The Toulmin model has been proved useful in law and argumentation theory. This model describes the basic process in justifying a claim, which comprises six elements, i.e., claim, data, warrant, backing, qualifier, and rebuttal. Specifically, in justifying a claim, one must put forward ‘data’ and a ‘warrant’, whereas the latter is authorized by ‘backing’. The force of the ‘claim’ being justified is represented by the ‘qualifier’, and the condition under which the claim cannot be justified is represented as the ‘rebuttal’. (...) To further improve the model, points out that the selection of a backing needs justification, which he calls legitimation justification. However, how such justification is constituted has not yet been clarified. To identify legitimation justification, we separate it into two parts. One justifies a backing’s eligibility ; the other justifies its superiority over other eligible backings. In this paper, we focus on LJ1 and apply it to the legal justification in hard cases for illustration purposes. We submit that LJ1 refers to the justification of the legal interpretation of a norm by its backing, which can be further separated into several orderable subjustifications. Taking the subjustification of a norm’s existence as an example, we show how it would be influenced by different positions in the philosophy of law. Taking the position of the theory of natural law, such subjustification is presented and evaluated. This paper aims not only to inform ongoing theoretical efforts to apply the Toulmin model in the legal field, but it also seeks to clarify the process in the justification of legal judgments in hard cases. It also offers background information for the possible construction of related AI systems. In our future work, LJ2 and other subjustifications of LJ1 will be discussed. (shrink)