Abstract
Recently, increasing efforts are put into learning continual representations for symbolic knowledge bases (KBs). However, these approaches either only embed the data-level knowledge (ABox) or suffer from inherent limitations when dealing with concept-level knowledge (TBox), i.e., they cannot faithfully model the logical structure present in the KBs. We present BoxEL, a geometric KB embedding approach that allows for better capturing the logical structure (i.e., ABox and TBox axioms) in the description logic \(\mathcal{E}\mathcal{L}^{++}\). BoxEL models concepts in a KB as axis-parallel boxes that are suitable for modeling concept intersection, entities as points inside boxes, and relations between concepts/entities as affine transformations. We show theoretical guarantees (soundness) of BoxEL for preserving logical structure. Namely, the learned model of BoxEL embedding with loss 0 is a (logical) model of the KB. Experimental results on (plausible) subsumption reasonings and a real-world application–protein-protein prediction show that BoxEL outperforms traditional knowledge graph embedding methods as well as state-of-the-art \(\mathcal{E}\mathcal{L}^{++}\) embedding approaches.
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Notes
- 1.
Under the translation setting, the embeddings will simply become \(\textsf {Parent} \equiv \textsf {Person}\), which is obviously not what we want as we can express \(\textsf {Parent} \not \equiv \textsf {Person}\) with \(\mathcal{E}\mathcal{L}^{++}\) by propositions like \(\textsf {Children} \sqcap \textsf {Parent} \sqsubseteq \bot \), \(\textsf {Children} \sqsubseteq \textsf {Person}\) and \(\textsf {Children}(a)\).
- 2.
Compared with the example given in [15], we add additional concept assertion statements that distinguish entities and concepts:.
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Acknowledgments
The authors thank the International Max Planck Research School for Intelligent Systems (IMPRS-IS) for supporting Bo Xiong. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No: 860801. Nico Potyka was partially funded by DFG projects Evowipe/COFFEE.
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Xiong, B., Potyka, N., Tran, TK., Nayyeri, M., Staab, S. (2022). Faithful Embeddings for \(\mathcal{E}\mathcal{L}^{++}\) Knowledge Bases. In: Sattler, U., et al. The Semantic Web – ISWC 2022. ISWC 2022. Lecture Notes in Computer Science, vol 13489. Springer, Cham. https://doi.org/10.1007/978-3-031-19433-7_2
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