Efficient Inference and Computation of Optimal Alternatives for Preference Languages Based On Lexicographic Models

Abstract

We analyse preference inference, through consistency, for general preference languages based on lexicographic models. We identify a property, which we call strong compositionality, that applies for many natural kinds of preference statement, and that allows a greedy algorithm for determining consistency of a set of preference statements. We also consider different natural definitions of optimality, and their relations to each other, for general preference languages based on lexicographic models. Based on our framework, we show that testing consistency, and thus inference, is polynomial for a specific preference language L pqT , which allows strict and non-strict statements, comparisons between outcomes and between partial tuples, both ceteris paribus and strong statements, and their combination. Computing different kinds of optimal sets is also shown to be polynomial; this is backed up by our experimental results.

Minimality and comparison of sets of multi-attribute vectors

“…11 for details and references about the computation of and for linear and convex utility functions. The possibly strictly optimal set and the maximally possibly optimal set have been considered much less [ 46 , 70 , 71 ]. Regret-based decision making has a long history, with recent work in AI including [ 7 , 14 , 18 ].…”

“…6 show that the -Extendable property holds very often for continuous sets of scenarios ; roughly speaking, it holds if is a completely smooth function of . Extendability also holds for classes of discrete such as for the sets of lexicographic preference models defined from the compositional preference languages in [ 70 ].…”