  The semantic framework for the modal logic of knowledge due to Halpern and
Moses provides a way to ascribe knowledge to agents in distributed and
multi-agent systems. In this paper we study two special cases of this
framework: full systems and hypercubes. Both model static situations in which
no agent has any information about another agent's state. Full systems and
hypercubes are an appropriate model for the initial configurations of many
systems of interest. We establish a correspondence between full systems and
hypercube systems and certain classes of Kripke frames. We show that these
classes of systems correspond to the same logic. Moreover, this logic is also
the same as that generated by the larger class of weakly directed frames. We
provide a sound and complete axiomatization, S5WDn, of this logic. Finally, we
show that under certain natural assumptions, in a model where knowledge evolves
over time, S5WDn characterizes the properties of knowledge not just at the
initial configuration, but also at all later configurations. In particular,
this holds for homogeneous broadcast systems, which capture settings in which
agents are initially ignorant of each others local states, operate
synchronously, have perfect recall and can communicate only by broadcasting.
