Conditional preference statements have been used to compactly represent preferences over combinatorial domains. They are at the core of CP-nets and their generalizations, and lexicographic preference trees. Several works have addressed the complexity of some queries (optimization, dominance in particular). We extend in this paper some of these results, and study other queries which have not been addressed so far, like equivalence, and transformations, like conditioning and variable elimination, thereby contributing to a knowledge compilation map for languages based on conditional preference statements. We also study the expressiveness and complexity of queries and transformations for generalized additive utilities.

翻译：条件偏好陈述被用于紧凑地表示组合域上的偏好，它们是CP-net及其推广形式、以及词典序偏好树的核心。已有部分工作研究了某些查询的复杂性（尤其是优化与支配性查询）。本文在已有结果基础上进行拓展，并研究了此前未被涉及的查询（如等价性）及变换（如条件化与变量消除），从而为基于条件偏好陈述的语言构建知识编译图谱。此外，我们还研究了广义加性效用的表达能力、查询复杂度及变换性质。