Order is one of the main instruments to measure the relationship between objects in (empirical) data. However, compared to methods that use numerical properties of objects, the amount of ordinal methods developed is rather small. One reason for this is the limited availability of computational resources in the last century that would have been required for ordinal computations. Another reason -- particularly important for this line of research -- is that order-based methods are often seen as too mathematically rigorous for applying them to real-world data. In this paper, we will therefore discuss different means for measuring and 'calculating' with ordinal structures -- a specific class of directed graphs -- and show how to infer knowledge from them. Our aim is to establish Ordinal Data Science as a fundamentally new research agenda. Besides cross-fertilization with other cornerstone machine learning and knowledge representation methods, a broad range of disciplines will benefit from this endeavor, including, psychology, sociology, economics, web science, knowledge engineering, scientometrics.

翻译：顺序是衡量（经验）数据中对象关系的主要工具之一。然而，与利用对象数值属性的方法相比，目前开发的序数方法数量较少。其中一个原因是上世纪用于序数计算的计算资源有限；另一个对这一研究方向尤为重要的原因是，基于顺序的方法常被认为在数学上过于严谨，难以应用于实际数据。因此，本文将讨论测量和“计算”序数结构（一类特殊的有向图）的不同方式，并展示如何从中推断知识。我们的目标是建立序数数据科学作为一项全新研究议程。除了与机器学习、知识表示等其他基石性方法相互促进外，心理学、社会学、经济学、网络科学、知识工程、科学计量学等广泛学科领域也将从中受益。