CP-nets with indifference

Conditional preference networks (CP-nets) offer a potentially compact representation of qualitative preferences. Much of the research on CP-nets limits attention to strict preferences over binary variables. We extend the work of previous researchers to allow modeling preferences over multi-valued variables over some of which the preference holder may be indifferent. We show how to leverage the power of SAT solvers to learn and reason with such CP-nets. We also consider the possibility of exponentially long flipping sequences, showing why in practice this is unlikely to be problematic.