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Conditional preference statements have been used to compactly representpreferences over combinatorial domains. They are at the core of CP-nets andtheir generalizations, and lexicographic preference trees. Several works haveaddressed the complexity of some queries (optimization, dominance inparticular). We extend in this paper some of these results, and study otherqueries which have not been addressed so far, like equivalence, andtransformations, like conditioning and variable elimination, therebycontributing to a knowledge compilation map for languages based on conditionalpreference statements. We also study the expressiveness and complexity ofqueries and transformations for generalized additive utilities.

An extended Knowledge Compilation Map for Conditional Preference Statements-based and Generalized Additive Utilities-based Languages