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

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.