Preference inference based on Pareto models

In this paper, we consider Preference Inference based on a generalised form of Pareto order. Preference Inference aims at reasoning over an incomplete specification of user preferences. We focus on two problems. The Preference Deduction Problem (PDP) asks if another preference statement can be deduced (with certainty) from a set of given preference statements. The Preference Consistency Problem (PCP) asks if a set of given preference statements is consistent, i.e., the statements are not contradicting each other. Here, preference statements are direct comparisons between alternatives (strict and non-strict). It is assumed that a set of evaluation functions is known by which all alternatives can be rated. We consider Pareto models which induce order relations on the set of alternatives in a Pareto manner, i.e., one alternative is preferred to another only if it is preferred on every component of the model. We describe characterisations for deduction and consistency based on an analysis of the set of evaluation functions, and present algorithmic solutions and complexity results for PDP and PCP, based on Pareto models in general and for a special case. Furthermore, a comparison shows that the inference based on Pareto models is less cautious than some other types of well-known preference model.