 Consider first the notion of distributed knowledge, understood as describing what the agents would know if they shared all their information. From this intuitive definition, it is clear that this concept can be defined semantically in terms of the agent’s individual epistemic relations. More precisely, a relation describing the distributed knowledge modality should correspond to the intersection of the individual epistemic relations, \(R_D := \bigcap_{i \in \ttA} R_i\). Thus, given an evaluation point w, a world u will be considered possible after the agents share all they know if and only if all of them considered it possible before the communication (or, in other words, u will be considered possible if and only if no one can discard it). One simply extends the language with a modality D, semantically interpreted with respect to this new relation: