  This paper addresses the question whether a variant of a modal interpretation
is conceivable that could accommodate property ascriptions associated with
nonorthogonal resolutions of the unity and nonorthogonal families of relative
states as they occur in imperfect or genuinely unsharp measurements. I will
review a recent formulation of the quantum measurement problem in the form of
an insolubility theorem that incorporates the case of unsharp object
observables as well as certain types of unsharp pointers. In addition to
demonstrating the necessity for some modification of quantum mechanics, this
allows me to specify the logical position of the modal interpretations as a
resolution to the measurement problem and to indicate why I think their current
versions are not yet capable of dealing adequately with unsharp quantum
observables. The technical tools that will have been explained along this line
of reasoning will finally serve to make precise the notion of (unsharp) value
ascription that I would find desirable for a modal interpretation to ascertain.
