High Quality Embeddings for Horn Logic Reasoning

Yifan Zhang, Yasir White, Dean Clark, Joseph Sanchez, Jevon Lipsey, Ashely Hirst, Jeff Heflin
Proceedings of The 19th International Conference on Neurosymbolic Learning and Reasoning, PMLR 284:116-129, 2025.

Abstract

Neural networks can be trained to rank the choices made by logical reasoners, resulting in more efficient searches for answers. A key step in this process is creating useful embeddings, i.e., numeric representations of logical statements. This paper introduces and evaluates several approaches to creating embeddings that result in better downstream results. We train embeddings using triplet loss, which requires examples consisting of an anchor, a positive example, and a negative example. We introduce three ideas: generating anchors that are more likely to have repeated terms, generating positive and negative examples in a way that ensures a good balance between easy, medium, and hard examples, and periodically emphasizing the hardest examples during training. We conduct several experiments to evaluate this approach, including a comparison of different embeddings across different knowledge bases, in an attempt to identify what characteristics make an embedding well-suited to a particular reasoning task.

Cite this Paper

BibTeX
@InProceedings{pmlr-v284-zhang25a, title = {High Quality Embeddings for Horn Logic Reasoning}, author = {Zhang, Yifan and White, Yasir and Clark, Dean and Sanchez, Joseph and Lipsey, Jevon and Hirst, Ashely and Heflin, Jeff}, booktitle = {Proceedings of The 19th International Conference on Neurosymbolic Learning and Reasoning}, pages = {116--129}, year = {2025}, editor = {H. Gilpin, Leilani and Giunchiglia, Eleonora and Hitzler, Pascal and van Krieken, Emile}, volume = {284}, series = {Proceedings of Machine Learning Research}, month = {08--10 Sep}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v284/main/assets/zhang25a/zhang25a.pdf}, url = {https://proceedings.mlr.press/v284/zhang25a.html}, abstract = {Neural networks can be trained to rank the choices made by logical reasoners, resulting in more efficient searches for answers. A key step in this process is creating useful embeddings, i.e., numeric representations of logical statements. This paper introduces and evaluates several approaches to creating embeddings that result in better downstream results. We train embeddings using triplet loss, which requires examples consisting of an anchor, a positive example, and a negative example. We introduce three ideas: generating anchors that are more likely to have repeated terms, generating positive and negative examples in a way that ensures a good balance between easy, medium, and hard examples, and periodically emphasizing the hardest examples during training. We conduct several experiments to evaluate this approach, including a comparison of different embeddings across different knowledge bases, in an attempt to identify what characteristics make an embedding well-suited to a particular reasoning task.} }
Endnote
%0 Conference Paper %T High Quality Embeddings for Horn Logic Reasoning %A Yifan Zhang %A Yasir White %A Dean Clark %A Joseph Sanchez %A Jevon Lipsey %A Ashely Hirst %A Jeff Heflin %B Proceedings of The 19th International Conference on Neurosymbolic Learning and Reasoning %C Proceedings of Machine Learning Research %D 2025 %E Leilani H. Gilpin %E Eleonora Giunchiglia %E Pascal Hitzler %E Emile van Krieken %F pmlr-v284-zhang25a %I PMLR %P 116--129 %U https://proceedings.mlr.press/v284/zhang25a.html %V 284 %X Neural networks can be trained to rank the choices made by logical reasoners, resulting in more efficient searches for answers. A key step in this process is creating useful embeddings, i.e., numeric representations of logical statements. This paper introduces and evaluates several approaches to creating embeddings that result in better downstream results. We train embeddings using triplet loss, which requires examples consisting of an anchor, a positive example, and a negative example. We introduce three ideas: generating anchors that are more likely to have repeated terms, generating positive and negative examples in a way that ensures a good balance between easy, medium, and hard examples, and periodically emphasizing the hardest examples during training. We conduct several experiments to evaluate this approach, including a comparison of different embeddings across different knowledge bases, in an attempt to identify what characteristics make an embedding well-suited to a particular reasoning task.
APA
Zhang, Y., White, Y., Clark, D., Sanchez, J., Lipsey, J., Hirst, A. & Heflin, J.. (2025). High Quality Embeddings for Horn Logic Reasoning. Proceedings of The 19th International Conference on Neurosymbolic Learning and Reasoning, in Proceedings of Machine Learning Research 284:116-129 Available from https://proceedings.mlr.press/v284/zhang25a.html.

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