Editing Logic programming (section)

===Inductive logic programming===
{{Main|Inductive logic programming}}

Inductive logic programming (ILP) is an approach to [[machine learning]] that [[Inductive reasoning|induces]] logic programs as hypothetical generalisations of positive and negative examples. Given a logic program representing background knowledge and positive examples together with constraints representing negative examples, an ILP system induces a logic program that generalises the positive examples while excluding the negative examples.

ILP is similar to ALP, in that both can be viewed as generating hypotheses to explain observations, and as employing constraints to exclude undesirable hypotheses. But in ALP the hypotheses are variable-free facts, and in ILP the hypotheses are general rules.<ref>{{Cite book |last1=Nienhuys-Cheng |first1=Shan-hwei |title=Foundations of inductive logic programming |last2=Wolf |first2=Ronald de |date=1997 |publisher=Springer |isbn=978-3-540-62927-6 |series=Lecture notes in computer science Lecture notes in artificial intelligence |location=Berlin Heidelberg |page=173}}</ref><ref>Flach, P.A. and Kakas, A.C., 2000. On the relation between abduction and inductive learning. In Abductive Reasoning and Learning (pp. 1-33). Dordrecht: Springer Netherlands.</ref>

For example, given only background knowledge of the mother_child and father_child relations, and suitable examples of the grandparent_child relation, current ILP systems can generate the definition of grandparent_child, inventing an auxiliary predicate, which can be interpreted as the parent_child relation:<ref>Cropper, A. and Dumančić, S., 2022. Inductive logic programming at 30: a new introduction. Journal of Artificial Intelligence Research, 74, pp.765-850.</ref>

<syntaxhighlight lang="prolog">
grandparent_child(X, Y):- auxiliary(X, Z), auxiliary(Z, Y).
auxiliary(X, Y):- mother_child(X, Y).
auxiliary(X, Y):- father_child(X, Y).
</syntaxhighlight>
Stuart Russell<ref>Russell, S., 2019. Human compatible: Artificial intelligence and the problem of control. Penguin.</ref> has referred to such invention of new concepts as the most important step needed for reaching human-level AI.

Recent work in ILP, combining logic programming, learning and probability, has given rise to the fields of [[statistical relational learning]] and [[probabilistic inductive logic programming]].