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From Chain to Tree: Refining Chain-like Rules into Tree-like Rules on Knowledge Graphs

Wangtao Sun, Shizhu He, Jun Zhao, Kang Liu

TL;DR

This work addresses the limited expressive power of chain-like rules in knowledge graph reasoning by introducing tree-like rules, which incorporate branch atoms to constrain grounding values. It presents a three-stage framework—Forward Reasoning, Backward Reasoning, and Candidate Atoms Selection—to refine chain-like rules into tree-like forms, leveraging a matrix-based KG representation for efficient reasoning. Across four public KGs and multiple chain-rule sources, the refined tree-like rules consistently achieve higher $sc$ and lead to improved link prediction performance, with gains correlating to graph density. The approach thus enhances interpretability and predictive accuracy in KG reasoning, providing a versatile method to upgrade existing rule-induction methods.

Abstract

With good explanatory power and controllability, rule-based methods play an important role in many tasks such as knowledge reasoning and decision support. However, existing studies primarily focused on learning chain-like rules, which limit their semantic expressions and accurate prediction abilities. As a result, chain-like rules usually fire on the incorrect grounding values, producing inaccurate or even erroneous reasoning results. In this paper, we propose the concept of tree-like rules on knowledge graphs to expand the application scope and improve the reasoning ability of rule-based methods. Meanwhile, we propose an effective framework for refining chain-like rules into tree-like rules. Experimental comparisons on four public datasets show that the proposed framework can easily adapt to other chain-like rule induction methods and the refined tree-like rules consistently achieve better performances than chain-like rules on link prediction. The data and code of this paper can be available at https://anonymous.4open.science/r/tree-rule-E3CD/.

From Chain to Tree: Refining Chain-like Rules into Tree-like Rules on Knowledge Graphs

TL;DR

This work addresses the limited expressive power of chain-like rules in knowledge graph reasoning by introducing tree-like rules, which incorporate branch atoms to constrain grounding values. It presents a three-stage framework—Forward Reasoning, Backward Reasoning, and Candidate Atoms Selection—to refine chain-like rules into tree-like forms, leveraging a matrix-based KG representation for efficient reasoning. Across four public KGs and multiple chain-rule sources, the refined tree-like rules consistently achieve higher and lead to improved link prediction performance, with gains correlating to graph density. The approach thus enhances interpretability and predictive accuracy in KG reasoning, providing a versatile method to upgrade existing rule-induction methods.

Abstract

With good explanatory power and controllability, rule-based methods play an important role in many tasks such as knowledge reasoning and decision support. However, existing studies primarily focused on learning chain-like rules, which limit their semantic expressions and accurate prediction abilities. As a result, chain-like rules usually fire on the incorrect grounding values, producing inaccurate or even erroneous reasoning results. In this paper, we propose the concept of tree-like rules on knowledge graphs to expand the application scope and improve the reasoning ability of rule-based methods. Meanwhile, we propose an effective framework for refining chain-like rules into tree-like rules. Experimental comparisons on four public datasets show that the proposed framework can easily adapt to other chain-like rule induction methods and the refined tree-like rules consistently achieve better performances than chain-like rules on link prediction. The data and code of this paper can be available at https://anonymous.4open.science/r/tree-rule-E3CD/.
Paper Structure (18 sections, 12 equations, 3 figures, 3 tables)

This paper contains 18 sections, 12 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Method
  4. Forward Reasoning
  5. Backward Reasoning
  6. Candidate Atoms Selection
  7. Experiments
  8. Datasets
  9. Chain-like Rules
  10. Implementations
  11. Setups
  12. Standard Confidence
  13. Link Prediction
  14. Performance Analysis
  15. Case Study
  16. ...and 3 more sections

Figures (3)

  • Figure 1: An example of an inaccurate chain-like rule and the refined tree-like rule. Although the chain-like rule (bottom-left) can predict most cases correctly, due to its chain structure, it has limited expressive power. The refined tree-like rule (bottom-right) leverages the information in the KG that originally ignored to improve the chain-like rule.
  • Figure 2: The framework of our proposed method. In the Forward Reasoning stage, the Query variable $X$ is first grounded with $b$ randomly sampled entities and by forward reasoning, we obtain the grounding values of $Y$ and $Z$. In the Backward Reasoning stage, we then abductively obtain the positive groundings and negative groundings of each variable in the rule body. Finally in the Candidate Atoms Selection stage, three types of candidate branch atoms are then selected according to their inner product scores with the variable representation.
  • Figure 3: Examples of the refinement of chain-like rules into tree-like rules from YAGO3-10, along with their respective Standard Confidences.