  The best developed formulation of closed system quantum theory that handles
multiple-time statements, is the consistent (or decoherent) histories approach.
The most important weaknesses of the approach is that it gives rise to many
different consistent sets, and it has been argued that a complete
interpretation should be accompanied with a natural mechanism leading to a
(possibly) unique preferred consistent set. The existence of multiple
consistent sets becomes more problematic because it allows the existence of
contrary inferences (Kent 1997). We analyse the conceptual difficulties that
arise from the existence of multiple consistent sets and provide a suggestion
for a natural set selection criterion. This criterion does not lead to a unique
physical consistent set, however it evades the existence of consistent sets
with contrary inferences. The criterion is based on the concept of preclusion
and the requirement that probability one propositions and their inferences
should be noncontextual. The allowed consistent sets turn-out to be compatible
with coevents which are the ontology of an alternative, histories based,
formulation.
