# Logical reduction of metarules

## TL;DR

This paper investigates logical reduction techniques for metarules in ILP, introducing a new derivation reduction method that improves learning efficiency and accuracy across multiple domains.

## Contribution

It introduces derivation reduction based on SLD-resolution and demonstrates its effectiveness over traditional reduction methods in ILP.

## Key findings

- Derivation reduction outperforms subsumption and entailment reductions.
- Reduced metarule sets improve learning times and predictive accuracy.
- Theoretical analysis of reductions for infinite metarule fragments.

## Abstract

Many forms of inductive logic programming (ILP) use \emph{metarules}, second-order Horn clauses, to define the structure of learnable programs and thus the hypothesis space. Deciding which metarules to use for a given learning task is a major open problem and is a trade-off between efficiency and expressivity: the hypothesis space grows given more metarules, so we wish to use fewer metarules, but if we use too few metarules then we lose expressivity. In this paper, we study whether fragments of metarules can be logically reduced to minimal finite subsets. We consider two traditional forms of logical reduction: subsumption and entailment. We also consider a new reduction technique called \emph{derivation reduction}, which is based on SLD-resolution. We compute reduced sets of metarules for fragments relevant to ILP and theoretically show whether these reduced sets are reductions for more general infinite fragments. We experimentally compare learning with reduced sets of metarules on three domains: Michalski trains, string transformations, and game rules. In general, derivation reduced sets of metarules outperforms subsumption and entailment reduced sets, both in terms of predictive accuracies and learning times.