# Logical reduction of metarules

arXiv: https://arxiv.org/abs/1907.10952 · HTML: https://mlsanity.com/paper/1907.10952/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jul 2019.

## Built on by (most cited first, 19 of 19)

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- [Latent Logic Tree Extraction for Event Sequence Explanation from LLMs](https://mlsanity.com/paper/2406.01124/) (2024)
- [A Critical Review of Inductive Logic Programming Techniques for Explainable AI](https://mlsanity.com/paper/2112.15319/) (2021)
- [Learning logic programs by combining programs](https://mlsanity.com/paper/2206.01614/) (2022)
- [Learning Logic Programs From Noisy Failures](https://mlsanity.com/paper/2201.03702/) (2021)
- [Generalisation Through Negation and Predicate Invention](https://mlsanity.com/paper/2301.07629/) (2023)
- [Learning logic programs by discovering where not to search](https://mlsanity.com/paper/2202.09806/) (2022)
- [Learning programs with magic values](https://mlsanity.com/paper/2208.03238/) (2022)
- [Learning logic programs through divide, constrain, and conquer](https://mlsanity.com/paper/2109.07818/) (2021)
- [Learning logic programs by discovering higher-order abstractions](https://mlsanity.com/paper/2308.08334/) (2023)
- [Boolean Matrix Logic Programming on the GPU](https://mlsanity.com/paper/2408.10369/) (2024)
- [Modelling Program Spaces in Program Synthesis with Constraints](https://mlsanity.com/paper/2508.00005/) (2025)
- [Towards One-Shot Learning for Text Classification using Inductive Logic Programming](https://mlsanity.com/paper/2308.15885/) (2023)
- [Honey, I shrunk the hypothesis space (through logical preprocessing)](https://mlsanity.com/paper/2506.06739/) (2025)
- [Object-Oriented Transition Modeling with Inductive Logic Programming](https://mlsanity.com/paper/2602.07602/) (2026)
- [Continual learning and refinement of causal models through dynamic predicate invention](https://mlsanity.com/paper/2602.17217/) (2026)

## Abstract (arXiv)

Many forms of inductive logic programming (ILP) use 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 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.