Many human diseases are attributable to complex interactions among genetic and environmental factors. Statistical tools capable of modeling such complex interactions are necessary to improve identification of genetic factors that increase a patient's risk of disease. Logic Forest (LF), a bagging ensemble algorithm based on logic regression (LR), is able to discover interactions among binary variables predictive of response such as the biologic interactions that predispose individuals to disease. However, LF's ability to recover interactions degrades for more infrequently occurring interactions. A rare genetic interaction may occur if, for example, the interaction increases disease risk in a patient subpopulation that represents only a small proportion of the overall patient population. We present an alternative ensemble adaptation of LR based on boosting rather than bagging called LBoost. We compare the ability of LBoost and LF to identify variable interactions in simulation studies. Results indicate that LBoost is superior to LF for identifying genetic interactions associated with disease that are infrequent in the population. We apply LBoost to a subset of single nucleotide polymorphisms on the PRDX genes from the Cancer Genetic Markers of Susceptibility Breast Cancer Scan to investigate genetic risk for breast cancer. LBoost is publicly available on CRAN as part of the LogicForest package, http://cran.r-project.org/.