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