RI: Small: Qualitative Preferences: Merging Paradigms, Extending the Language, Reasoning about Incomplete Outcomes

决策理论中最常见的方法涉及以效用函数表示的偏好，而对不同选择的优化考虑了世界可能状态的概率分布。另一种方法以定性的形式表示偏好，其部分动机是难以构建良好的效用函数、确定准确的概率分布以及相关问题。本项目通过关注两种有前途的表示和推理定性偏好的形式来推进定性决策理论：条件偏好网络(CP-net)和答案集优化(ASO)程序。CP网和ASO程序都提供了几类偏好问题的表示，但它们都有很大的局限性。这个项目通过开发一种形式主义来解决这些限制。ASO(CP)程序，它通过利用ASO程序和CP-Net的关键性质来扩展两者。该项目的主要目标是：通过将CP网的广义条件(等同)偏好引入ASO(CP)程序，形式化地引入ASO(CP)程序；建立ASO(CP)程序的可表现性，研究可由ASO(CP)程序定义的前序的性质，并解决相关的计算问题；研究自动偏好操纵所必需的偏好等价的关键问题；研究ASO(CP)程序对不完全指定结果的情况的扩展，这对于实际应用是必要的；将ASO(CP)程序扩展到带有聚集算子的一阶语言，定性地表示偏好并对偏好进行优化是定性决策理论的一个基本问题。通过整合和促进对ASO程序和CP网捕获的主要类型的公共偏好的理解，该项目将在偏好的表示和推理方面产生理论和实践上的进步，使其能够有效地用于实际的决策支持系统。

The most common approach in decision theory involves preferences expressed numerically in terms of utility functions, while optimization over different choices takes into account the probability distribution over possible states of the world. An alternative approach represents preferences in qualitative terms, and is motivated, in part, by difficulties in building good utility functions, ascertaining accurate probability distributions, and related problems.This project is advancing qualitative decision theory by focusing on two promising formalisms for representing and reasoning about qualitative preferences: conditional preference networks (CP-nets) and answer-set optimization (ASO) programs. Both CP-nets and ASO programs offer representations for several classes of preference problems, but each has major limitations. This project addresses these limitations by developing a formalism. ASO(CP) programs, which extend both ASO programs and CP-nets by exploiting key properties of both. The project's major objectives are: to introduce formally ASO(CP) programs by integrating into ASO programs generalized conditional (ceteris paribus) preferences of CP-nets; to establish expressivity of ASO(CP) programs, to study properties of preorders that can be defined by means of ASO(CP) programs, and to address relevant computational issues; to investigate a crucial problem of preference equivalence, essential for automated preference manipulation; to study an extension of ASO(CP) programs to the case of incompletely specified outcomes, essential for practical applications; and, to extend ASO(CP) programs to the first-order language extended with aggregate operators.Representing preferences qualitatively and optimizing over such preferences is a fundamental problem of qualitative decision theory. By integrating and advancing understanding of major types of common preferences that are captured by ASO programs and CP-nets, this project will produce theoretical and practical advances in representation and reasoning about preferences, bringing it to the point where it can be effectively used in practical decision support systems.