We propose an integrated theoretical framework, grounded in possibility theory, to account for all the aspects involved in representing and changing beliefs, representing and generating justified desires, and selecting goals based on current and uncertain beliefs about the world, and the preferences of the agent. Beliefs and desires of a cognitive agent are represented as (two distinct) possibility distributions. This is the original part of the proposed framework in the sense that there does not really exist a full-fledged possibilistic approach to BDI. In the proposed framework:(i) the possibility distribution representing the qualitative utilities associated with desires are the result of a rule-based deliberative process, that is, they depend on the mental state of the agent and are not given a priori; and (ii) the criteria for choosing goals take into account not only the fact that goals must be consistent in the logical sense, but also in the cognitive sense.