Reasoning with preference trees over combinatorial domains

Abstract

Preference trees, or P-trees for short, offer an intuitive and often concise way of representing preferences over combinatorial domains. In this paper, we propose an alternative definition of P-trees, and formally introduce their compact representation that exploits occurrences of identical subtrees. We show that P-trees generalize lexicographic preference trees and are strictly more expressive. We relate P-trees to answerset optimization programs and possibilistic logic theories. Finally, we study reasoning with P-trees and establish computational complexity results for the key reasoning tasks of comparing outcomes with respect to orders defined by P-trees, and of finding optimal outcomes.