When modeling cell signaling networks, a balance must be struck between mechanistic detail and ease of interpretation. In this paper we apply a fuzzy logic framework to the analysis of a large, systematic dataset describing the dynamics of cell signaling downstream of TNF, EGF, and insulin receptors in human colon carcinoma cells. Simulations based on fuzzy logic recapitulate most features of the data and generate several predictions involving pathway crosstalk and regulation. We uncover a relationship between MK2 and ERK pathways that might account for the previously identified pro-survival influence of MK2. We also find unexpected inhibition of IKK following EGF treatment, possibly due to down-regulation of autocrine signaling. More generally, fuzzy logic models are flexible, able to incorporate qualitative and noisy data, and powerful enough to produce quantitative predictions and new biological insights about the operation of signaling networks.