AbstractThis paper contributes to the area of inductive logic programming by presenting a new learning framework that allows the learning of weak constraints in Answer Set Programming (ASP). The framework, calledLearning from Ordered Answer Sets, generalises our previous work on learning ASP programs without weak constraints, by considering a new notion of examples asorderedpairs of partial answer sets that exemplify which answer sets of a learned hypothesis (together with a given background knowledge) arepreferredto others. In this new learning task inductive solutions are searched within a hypothesis space of normal rules, choice rules, and hard and weak constraints. We propose a new algorithm, ILASP2, which is sound and complete with respect to our new learning framework. We investigate its applicability to learning preferences in an interview scheduling problem and also demonstrate that when restricted to the task of learning ASP programs without weak constraints, ILASP2 can be much more efficient than our previously proposed system.