The development of most tissues and organs relies on a limited number of signal transduction pathways enabling the coordination of cellular differentiation. A proper understanding of the roles of signal transduction pathways requires the definition of formal models capturing the main qualitative features of these patterning processes. This is a challenging task because the underlying processes, diffusion, regulatory modifications, reception and sequestration of signalling molecules, transcriptional regulation of target genes, etc. are only partly characterized. In this context, qualitative models can be more readily proposed on the basis of available (molecular) genetic data. But this requires novel computational tools and proper qualitative representations of phenomena such as diffusion or sequestration. To assess the power and limits of a logical formalism in this context, we propose a multi-level model of the multi-cellular network involved in the definition of the anterior-posterior boundary during the development of the wing disc of Drosophila melanogaster. The morphogen Hedgehog (Hh) is the inter-cellular signal coordinating this process. It diffuses from the posterior compartment of the disc to activate its pathway in cells immediately anterior to the boundary. In these boundary cells, the Hh gradient induces target genes in distinct domains as a function of the Hh concentration. One target of Hh signalling is the gene coding for the receptor Patched (Ptc), which sequesters Hh and impedes further diffusion, thereby refining the boundary.