  CP-nets and their variants constitute one of the main AI approaches for
specifying and reasoning about preferences. CI-nets, in particular, are a
CP-inspired formalism for representing ordinal preferences over sets of goods,
which are typically required to be monotonic.
  Considering also that goods often come in multi-sets rather than sets, a
natural question is whether CI-nets can be used more or less directly to encode
preferences over multi-sets. We here provide some initial ideas on how to
achieve this, in the sense that at least a restricted form of reasoning on our
framework, which we call "confined reasoning", can be efficiently reduced to
reasoning on CI-nets. Our framework nevertheless allows for encoding
preferences over multi-sets with unbounded multiplicities. We also show the
extent to which it can be used to represent preferences where multiplicites of
the goods are not stated explicitly ("purely qualitative preferences") as well
as a potential use of our generalization of CI-nets as a component of a recent
system for evidence aggregation.
