Signaling events that direct mouse embryonic stem (ES) cell self-renewal and differentiation are complex and accordingly difficult to understand in an integrated manner. We address this problem by adapting a Bayesian network learning algorithm to model proteomic signaling data for ES cell fate responses to external cues. Using this model we were able to characterize the signaling pathway influences as quantitative, logic-circuit type interactions. Our experimental dataset includes measurements for 28 signaling protein phosphorylation states across 16 different factorial combinations of cytokine and matrix stimuli as reported previously.