Beyond numerical simulation, the possibility of performing symbolic computation on bio-molecular interaction networks opens the way to the design of new automated reasoning tools for biologists/modelers. The Biochemical Abstract machine BIOCHAM provides a precise semantics to biomolecular interaction maps as concurrent transition systems. Based on this formal semantics, BIOCHAM offers a compositional rule-based language for modeling biochemical systems, and an original query language based on temporal logic for expressing biological queries about reachability, checkpoints, oscillations or stability. Turning the temporal logic query language into a specification language for expressing the observed behavior of the system (in wild-life and mutated organisms) makes it possible to use machine learning techniques for completing or correcting biological models semi-automatically. Machine learning from temporal logic formulae is quite new however, both from the machine learning perspective and from the Systems Biology perspective. In this paper, we report on the machine learning system of BIOCHAM which allows to discover, on the one hand, interaction rules from a partial model with constraints on the system behavior expressed in temporal logic, and on the other hand, kinetic parameter values from a temporal logic specification with constraints on numerical concentrations.