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This work deals with the problem of intentional learning in a multi-agent system (MAS). Smile (sound multi-agent incremental learning), a collaborative learning protocol which shows interesting results in the distributed learning of well known complex boolean formulae, is adopted here by a MAS of BDI agents to update their practical reasons while keeping MAS-consistency. An incremental algorithm for first-order induction of logical decision trees enables the BDI agents to adopt Smile, reducing the amount of communicated learning examples when compared to our previous non-incremental approaches to intentional learning. The protocol is formalized extending the operational semantics of AgentSpeak(L), and implemented in Jason, its well known Java-based extended interpreter.