  We introduce a logic modelling some aspects of the behaviour of the
measurement process, in such a way that no direct mention of quantum states is
made, thus avoiding the problems associated to this rather evasive notion. We
then study some properties of the models of this logic, and deduce some
characteristics that any model (and hence, any formulation of quantum mechanics
compatible with its predictions and relying on a notion of measurement) should
verify. The main results we obtain are that in the case of a Hilbert space of
dimension at least 3, using a strengthening of the Kochen-Specker theorem, we
show that no model can lead to the certain prediction of more than one atomic
outcome. Moreover, if the Hilbert space is finite dimensional, then we are able
to precisely describe the structure of the predictions of any model of our
logic. In particular, we show that all the models of our logic do exactly make
the same predictions regarding whether a given sequence of outcomes is possible
or not, so that quantum mechanics can be considered complete as long as the
possibility of outcomes is considered.
