Central to the functioning of any living cell, the metabolic network is a complex network of biochemical reactions. It may also be viewed as an elaborate production system, integrating a diversity of internal and external signals in order to efficiently produce the energy and the biochemical precursors to ensure all cellular functions. Even in simple organisms like bacteria, it shows a striking level of coordination, adapting to very different growth media. Constraint-based models constitute an efficient mathematical framework to compute optimal metabolic configurations, at the scale of a whole genome. Combining the constraint-based approach "Resource Balance Analysis" with combinatorial optimization techniques, we propose a general method to explore these configurations, based on the inference of logical rules governing the activation of metabolic fluxes in response to diverse extracellular media. Using the concept of partial Boolean functions, we notably introduce a novel tractable algorithm to infer monotone Boolean functions on a minimal support. Monotonicity seems particularly relevant in this context, since the orderliness exhibited by the metabolic network's dynamical behavior is expected to give rise to relatively simple rules. First results are promising, as the application of the method on Bacillus subtilis central carbon metabolism allows to recover known regulations as well as to investigate lesser known parts of the global regulatory network.