Why is there so little literature on partial order production? Please excuse or improve the poor title of this question.
My question is rather undirected, but I guess I am trying to find out if I might be missing a keyword for my problem.
So there is plenty of work on sorting algorithms.
Sorting is usually understood as creating a / the one correct total order given a set of elements X and their pairwise relationship x &gt;= x' for all x in X. Or  actually &gt;= is the total order and the task is to create a sequence or directed graph s.t. x comes after x' iff x&gt;=x'.
Now you want to do the exact same thing, only &gt;= does not define a total order over X, but only a partial order.
This seems like a very straightforward generalization that I can only imagine is required quite often. Still, under the term partial order production, I find only very little literature on the topic / task.
Am I missing something?
EDIT: Alternative Formulation
Given a set of elements X and a function f that returns the relationship between any two elements x,x' in X. Create a DAG with an edge x-&gt;x' if the relationship is &gt;= and x'-&gt;x if the relationship f((x,x')) is &lt;. Then create the transitive reduction of the DAG.

f(x,x') is either &gt;= or &lt;. This is normal sorting.

f(x,x') is either &gt;=, &lt; or ? (not comparable). This is partial order production.


I would say both are clearly ordering problems, given the relationship function f (the order) and the elements X to order.
Still you find so much on case (1) and hardly anything on case (2).
This is a very well-known problem, known as topological sorting.
Often it is difficult to find material on a subject because we don't know the proper terms to look for. That's why we have sites such as this.