High Quality Embeddings for Horn Logic Reasoning

2026-05-19

AI Summary

This work proposes a high-quality embedding method for logical statements to enhance the ranking efficiency of neural networks in Horn clause reasoning. The approach leverages triplet loss and introduces several key innovations: an anchor generation strategy that incorporates duplicate elements, a balanced sampling mechanism for constructing positive and negative examples based on difficulty, and a dynamic training scheme that periodically focuses on the hardest samples. Experimental results demonstrate that the proposed method significantly improves both search efficiency and accuracy in logical reasoning across multiple knowledge bases, thereby providing effective support for neuro-symbolic reasoning tasks.

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.

Problem

• Horn logic
• embeddings
• logical reasoning
• triplet loss
• knowledge base

Innovation

• Horn logic
• embedding
• triplet loss
• hard example mining
• logical reasoning