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Neurosymbolic Methods for Rule Mining

Agnieszka Lawrynowicz, Luis Galarraga, Mehwish Alam, Berenice Jaulmes, Vaclav Zeman, Tomas Kliegr

TL;DR

The chapter surveys rule mining and rule learning for knowledge graphs, framing the problem around Horn rules and multiple evaluation metrics under open-world assumptions. It contrasts traditional ILP approaches (e.g., AMIE, AMIE3), path-based and LP-based rule mining (RuDiK, AnyBURL, RARL, LPRules) with neurosymbolic methods that fuse deep learning, embeddings, and matrix-based rule evaluation (Neural-LP, TensorLog, RLvLR, ChatRule, HtT). It highlights the strengths and trade-offs of each paradigm, including explainability, scalability, and data-completeness considerations, and discusses how large language models are being integrated to generate and reason over rule libraries. The practical significance lies in advancing scalable, interpretable, and accurate KG inference by combining symbolic rules with neural representations and language-model-driven rule generation. The coverage points to a future where neuro-symbolic rule learning enables robust, explainable KG completion and reasoning in the presence of incomplete or evolving data.

Abstract

In this chapter, we address the problem of rule mining, beginning with essential background information, including measures of rule quality. We then explore various rule mining methodologies, categorized into three groups: inductive logic programming, path sampling and generalization, and linear programming. Following this, we delve into neurosymbolic methods, covering topics such as the integration of deep learning with rules, the use of embeddings for rule learning, and the application of large language models in rule learning.

Neurosymbolic Methods for Rule Mining

TL;DR

The chapter surveys rule mining and rule learning for knowledge graphs, framing the problem around Horn rules and multiple evaluation metrics under open-world assumptions. It contrasts traditional ILP approaches (e.g., AMIE, AMIE3), path-based and LP-based rule mining (RuDiK, AnyBURL, RARL, LPRules) with neurosymbolic methods that fuse deep learning, embeddings, and matrix-based rule evaluation (Neural-LP, TensorLog, RLvLR, ChatRule, HtT). It highlights the strengths and trade-offs of each paradigm, including explainability, scalability, and data-completeness considerations, and discusses how large language models are being integrated to generate and reason over rule libraries. The practical significance lies in advancing scalable, interpretable, and accurate KG inference by combining symbolic rules with neural representations and language-model-driven rule generation. The coverage points to a future where neuro-symbolic rule learning enables robust, explainable KG completion and reasoning in the presence of incomplete or evolving data.

Abstract

In this chapter, we address the problem of rule mining, beginning with essential background information, including measures of rule quality. We then explore various rule mining methodologies, categorized into three groups: inductive logic programming, path sampling and generalization, and linear programming. Following this, we delve into neurosymbolic methods, covering topics such as the integration of deep learning with rules, the use of embeddings for rule learning, and the application of large language models in rule learning.
Paper Structure (33 sections, 28 equations, 2 figures)

This paper contains 33 sections, 28 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Rules
  4. Closed World vs Open World Assumption
  5. Rule Mining
  6. Inductive Logic Programming
  7. AMIE
  8. AMIE+ galarraga_fast_2015
  9. AMIE 3
  10. Path Sampling and Generalization
  11. RuDiK ortona_robust_2018
  12. AnyBURL meilicke2019introduction
  13. RARL pirro_relatedness_2020
  14. Linear programming
  15. Neurosymbolic Methods
  16. ...and 18 more sections

Figures (2)

  • Figure 1: Sample knowledge graph.
  • Figure 2: The classification of predictions made by a rule $B_1 \wedge B_2 \wedge ... \wedge B_n \implies p(x, y)$ pertains to a fact in the rule head. This fact can be either true or false in the real world and can be known or unknown to the KG. This results in four possible situations regarding the KG and the real world. Predictions made by the rule with respect to the KG are represented inside the circle.