Logic models of signaling pathways are a promising way of building effective in silico functional models of a cell. The automated learning of Boolean logic models describing signaling pathways can be achieved by training to phosphoproteomics data. This data is unavoidably subject to noise. As a result, the learning process results in a family of feasible logical networks rather than in a single model. This family is composed of logic models proposing different internal wirings for the system, implying that the logical predictions from this family may suffer a significant level of variability leading to uncertainty. In this talk we will survey how combinatorial optimization methods based on recent logic programming paradigm allow for enumerating, controlling and discriminating the family of logical explaining data. Together, these approaches enable a robust understanding of the system response.