Expressive Power of Weighted Propositional Formulas for Cardinal Preference Modelling
Yann Chevaleyre, Ulle Endriss, Jérôme Lang

Abstract:
As proposed in various places, a set of propositional formulas, each
associated with a numerical weight, can be used to model the
preferences of an agent in combinatorial domains.  If the range of
possible choices can be represented by the set of possible assignments
of propositional symbols to truth values, then the utility of an
assignment is given by the sum of the weights of the formulas it
satisfies. Our aim in this paper is twofold: (1) to establish
correspondences between certain types of weighted formulas and
well-known classes of utility functions (such as monotonic, concave or
k-additive functions); and (2) to obtain results on the comparative
succinctness of different types of weighted formulas for representing
the same class of utility functions.