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

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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.