Representing Utility Functions via Weighted Goals
Joel Uckelman, Yann Chevaleyre, Ulle Endriss, Jérôme Lang
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.