Expressive Power and Succinctness of Propositional Languages for Preference Representation

Several logical languages have been considered in AI for en-coding compactly preference relations over a set of alterna-tives. In this paper, we analyze both the expressiveness and the spatial efficiency (succinctness) of such preference rep-resentation languages. The first issue is concerned with the nature of the preorders that can be encoded (for instance, all preorders, all complete preorders). The second issue is about how succinctly a preference relation can be expressed in those languages. We give polynomial-size translations in some cases, and prove the impossibility of such translations in other cases