Constraints and preferences are ubiquitous in real-life. Moreover, preferences can be of many kinds: qualitative, quantitative, conditional, positive or negative, to name a few. Our ultimate goal is to define and study formalisms that can model problems with both constraints and many kind of preferences, possibly defined by several agents, and to develop tools to solve such problems efficiently. In this paper we briefly report on recent work towards this goal. Motivation and main goal.

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... es are ubiquitous in real life. In fact, most problems are over-constrained and would not be solvable if we insist that all their requirements are strictly met. Moreover, solvable problems have solutions with different desirability. Finally, many problems are more naturally described via preferences rather than hard statements. In some cases it could be more natural to express preferences in quantitative terms, while in other situations it could be better to use qualitative statements. Moreover, preferences can be unconditional or conditional. Furthermore, in many real life problems, constraints and preferences of various kinds may coexist. Unfortunately, there is no single formalism which allows all the different kinds of preferences to be specified efficiently and reasoned with effectively. For example, soft constraints [1] are most suited for reasoning about constraints and quantitative preferences, while CP-nets [2] are most suited for representing qualitative and possibly conditional preferences. Our ultimate goal is to define and study formalisms that can model problems with both constraints and many kind of preferences, and to develop tools to solve such problems efficiently. Moreover, we also want to be able to deal with scenarios where preferences are expressed by several agents, and preference aggregation is therefore needed to find the optimal outcomes.