Despite the relevance of the belief-desire-intention (BDI) model of rational agency, little work has been done to deal with its two main limitations: the lack of learning competences and explicit multi-agent functionality. Our work deals with the problem of designing BDI learning agents situated in a multi-agent system (MAS). From the MAS learning perspective, we have proposed an extended BDI architecture, where agents are able to perform induction of first-order logical decision trees. These agents learn about their practical reasons to adopt a plan as an intention. Particularly, induction is used to update these reasons (the context of plans), if a plan fails when executed, after it had been selected to form an intention. Here, we emphasize the way MAS concepts, as cooperative goal adoption, enable distributed forms of learning, e.g., distributed data gathering. Consistency between learning and the theory of practical reasoning is guaranteed, i.e., learning is just another competence of the agents, performed under BDI rationality.