Teaching Probabilistic Logical Reasoning to Transformers

Abstract: In this paper, we evaluate the capability of transformer-based LLMs in making inferences over uncertain text that includes uncertain rules of reasoning. We cover both Pre-trained LLMs (PLMs) and generative LLMs. Our evaluation results show that both generations of LLMs struggle with reasoning over uncertain text. We propose a novel end-to-end fine-tuning approach, Probabilistic Constraint Training (PCT), that utilizes probabilistic logical rules as constraints in the fine-tuning phase without relying on these rules in the inference stage. To assess the effectiveness of PCT, we utilize the related corpora and, additionally, create a new and more challenging benchmark that, unlike the previous ones, uses instance-specific rules. Our study demonstrates that PCT improves the transformer-based LLM's intrinsic reasoning and makes their probabilistic logical reasoning process more explicit and explainable. Furthermore, PCT equips these models to effectively handle novel situations, including higher reasoning depth, new domains, and complex probabilistic structures.