overdiagnosis. This work introduces novel machine learning algorithms to improve diagnostic accuracy of breast cancer in aging populations. At the same time, we aim at minimizing unnecessary invasive procedures (thus decreasing false positives) and concomitantly addressing overdiagnosis. We develop a novel algorithm. Logical Differential Prediction Bayes Net (LDP-BN), that calculates the risk of breast disease based on mammography findings. LDP-BN uses Inductive Logic Programming (ILP) to learn relational rules, selects older-specific differentially predictive rules, and incorporates them into a Bayes Net, significantly improving its performance. In addition, LDP-BN offers valuable insight into the classification process, revealing novel older-specific rules that link mass presence to invasive, and calcification presence and lack of detectable mass to DCIS.