Metarule

A metarule is a higher-level rule used in logic programming and inductive logic programming (ILP) to specify the allowable form of learned clauses. Rather than directly learning every predicate, a learner searches within a library of metarules that define templates for how base predicates can be composed to form new rules. Metarules act as a bias or constraint on the hypothesis space, guiding the induction process toward human-plausible or task-suitable programs.

In ILP systems, metarules are instantiated by substituting concrete predicates for the placeholders in the templates. The resulting ground clauses become candidate hypotheses that the learner tests against the data. This approach helps to manage search complexity and to encode domain knowledge about how relations tend to combine.

Common metarule templates include:

- Chain: P(A,B) :- Q(A,C), R(C,B). This expresses the idea that P can be derived by composing Q and R.

- Identity: P(A,B) :- Q(A,B). Here P directly inherits the relation Q.

- Tail recursion (a recursive metarule): P(A,B) :- Q(A,C), P(C,B). This template supports learning recursive definitions.

Metarules are central to meta-interpretive learning frameworks such as Metagol, which use a library of metarules to search for explanations in a top-down or bottom-up fashion while leveraging background knowledge. They enable relational and relationally recursive learning from examples, but their usefulness depends on the chosen metarule library and available predicates.

Limitations include potential bias from the metarules, the need for appropriate background knowledge, and computational complexity in the search over instantiations. When well chosen, metarules can produce compact, interpretable, and generalizable rules.