In my work, I have studied two inverse problems: extracting facts in the form (subject, predicate, object) from text, and, given such facts, transforming them back into text. These problems are very interesting as they touch upon the issue of hallucinations in large language models. But they also open the question of when two sentences describe the same facts and how we can measure textual similarity in an informative and explainable manner. In this presentation, I will give a short overview of hallucinations and constraint generation, i.e., forcing the model to respect constraints defined for the task.