In the EcoBioCap project (www.ecobiocap.eu) about the next generation of packaging, a decision support system has been built that uses argumentation to deal with stakeholder preferences. However, when testing the tool the domain experts did not always understand the output of the system. The approach developed in this paper is the first step to the construction of a decision support system endowed with an explanation module. We place ourselves in the equivalent setting of inconsistent Ontology-Based Data Access (OBDA) and addresses the problem of explaining Boolean Conjunctive Query (BCQ) failure. Our proposal relies on an interactive and argumentative approach where the processes of explanation takes the form of a dialogue between the User and the Reasoner. We exploit the equivalence between argumentation and inconsistency tolerant semantics to prove that the Reasoner can always provide an answer for user’s questions.