  In this paper, we evaluate the capability of transformer-based language
models in making inferences over uncertain text that includes uncertain rules
of reasoning. We cover both Pre-trained Language Models (PLMs) and generative
Large Language Models (LLMs). Our evaluation results show that both generations
of language models 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 language model'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.
