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

Hélène Fargier (1, 2) , Stefan Mengel (3, 4) , Jérôme Mengin (1, 5)

1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
2 CNRS - Centre National de la Recherche Scientifique
3 CRIL - Centre de Recherche en Informatique de Lens
4 UA - Université d'Artois
5 UT3 - Université Toulouse III - Paul Sabatier

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, and introduce a new parameterized family of languages, which enables to balance expressiveness against the complexity of some queries. This paper is an extended version of [29]-in addition to the results of [29], it contains a study of several transformations (Section 7). We have also added the GAI language to the map.

Domaines: Intelligence artificielle [cs.AI]; Complexité [cs.CC]

Hélène Fargier, Stefan Mengel, Jérôme Mengin. An extended Knowledge Compilation Map for Conditional Preference Statements-based and Generalized Additive Utilities-based Languages. RR–2023–03–FR, Institut de recherche en informatique de Toulouse (IRIT). 2023. ⟨hal-04356562⟩