Reasoning with qualitative preferences and cardinalities using generalized circumscription
Patrick Doherty, Andrzej Szałas · 2008
The topic of preference modeling has recently attracted the interest of a number of sub-disciplines in artificial intelli-gence such as the nonmonotonic reasoning and action and change communities. The approach in these communities fo-cuses on qualitative preferences and preference models which provide more natural representations from a commonsense perspective. In this paper, we show how generalized circum-scription can be used as a highly expressive framework for qualitative preference modeling. Generalized circumscrip-tion proposed by Lifschitz allows for predicates (and thus formulas) to be minimized relative to arbitrary pre-orders (reflexive and transitive). Although it has received little at-tention, we show how it may be used to model and reason about elaborate qualitative preference relations. One of the perceived weaknesses with any type of circumscription is the 2nd-order nature of the representation. The paper shows how a large variety of preference theories represented using gen-eralized circumscription can in fact be reduced to logically equivalent first-order theories in a constructive way. Finally, we also show how preference relations represented using gen-eral circumscription can be extended with cardinality con-straints and when these extensions can also be reduced to log-ically equivalent first-order theories.