Can the Decoherent Histories Description of Reality be Considered Satisfactory?

In this letter, we discuss some features of the Decoherent Histories approach; more specifically, we put forward four assumptions, the first three of which, according to us, are necessary for a sound interpretation of the theory, while the fourth one is accepted by the supporters of the DH approach. We then prove that such assumptions lead to a logical contradiction and thus cannot hold simultaneously. In the last section, we discuss the consequences of relaxing any one of them: our conclusion is that the theory is either incomplete or it does not yield a realistic description of physical world.