Most of preference representation languages developed in the literature are based on comparative preference statements. The latter offer a simple and intuitive way for expressing preferences. They can be interpreted following different semantics. This paper presents a postulate-based analysis of the different semantics describing their behavior w.r.t. three criteria: coherence, syntax independence and inference.

A fundamental task for reasoning with preferences is the following: given inputpreference information from a user, and outcomes α and β, should we infer that the user will prefer α to β? For CP-nets and related comparative preference formalisms, inferring a preference of α over β using the standard definition of derived preference appears to be extremely hard, and has been proved to be PSPACE-complete in general for CP-nets. Such inference is also rather conservative, only making the assumption of transitivity. This paper defines a less conservative approach to inference which can be applied for very general forms of input. It is shown to be efficient for expressive comparative preference languages, allowing comparisons between arbitrary partial tuples (including complete assignments), and with the preferences being ceteris paribus or not.