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Learning big logical rules by joining small rules

Céline Hocquette, Andreas Niskanen, Rolf Morel, Matti Järvisalo, Andrew Cropper

TL;DR

The paper tackles the challenge of learning large rules in inductive logic programming by proposing to join small rules into bigger rules. It introduces Joiner, a constraint-driven extension of Combocombo that employs a SAT-based join stage with incomplete and complete search phases and two optimal-sound constraints to guarantee optimality. The approach enables learning rules with over 100 literals and delivers substantial predictive-accuracy gains across diverse domains, while outperforming state-of-the-art ILP baselines like Combo and Aleph. This work demonstrates that decomposition, constraint pruning, and SAT-based search can make scalable, interpretable big-rule learning practical for real-world relational tasks.

Abstract

A major challenge in inductive logic programming is learning big rules. To address this challenge, we introduce an approach where we join small rules to learn big rules. We implement our approach in a constraint-driven system and use constraint solvers to efficiently join rules. Our experiments on many domains, including game playing and drug design, show that our approach can (i) learn rules with more than 100 literals, and (ii) drastically outperform existing approaches in terms of predictive accuracies.

Learning big logical rules by joining small rules

TL;DR

The paper tackles the challenge of learning large rules in inductive logic programming by proposing to join small rules into bigger rules. It introduces Joiner, a constraint-driven extension of Combocombo that employs a SAT-based join stage with incomplete and complete search phases and two optimal-sound constraints to guarantee optimality. The approach enables learning rules with over 100 literals and delivers substantial predictive-accuracy gains across diverse domains, while outperforming state-of-the-art ILP baselines like Combo and Aleph. This work demonstrates that decomposition, constraint pruning, and SAT-based search can make scalable, interpretable big-rule learning practical for real-world relational tasks.

Abstract

A major challenge in inductive logic programming is learning big rules. To address this challenge, we introduce an approach where we join small rules to learn big rules. We implement our approach in a constraint-driven system and use constraint solvers to efficiently join rules. Our experiments on many domains, including game playing and drug design, show that our approach can (i) learn rules with more than 100 literals, and (ii) drastically outperform existing approaches in terms of predictive accuracies.
Paper Structure (44 sections, 21 theorems, 13 equations, 9 figures, 5 tables, 2 algorithms)

This paper contains 44 sections, 21 theorems, 13 equations, 9 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Novelty and Contributions.
  3. Related Work
  4. Problem Setting
  5. Algorithm
  6. Combo.
  7. Joiner
  8. Generate
  9. Join
  10. Incomplete Join Stage
  11. Complete Join Stage
  12. Finding Conjunctions using SAT
  13. Subset-maximal coverage conjunctions.
  14. Maximal coverage conjunctions.
  15. Constrain
  16. ...and 29 more sections

Key Result

Proposition 1

Let $c_1$ and $c_2$ be two conjunctions which do not entail any negative examples, $c_1 \models E^{+}_1$, $c_2 \models E^{+}_2$, $E^{+}_2 \subseteq E^{+}_1$, and $size(c_1) < size(c_2)$. Then $c_2$ cannot be in an optimal solution.

Figures (9)

  • Figure 1: Two positive Zendo examples.
  • Figure 2: Three negative Zendo examples.
  • Figure 3: Predictive accuracy (%) with and without join stage with 60s (left) and 600s (right) timeouts.
  • Figure 4: Predictive accuracies (%) with and without generating splittable programs with 60s (left) and 600s (right) timeouts.
  • Figure 5: Predictive accuracies (%) when varying the optimal solution size for zendo (left) and string (right) with a 600s timeout.
  • ...and 4 more figures

Theorems & Definitions (57)

  • Definition 1: LFF input
  • Definition 2: Solution
  • Definition 3: Optimal solution
  • Definition 4: Splittable rule
  • Example 1
  • Example 2
  • Definition 5: Splittable program
  • Definition 6: Conjunction
  • Proposition 1
  • Example 3: Join stage
  • ...and 47 more