Abstract: Since the 80s, various fields of AI have studied the formal modelling of human reasoning, including some which are relevant in the legal domain, such as handling exceptions (e.g. with default logic) or argumentation. In this talk, after a short description of these formal models, we present work in progress in the context of the AIDAL chair. More precisely, we will focus on three directions: how to incorporate new (unexpected) exceptions in the reasoning, following ideas from case-based reasoning; how to take into account argument strength in reasoning; and how to use Large Language Models to facilitate the extraction of arguments in legal text.