Learning various classes of models of lexicographic orderings

We consider the problem of learning a user's ordinal preferences on multiattribute domains, assuming that the user's preferences may be modelled as a kind of lexicographic ordering. We introduce a general graphical representation called LP-structures which captures various natural classes of such ordering in which both the order of importance between attributes and the local preferences over each attribute may or may not be conditional on the values of other attributes. For each class we determine the Vapnik-Chernovenkis dimension, the communi- cation complexity of learning preferences, and the complexity of identifying a model in the class consistent with some given user-provided examples.