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.