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The complexity of intracellular molecular pathways can be simplified by the use of Network Biology that breaks down the intricacy of biological processes into components and interactions among them (interactome). In the paper we show that any complex interactome, that is, a biological network representing protein-protein, protein-DNA and DNA-RNA interactions, can be decomposed into a conjunction of logical theorems expressed in terms of Zsyntax, a formal language which allows representing (as long as you want) biological pathways. This result, illustrated with the case study of melanoma network, opens the possibility for a computable model of the cell expressed in a logical language and shows how a formal way of intending philosophy can be useful to cope with the complexity of the biological world.