  Modal interpretations constitute a particular approach to associating
dynamical variables with physical systems in quantum mechanics. Given the
`quantum logical' constraints that are typically adopted by such
interpretations, only certain sets of variables can be taken to be
simultaneously definite-valued, and only certain sets of values can be ascribed
to these variables at a given time. Moreover, each allowable set of variables
and values can be uniquely specified by a single `preferred' projector in the
Hilbert space associated with the system. In general, the preferred projector
can be one of several possibilities at a given time. In previous modal
interpretations, the different possible preferred projectors have formed an
orthogonal set. This paper investigates the consequences of adopting a
non-orthogonal set. We present three contributions on this issue: (1) we
provide an argument for such non-orthogonality, based on the assumption that
perfectly predictable measurements reveal pre-existing values of variables, an
assumption which has traditionally constituted a strong motivation for the
modal approach; (2) we generalize the existing framework for modal
interpretations to accommodate non-orthogonal preferred projectors; (3) we
present a novel type of modal interpretation wherein the set of preferred
projectors is fixed by a principle of entropy minimization, and we discuss some
of the successes and shortcomings of this proposal.
