An extended Knowledge Compilation Map for Conditional Preference Statements-based and Generalized Additive Utilities-based Languages
This work provides an incremental extension to the theoretical understanding of preference representation and reasoning for researchers in AI and knowledge representation.
This paper extends the knowledge compilation map for languages based on conditional preference statements and generalized additive utilities. It addresses the complexity of new queries such as equivalence, and transformations like conditioning and variable elimination, which were previously unaddressed.
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, and transformations, like conditioning and variable elimination, thereby contributing to a knowledge compilation map for languages based on conditional preference statements. We also study the expressiveness and complexity of queries and transformations for generalized additive utilities.