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Access to the full text of the published version may require a subscription. Abstract. A depth-first search algorithm can be used to find optimal solutions of a Constraint Satisfaction Problem (CSP) with respect to a set of conditional preferences statements (e.g., a CP-net). This involves checking at each leaf node if the corresponding solution of the CSP is dominated by any of the optimal solutions found so far; if not, then we add this solution to the set of optimal solutions. This kind of algorithm can clearly be computationally expensive if the number of solutions is large. At a node N of the search tree, with associated assignment b to a subset of the variables B, it may happen that, for some previously found solution α, either (a) α dominates all extensions of b; or (b) α does not dominate any extension of b. The algorithm can be significantly improved if we can find sufficient conditions for (a) and (b) that can be efficiently checked. In case (a), we can backtrack since we need not continue the search below N ; in case (b), α does not need to be considered in any node below the current node N . We derive a sufficient condition for (b), and three sufficient conditions for (a). Our experimental testing indicates that this can make a major difference to the efficiency of constrained optimisation for conditional preference theories including CP-nets. Rights

A conversational recommender system iteratively shows a small set of options for its user to choose between. In order to select these options, the system may analyze the queries tried by the user to derive whether one option is dominated by others with respect to the user's preferences. The system can then suggest that the user try one of the undominated options, as they represent the best options in the light of the user preferences elicited so far. This paper describes a framework for preference dominance. Two instances of the framework are developed for query suggestion in a conversational recommender system. The first instance of the framework is based on a basic quantitative preferences formalism, where options are compared using sums of weights of their features. The second is a qualitative preference formalism, using a language that generalises CP-nets, where models are a kind of generalised lexicographic order. A key feature of both methods is that deductions of preference dominance can be made efficiently, since 1 April 12, 2011 20:45 WSPC/INSTRUCTION FILE ijait2011-twbr 2 this procedure needs to be applied for many pairs of options. We show that, by allowing the recommender to focus on undominated options, which are ones that the user is likely to be contemplating, both approaches can dramatically reduce the amount of advice the recommender needs to give to a user compared to what would be given by systems without this kind of reasoning.

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Abstract. In an era of overwhelming choices, recommender systems aim at recommending the most suitable items to the user. Preference handling is one of the core issues in the design of recommender systems and so it is important for them to catch and model the user's preferences as accurately as possible. In previous work, comparative preferences-based patterns were developed to handle preferences deduced by the system. These patterns assume there are only two values for each feature. However, real-world features can be multi-valued. In this paper, we develop preference induction methods which aim at capturing several preference nuances from the user feedback when features have more than two values. We prove the efficiency of the proposed methods through an experimental study.