PP-2009-10: Representing Utility Functions via Weighted Goals

PP-2009-10: Uckelman, Joel and Chevaleyre, Yann and Endriss, Ulle and Lang, Jérôme (2009) Representing Utility Functions via Weighted Goals. [Report]

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Abstract

We analyze the expressivity, succinctness, and complexity of a family of languages based on weighted propositional formulas for the representation of utility functions. The central idea underlying this form of preference modeling is to associate numerical weights with goals specified in terms of propositional formulas, and to compute the utility value of an alternative as the sum of the weights of the goals it satisfies. We define a large number of representation languages based on this idea, each characterized by a set of restrictions on the syntax of formulas and the range of weights. Our aims are threefold. First, for each language we try to identify the class of utility functions it can express. Second, when different languages can express the same class of utility functions, one may allow for a more succinct representation than another. Therefore, we analyze the relative succinctness of languages. Third, for each language we study the computational complexity of the problem of finding the most preferred alternative given a utility function expressed in that language.

Item Type: Report
Report Nr: PP-2009-10
Series Name: Prepublication (PP) Series
Year: 2009
Uncontrolled Keywords: preferences; computational complexity; knowledge representation; computational social choice
Subjects: Computation
Depositing User: Ulle Endriss
Date Deposited: 12 Oct 2016 14:37
Last Modified: 12 Oct 2016 14:37
URI: https://eprints.illc.uva.nl/id/eprint/340

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