Explainability of algorithmic decision-making systems is both a regulatory objective and an area of intense research. The article argues that a crucial condition for the acceptability of algorithmic decision-making systems is that decisions must be justified in the eyes of their recipients. We make a clear distinction between explanation and justification. Explanations describe how a decision was made, while justifications give reasons that aim to make the decision acceptable. We propose a conceptual framework of explanations and justifications, based on Habermas's theory of communicative action and Perelman's New Rhetoric theory of law. This framework helps to analyze how different forms of explanation can support or fail to support justification. We illustrate our approach with a case study on university admissions in France.

翻译：算法决策系统的可解释性既是监管目标，也是当前研究的热点领域。本文认为，算法决策系统可被接受的关键条件在于其决策必须在接收者眼中具有正当性。我们明确区分了"解释"与"正当性论证"：解释描述决策如何形成，而正当性论证则提供旨在使决策被接受的理由。基于哈贝马斯的交往行动理论与佩雷尔曼的新修辞法学理论，我们提出了一个解释与正当性论证的概念框架。该框架有助于分析不同形式的解释如何支持或无法支持正当性论证。我们以法国大学招生案例研究为例，具体阐述了该方法的应用。