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An original model for multi-target learning of logical rules for knowledge graph reasoning

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Abstract

Large-scale knowledge graphs are crucial for structuring human knowledge; however, they often remain incomplete. This paper tackles the challenge of completing missing factual triples in knowledge graphs using through rule reasoning. Current rule learning methods tend to allocate a significant portion of triples to constructing the graph during training, while neglecting multi-target reasoning scenarios. Furthermore, these methods typically depend on qualitative assessments of mined rules, lacking a quantitative method to evaluate rule quality. We propose a model that optimizes training data usage and supports multi-target reasoning. To overcome limitations in evaluating model performance and rule quality, we propose two novel metrics. Experimental results show that our model outperforms baseline methods on five benchmark datasets, validating the effectiveness of these metrics.

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Data Availability

The experimental data that supports the findings of this study is available in GitHub at the following URL: https://github.com/lirt1231/MPLR

Notes

  1. In Neural LP framework, they view tail as the question to query, and only one head the answer to the query. Then a confidence \(\alpha _i\) is assigned to one particular path \(p_i\).

  2. To be more precise, our model simulates the removal of edges associated with the input query are removed, as previously detailed in Section 4.2.It is worth noting that in Neural LP [43], DRUM [32], and similar models, a reversed query (?, q, t) with answer h is added for each triple. However, for a fair comparison, we only use the query (h, q, ?)

  3. The URLs we use to implement these models are listed in Appendix B.2.

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Acknowledgements

The work of this paper is supported by the "National Key R&D Program of China" (2021YFB2012400), "National Natural Science Foundation of China" (Grant No. 62272129).

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Authors and Affiliations

  1. Research Institute of Cyberspace Security, Harbin Institute of Technology, Harbin, 150001, China

    Haotian Li, Bailing Wang, Kai Wang, Rui Zhang & Yuliang Wei

  2. School of Computer Science and Technology, Harbin Institute of Technology, Weihai, 264209, China

    Haotian Li, Kai Wang, Rui Zhang & Yuliang Wei

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  2. Bailing Wang
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Contributions

1. Haotian Li: Software, Data Curation, Writing - Original Draft 2. Bailing Wang: Conceptualization, Methodology, Writing - Original Draft 3. Kai Wang: Writing - Review 4. Rui Zhang: Validation, Writing - Review 5. Yuliang Wei: Conceptualization, Funding acquisition

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Appendices

Appendix A    An example of TensorLog for KG reasoning

Each KG entity \(e \in \mathcal {E}\) depicted in Fig. 1 is encoded into a binary vector of length \(|\mathcal {E}| = 6\). For each predicate \(p \in \mathcal {P}\) and each pair of entities \(e_i, e_j \in \mathcal {E}\), the TensorLog operator associated with p is defined as a matrix \(\textrm{M}_p \in \{0,1\}^{|\mathcal {E}| \times |\mathcal {E}|}\). The (i, j)-th element of this matrix is set to 1 (indicated in in the matrices) if the triple \((e_i, p, e_j)\) exists in \(\mathcal {G}\). Taking the KG illustrated in Fig. 1 as an example, for the predicate \(p = \texttt {daughterOf}\), we have:

The rule sisterOf(X, Z) \(\wedge \) sonOf(Z, Y) \(\Rightarrow \) daughterOf(X, Y) can be simulated by performing the following sparse matrix multiplication:

By setting \(\textrm{v}_{z_1} = [0, 0, 1, 0, 0, 0]^{\top }\) as the one-hot vector of \(z_1\) and performing left multiplication with \(\textrm{v}_{z_1}^{\top }\), we compute \(s^{\top } = \textrm{v}_{z_1}^{\top } \cdot \mathrm {M_{p'}}\). This operation effectively selects the row in \(\mathrm {M_{p'}}\) corresponding to \(z_1\). Subsequent right-hand side multiplication by \(\textrm{v}_{x_1}\) yields the number of unique paths following the pattern \(\texttt {sisterOf} \wedge \texttt {sonOf}\) from \(z_1\) to \(x_1\): \(s^{\top } \cdot \textrm{v}_{x_1} = 1\).

Appendix B    Experiment

1.1 B.1    Extension to Table 3: saturations of UMLS

Table 8 Saturation metrics obtained from the UMLS dataset (without sampling)
Full size table

1.2 B.2    Implementation details

The models we use are available at the following URLs:

1.3 B.3    Extension to Table 4: bifurcation of all datasets

Table 9 Bifurcation(%) of all datasets
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1.4 B.4    Extension to Table 2: results on FB15K-237 and WN18

Table 10 Knowledge graph completion results on the FB15K-237 and WN18 datasets
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1.5 B.5    Extension to Table 7: more mined rules from the Family dataset

Table 11 Rules mined by MPLR from the Family dataset
Full size table

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Li, H., Wang, B., Wang, K. et al. An original model for multi-target learning of logical rules for knowledge graph reasoning. Appl Intell 55, 138 (2025). https://doi.org/10.1007/s10489-024-05966-1

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