Reasoning about multi-attribute preferences

Introduction Many preference models are quantitative. These kinds of models are based on utilities; a utility function determines for each outcome a numerical value of desirability. However, it is difficult to elicit such models from users. Humans generally express their preferences in a more qualitative way. Therefore, qualitative preference models would provide a better correspondence with human cognitive representations. One of the binary preferences in [3] expresses that any state where φ is true is strictly better than any state where ψ is true. If applied to object names, it can express that object i is preferred over object j. The preference expressed in this way is a very strong kind of preference. It requires that all of i’s relevant properties are considered more important than j’s properties. The motivation to introduce multi-attribute preference logic is to enable the specification of principles that allow to derive preferences over objects from their properties in a weaker sense. In most qualitative preference orderings it is possible that i has at least one property that is considered more important than a property that j has but j is still preferred over i. Moreover, the logic should provide the means to derive a preference of one object over another from a specification of the properties of these objects and an importance ranking associated with these properties. [1, 2] have defined various orderings (called #, ⊺ and κ ordering) to obtain object preferences from a property ranking, which indicates the relative importance or priority of each property. These orderings are explained below. The advantage of defining preference orderings in a logic instead of providing settheoretical definitions is that it formalizes the reasoning about object preferences. From a practical point of view, the logic allows to provide rigorous formal proofs for object preferences derived from property rankings. From a theoretical point of view, it provides the tools to reason about preference orderings and allows, for example, to prove that whenever an object is preferred over another by the ⊺ ordering it also is preferred by the # ordering.