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

TL;DR

This paper extends the knowledge compilation map for conditional preference languages, analyzing complexity and expressiveness of various queries and transformations, including equivalence, conditioning, and variable elimination.

Contribution

It provides new complexity results and insights into the expressiveness of conditional preference statements and generalized additive utilities, covering previously unaddressed queries.

Findings

Extended the knowledge compilation map for preference languages.

Analyzed complexity of equivalence and transformations.

Studied expressiveness of generalized additive utilities.

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.