The fundamental operation of dominance testing, i.e., determining if one alternative is preferred to another, is in general very hard for methods of reasoning with qualitative conditional preferences such as CP-nets and conditional preference theories (CP-theories). It is therefore natural to consider approximations of preference, and upper approximations are of particular interest, since they can be used within a constraint optimisation algorithm to find some of the optimal solutions. Upper approximations for preference in CP-theories have previously been suggested, but they require consistency, as well as strong acyclicity conditions on the variables. We define an upper approximation of conditional preference for which dominance checking is efficient, and which can be applied very generally for CP-theories.
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