Constraints and Preferences: Modelling Frameworks and Multi-agent Settings

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 our recent work towards this goal. 1 Motivation and main goal Constraints (Dechter, 2003; Rossi et al., 2006a) are requirements that we may state over the possible scenarios, and they must be met, otherwise we are not satisfied. Many scenarios can meet the given constraints, and they are all equally good, since they all satisfy the constraints. On the other hand, if a scenario does not satisfy some of the constraints, it is not acceptable. For example, when choosing a camera, we may be interested only in those that have a certain lens, and don’t care about the other features. If a shop does not have cameras with that lens, then we would not buy a camera there. On the other hand, preferences are a way to model the fact that some scenarios are more desirable than others. Preferences are ubiquitous in real life. In fact, as in the above example, 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. For example, when choosing a menu at the restaurant, we may prefer red wine ∗ This paper describes joint work done with the following collegues: K. Apt, S. Bistarelli, C. Domshlak, L. Khatib, J. Lang, P. Morris, R. Morris, M. S. Pini, S. Prestwich, A. Sperduti, K. B. Venable, T. Walsh, and N. Yorke-Smith.