Curated cellular signaling databases such as Reactome, Panther and NCI are approaching or exceeding many metabolic models. Conventional tools used for signal transduction models are unsuited for modeling networks with 1,000+ let alone 10,000+ entities. While catalytic cascades cancel the advantage of flux balance modeling (and flux model formulation carries significant overheads), a direct logical translation of biochemical reaction networks is possible. Moreover, a biochemical interpretation of inhibition overcomes a common problem of Boolean formulation and greatly reduces logical incoherence in large models. Using efficient pruning strategies and a linearly scalable algorithm, it is possible on a standard PC to compute all minimal (unique) input sets from 2909 sources capable of generating each of 1851 outputs in Reactome. While the framework was initially restricted to point-stable signal transduction systems, several extensions to differentiating or oscillating systems have been developed.