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.

We demonstrate a library for the integration of domain knowledge in deep learning architectures. Using this library, the structure of the data is expressed symbolically via graph declarations and the logical constraints over outputs or latent variables can be seamlessly added to the deep models. The domain knowledge can be defined explicitly, which improves the explainability of the models in addition to their performance and generalizability in the low-data regime. Several approaches for such integration of symbolic and sub-symbolic models have been introduced; however, there is no library to facilitate the programming for such integration in a generic way while various underlying algorithms can be used. Our library aims to simplify programming for such integration in both training and inference phases while separating the knowledge representation from learning algorithms. We showcase various NLP benchmark tasks and beyond. The framework is publicly available at Github(https://github.com/HLR/DomiKnowS).