Based on the notion of time translation, we develop a formalism to deal with the logic of quantum properties at different times. In our formalism it is possible to enlarge the usual notion of context to include composed properties involving propertie
s at different times. We compare our results with the theory of consistent histories.
The aim of this paper is to argue that the preferred basis problem is not a real problem in measurement. We will show that, given an apparatus, among the infinite corrrelations that can be established in the final state by means of a change of basis,
one and only one makes physical sense. It is the apparatus, through its interaction Hamiltonian, what selects a single basis and determines the observable to be measured, even without decoherence.
We show that including both the system and the apparatus in the quantum description of the measurement process, and using the concept of conditional probabilities, it is possible to deduce the statistical operator of the system after a measurement wi
th a given result, which gives the probability distribution for all possible consecutive measurements on the system. This statistical operator, representing the state of the system after the first measurement, is in general not the same that would be obtained using the postulate of collapse.
