Residuation for bipolar preferences in soft constraints

Soft constraint formalisms are an abstract representation of Constraint Satisfaction Problems (CSPs): the set of preferences is now parametric, often forming (a variety of) an absorptive semiring. However, the latter is suitable only for negative preferences, i.e., such that the combination of constraints worsens the quality of the solution. This work comments on related work and exploits residuated semirings in order to lift the Local Consistency heuristics that hold for classical CSPs. As a result, we merge and generalise existent formalisms for modelling soft CSPs with bipolar (positive and negative) preferences.