An extended Knowledge Compilation Map for Conditional Preference Statements-based and Generalized Additive Utilities-based Languages
Hélène Fargier, Stefan Mengel, Jérôme Mengin
TL;DR
This work builds an extended knowledge compilation map for preferences represented by conditional CP statements and Generalized Additive Utilities (GAIs). It compares CP-based languages (including CP-nets and LP-trees) with GAIs across expressiveness, succinctness, and a broad set of queries and transformations, establishing hierarchies and canonical forms under various restrictions. The paper shows that CP languages can express arbitrary preorders but incur PSPACE- and NP-hardness for key queries, while GAIs and LP-trees offer favorable tractability in several settings, at the cost of restricted expressiveness. It also analyzes transformations such as conditioning, conjunction, disjunction, and variable elimination, revealing which operations preserve language boundaries and which produce outside-language outputs. Overall, the results guide design choices for preference-handling components in decision-support systems, highlighting trade-offs between expressiveness and computational efficiency and pointing to directions for learning-based applications.
Abstract
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.