Preference Representation with Weighted Goals: Expressivity, Succinctness, Complexity

Joel Uckelman, Ulle Endriss

The representation of preferences of agents is a central feature in many AI systems. In particular when the number of alternatives to be considered may become large, the use of compact preference representation languages is crucial. The framework of weighted propositional formulas can be used to define several such languages. The central idea 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. In this paper, we analyze several properties of languages defined by weighted goals: their expressivity, the relative succinctness of different sublanguages, and the computational complexity of finding the best alternative with respect to a given utility function expressed in terms of weighted goals.

Subjects: 11. Knowledge Representation; 7.1 Multi-Agent Systems

Submitted: May 14, 2007

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