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：序关系是衡量（实证）数据中对象之间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，基于序关系的方法数量相对较少。其原因之一在于上世纪计算资源有限，难以支撑序关系运算所需；另一个尤其与此研究方向相关的原因是，基于序关系的方法常被认为数学上过于严谨，难以应用于真实世界数据。因此，本文旨在探讨针对序结构（一类特殊的有向图）进行度量与"计算"的不同方式，并展示如何从中推断知识。我们的目标是建立有序数据科学作为一项全新的研究议程。除了与机器学习及知识表征等其他基石方法相互促进外，心理学、社会学、经济学、网络科学、知识工程、科学计量学等多个学科也将从这一研究中受益。