  Sound and complete axiomatizations are provided for a number of different
logics involving modalities for knowledge and time. These logics arise from
different choices for various parameters. All the logics considered involve the
discrete time linear temporal logic operators `next' and `until' and an
operator for the knowledge of each of a number of agents. Both the single agent
and multiple agent cases are studied: in some instances of the latter there is
also an operator for the common knowledge of the group of all agents. Four
different semantic properties of agents are considered: whether they have a
unique initial state, whether they operate synchronously, whether they have
perfect recall, and whether they learn. The property of no learning is
essentially dual to perfect recall. Not all settings of these parameters lead
to recursively axiomatizable logics, but sound and complete axiomatizations are
presented for all the ones that do.
