Reasoning with legal cases has long been modelled using symbolic methods. In recent years, the increased availability of legal data together with improved machine learning techniques has led to an explosion of interest in data-driven methods being applied to the problem of predicting outcomes of legal cases. Although encouraging results have been reported, they are unable to justify the outcomes produced in satisfactory legal terms and do not exploit the structure inherent within legal domains; in particular, with respect to the issues and factors relevant to the decision. In this paper we present the technical foundations of a novel hybrid approach to reasoning with legal cases, using Abstract Dialectical Frameworks (ADFs) in conjunction with hierarchical BERT. ADFs are used to represent the legal knowledge of a domain in a structured way to enable justifications and improve performance. The machine learning is targeted at the task of factor ascription; once factors present in a case are ascribed, the outcome follows from reasoning over the ADF. To realise this hybrid approach, we present a new hybrid system to enable factor ascription, envisioned for use in legal domains, such as the European Convention on Human Rights that is used frequently in modelling experiments.