Some Experiments on Learning Soft Constraints

Classical constraint problems (CSPs) are a very expressive and natural formalism to specify many kinds of real-life problems. However, sometimes they are not very exible when trying to represent real-life scenarios where the knowledge is not completely available nor crisp. For this reason, many extensions of the classical CSP framework have been proposed in the literature: fuzzy, partial, probabilistic, hierarchical. More recently, all these extensions have been unified in a general framework [1], called SCSP, which uses a semiring to associate with each tuple of values for the variables of each constraint an appropriate “degree of preference”, which can also be interpreted as a cost, or an award, or others