# Define a directed edge in a DAG using partial ordering

I am trying to describe a novel type of DAG's construction algorithm. The directed edges of the graph corresponds to a partial ordering: i.e. any directed edge $$e$$ spanning from $$f$$ to $$t$$ also observes: $$f \preceq t$$.

Q: How can I precisely define the main task of edge construction: that is finding the node $$f$$ for a given $$t$$?

It is something like this:

find all $$f_a \in \{ f_i \}$$ s.t. $$f_a \preceq t$$ $$\land \nexists f_j$$ s.t. $$f_i \preceq f_j$$

but I'm not sure if this is sufficient or even understandable?

### Some Background

Without getting too specific: the DAG itself is that of an executed program, and is used for dynamic runtime analysis. Each node represents the execution of some event, while an edge $$e = f \rightarrow t$$ means that $$f$$ triggered $$t$$.