Abductive reasoning is logical reasoning that makes educated guesses to infer the most likely reasons to explain the observations. However, the abductive logical reasoning over knowledge graphs (KGs) is underexplored in KG literature. In this paper, we initially and formally raise the task of abductive logical reasoning over KGs, which involves inferring the most probable logic hypothesis from the KGs to explain an observed entity set. Traditional approaches use symbolic methods, like searching, to tackle the knowledge graph problem. However, the symbolic methods are unsuitable for this task, because the KGs are naturally incomplete, and the logical hypotheses can be complex with multiple variables and relations. To address these issues, we propose a generative approach to create logical expressions based on observations. First, we sample hypothesis-observation pairs from the KG and use supervised training to train a generative model that generates hypotheses from observations. Since supervised learning only minimizes structural differences between generated and reference hypotheses, higher structural similarity does not guarantee a better explanation for observations. To tackle this issue, we introduce the Reinforcement Learning from the Knowledge Graph (RLF-KG) method, which minimizes the differences between observations and conclusions drawn from the generated hypotheses according to the KG. Experimental results demonstrate that transformer-based generative models can generate logical explanations robustly and efficiently. Moreover, with the assistance of RLF-KG, the generated hypothesis can provide better explanations for the observations, and the method of supervised learning with RLF-KG achieves state-of-the-art results on abductive knowledge graph reasoning on three widely used KGs.

翻译：溯因推理是通过有根据的猜测推断出最可能解释观测结果的逻辑推理方式。然而，知识图谱中的溯因逻辑推理在现有文献中尚未得到充分探索。本文首次正式提出知识图谱上的溯因逻辑推理任务，该任务旨在从知识图谱中推断出最可能的逻辑假设以解释观测到的实体集合。传统方法采用符号化方法（如搜索）来处理知识图谱问题，但由于知识图谱天然存在不完备性，且逻辑假设可能包含多变量和多关系的复杂结构，这类符号方法并不适用于此任务。针对上述问题，我们提出一种基于观测生成逻辑表达式的生成式方法：首先从知识图谱中采样假设-观测对，通过监督训练使生成模型能够从观测结果生成假设。由于监督学习仅最小化生成假设与参考假设的结构差异，而较高的结构相似性并不能保证对观测结果的更好解释，为此我们引入基于知识图谱的强化学习（RLF-KG）方法，通过最小化根据知识图谱从生成假设推导出的结论与观测结果之间的差异来优化模型。实验结果表明，基于Transformer的生成模型能够稳健高效地生成逻辑解释。在RLF-KG的辅助下，生成假设能为观测结果提供更优解释，结合RLF-KG的监督学习方法在三个广泛使用的知识图谱溯因推理基准上取得了最先进的性能。