A Knowledge Compilation Map for Conditional Preference Statements-based Languages

Conditional preference statements have been used to compactly represent preferences over combinatorial domains. They are at the core of CP-nets and their generalizations, and lexicographic preference trees. Several works have addressed the complexity of some queries (optimization, dominance in particular). We extend in this paper some of these results, and study other queries which have not been addressed so far, like equivalence, thereby contributing to a knowledge compilation map for languages based on conditional preference statements. We also introduce a new parameterised family of languages, which enables to balance expressiveness against the complexity of some queries.