  Distributed knowledge is the sum of the knowledge in a group; what someone
who is able to discern between two possible worlds whenever any member of the
group can discern between them, would know. Sometimes distributed knowledge is
referred to as the potential knowledge of a group, or the joint knowledge they
could obtain if they had unlimited means of communication. In epistemic logic,
the formula D_G{\phi} is intended to express the fact that group G has
distributed knowledge of {\phi}, that there is enough information in the group
to infer {\phi}. But this is not the same as reasoning about what happens if
the members of the group share their information. In this paper we introduce an
operator R_G, such that R_G{\phi} means that {\phi} is true after G have shared
all their information with each other - after G's distributed knowledge has
been resolved. The R_G operators are called resolution operators. Semantically,
we say that an expression R_G{\phi} is true iff {\phi} is true in what van
Benthem [11, p. 249] calls (G's) communication core; the model update obtained
by removing links to states for members of G that are not linked by all members
of G. We study logics with different combinations of resolution operators and
operators for common and distributed knowledge. Of particular interest is the
relationship between distributed and common knowledge. The main results are
sound and complete axiomatizations.
