# Exploiting Answer Set Programming with External Sources for Meta-Interpretive Learning

arXiv: https://arxiv.org/abs/1805.00068 · HTML: https://mlsanity.com/paper/1805.00068/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2018.

## Built on by (most cited first, 12 of 12)

- [Inductive logic programming at 30](https://mlsanity.com/paper/2102.10556/) (2021)
- [Learning Higher-Order Programs without Meta-Interpretive Learning](https://mlsanity.com/paper/2112.14603/) (2021)
- [Top Program Construction and Reduction for polynomial time Meta-Interpretive Learning](https://mlsanity.com/paper/2101.05050/) (2021)
- [Learning Logic Programs From Noisy Failures](https://mlsanity.com/paper/2201.03702/) (2021)
- [Learning First-Order Rules with Differentiable Logic Program Semantics](https://mlsanity.com/paper/2204.13570/) (2022)
- [Meta-Interpretive Learning as Metarule Specialisation](https://mlsanity.com/paper/2106.07464/) (2021)
- [Learning programs with magic values](https://mlsanity.com/paper/2208.03238/) (2022)
- [Relational program synthesis with numerical reasoning](https://mlsanity.com/paper/2210.00764/) (2022)
- [Learning logic programs through divide, constrain, and conquer](https://mlsanity.com/paper/2109.07818/) (2021)
- [Parallel Constraint-Driven Inductive Logic Programming](https://mlsanity.com/paper/2109.07132/) (2021)
- [Neuro-Symbolic Contrastive Learning for Cross-domain Inference](https://mlsanity.com/paper/2502.09213/) (2025)
- [Visual Perceptual to Conceptual First-Order Rule Learning Networks](https://mlsanity.com/paper/2604.07897/) (2026)

## Abstract (arXiv)

Meta-Interpretive Learning (MIL) learns logic programs from examples by instantiating meta-rules, which is implemented by the Metagol system based on Prolog. Viewing MIL-problems as combinatorial search problems, they can alternatively be solved by employing Answer Set Programming (ASP), which may result in performance gains as a result of efficient conflict propagation. However, a straightforward ASP-encoding of MIL results in a huge search space due to a lack of procedural bias and the need for grounding. To address these challenging issues, we encode MIL in the HEX-formalism, which is an extension of ASP that allows us to outsource the background knowledge, and we restrict the search space to compensate for a procedural bias in ASP. This way, the import of constants from the background knowledge can for a given type of meta-rules be limited to relevant ones. Moreover, by abstracting from term manipulations in the encoding and by exploiting the HEX interface mechanism, the import of such constants can be entirely avoided in order to mitigate the grounding bottleneck. An experimental evaluation shows promising results.