Modelling and solving bipolar preference problems

Real-life problems present several kinds of preferences. In this paper we focus on problems with both positive and negative preferences, that we call bipolar problems. Although seemingly specular notions, these two kinds of preferences should be dealt with differently to obtain the desired natural behaviour. We technically address this by generalizing the soft constraint formalism, which is able to model problems with one kind of preferences. We show that soft constraints model only negative preferences, and we define a new mathematical structure which allows to handle positive preferences as well. We also address the issue of the compensation between positive and negative preferences, studying the properties of this operation. Finally, we suggest how constraint propagation and branch and bound can be adapted to deal with bipolar problems.