Relating Preference Languages By Their Expressive Power

There has been a great deal of research into methods for representing preferences, called preference representation languages. Often, research in this area deals with a limited number of similar languages, in isolation. This work establishes a new method of analyzing the similarity of different languages by considering the class of preference orders that each language is capable of expressing. Our method involves the definition of a relation called preference representation language subsumption, which allows us to relate various languages by their expressive power. We demonstrate several general proof techniques for showing that such a relation exists or does not exist. Additionally, we provide a small case study for several languages that express preferences over combinatorial domains and discuss several analytical uses for the proposed subsumption relation.