Representation of procedural knowledge I know that knowledge about relationships between things can be represented using ontologies and stored in some sort of file or database system.

Can a network of procedural knowledge also be created in this way? Such that complex algorithms can be defined and stored efficiently, translated into other languages and forms (such as finite state machines or machine language), changed, and form the basis for other AI axioms?

i.e. Procedural Reasoning Systems -- how would a Knowledge Area (KA) be represented as a cognitive primitive in a computer system?
You are probably speaking about something like a process ontology. Lately, that research has focused (moved?) on semantic workflows, e.g. to model processes in science, related with reproducibility. Similarly, we can also find the application of ontologies to business processes.

For more classical (lower level?) approaches, you may be interested in the homoiconicity property of programming languages like Lisp. In such a case these "networks" usually take the shape of parse trees, i.e. the representation is at a syntactic level and semantics are implicit, e.g. loops and recursive calls are still just a syntactic tree, even if the execution would not result into a tree.