  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.
