Decoherent histories and realism

We reconsider the decoherent histories approach to quantum mechanics and an alyze some problems related to its interpretation which we believe have not been adequately clarified by its proponents. We put forward some assumptio ns which. in our opinion, are necessary ibr a realistic interpretation of t he probabilities that the formalism attaches to decoherent histories. We pr ove that such assumptions, unless one limits the set of the decoherent fami lies which can be taken into account. lead to a logical contradiction The l ine of reasoning we follow is conceptually different from other arguments w hich have been presented and which have been rejected by the supporters of the decoherent histories approach. The conclusion is that the decoherent hi stories approach, to be considered as an interesting realistic alternative to the orthodox interpretation of quantum mechanics, requires the identific ation of a mathematically precise criterion to characterize an appropriate set of decoherent families which does not give rise to any problem.