Learning Weak Constraints in Answer Set Programming
  This 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, called Learning
from Ordered Answer Sets, generalises our previous work on learning ASP
programs without weak constraints, by considering a new notion of examples as
ordered pairs of partial answer sets that exemplify which answer sets of a
learned hypothesis (together with a given background knowledge) are preferred
to 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.
