Many ILP systems learn from (positive and negative) examples of atoms which should be true or false. This is because many ILP systems are targeted at learning Prolog programs, where the main “output” of a program is a query of a single atom. In ASP, the main “output” of a program is a set of answer sets. For this reason, ILASP learns from positive and negative examples of (partial) interpretations, which should or should not (respectively) be an answer set of the learned program. These examples are sufficient to learn any ASP program consisting of normal rules, choice rules and hard constraints (up to strong equivalence); however, it is not possible to learn weak constraints using only positive and negative examples, because they can only specify what should (or should not) be an answer set. Weak constraints do not have any effect on what is or is not an answer set – they only create a preference ordering over the answer sets. For this reason, ILASP allows a second type of example called an ordering example, the semantic property of which is a preference ordering over a pair of answer sets of the learned program. Learning weak constraints corresponds to a form of preference learning.
The remainder of this section is structured as follows: