Contrary quantum histories and contrary inferences

In the context of the quantum histories approach to quantum mechanics, we define a contrary relation between quantum histories, generalizing the standard definition of contrary quantum properties. Using this contrary relation, we study the possibility of inferring contrary quantum histories. We consider the quantum histories approach with three different consistency conditions: weak, medium and global consistency conditions. For the first two conditions, we show that, it is possible to infer contrary histories from different families of histories, in accordance with previous results. For global consistency condition, we prove that it is not possible to infer contrary histories.