Probabilistic Inductive Logic Programming Based on Answer Set
  Programming
  We propose a new formal language for the expressive representation of
probabilistic knowledge based on Answer Set Programming (ASP). It allows for
the annotation of first-order formulas as well as ASP rules and facts with
probabilities and for learning of such weights from data (parameter
estimation). Weighted formulas are given a semantics in terms of soft and hard
constraints which determine a probability distribution over answer sets. In
contrast to related approaches, we approach inference by optionally utilizing
so-called streamlining XOR constraints, in order to reduce the number of
computed answer sets. Our approach is prototypically implemented. Examples
illustrate the introduced concepts and point at issues and topics for future
research.
