Many biological and clinical outcomes are based not on single proteins, but on modules of proteins embedded in protein networks. A fundamental question is how the proteins within each module contribute to the overall module activity. Here, we study the modules underlying three representative biological programs related to tissue development, breast cancer metastasis, or progression of brain cancer, respectively. For each case we apply a new method, called Network-Guided Forests, to identify predictive modules together with logic functions which tie the activity of each module to the activity of its component genes. The resulting modules implement a diverse repertoire of decision logic which cannot be captured using the simple approximations suggested in previous work such as gene summation or subtraction. We show that in cancer, certain combinations of oncogenes and tumor suppressors exert competing forces on the system, suggesting that medical genetics should move beyond cataloguing individual cancer genes to cataloguing their combinatorial logic.