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CP-nets and their variants constitute one of the main AI approaches forspecifying and reasoning about preferences. CI-nets, in particular, are aCP-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, anatural question is whether CI-nets can be used more or less directly to encodepreferences over multi-sets. We here provide some initial ideas on how toachieve this, in the sense that at least a restricted form of reasoning on ourframework, which we call "confined reasoning", can be efficiently reduced toreasoning on CI-nets. Our framework nevertheless allows for encodingpreferences over multi-sets with unbounded multiplicities. We also show theextent to which it can be used to represent preferences where multiplicites ofthe goods are not stated explicitly ("purely qualitative preferences") as wellas a potential use of our generalization of CI-nets as a component of a recentsystem for evidence aggregation.

Encoding monotonic multi-set preferences using CI-nets: preliminary report