Contrary Inferences in Consistent Histories and a Set Selection   Criterion
  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. 
Petros Wallden
quant-ph