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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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

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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