Extending the construction to POWL

Construct a cospan-algebra signature presentation for Partially Ordered Workflow Language (POWL) models and establish how the resulting structural certificate relates to POWL’s language-preserving workflow-net translation.

Background

POWL is identified as a possible fifth notation for the common framework. It combines arbitrary partial-order composition with choice and loop operators, suggesting that its syntax could be represented by an AND/OR graph and mapped to the paper’s generator-cospan signatures.

The unresolved work is to carry out this construction formally, thereby extending the framework beyond Petri nets, causal nets, process trees, and BPMN, and to compare the resulting signature-based certificate with POWL’s existing language-preserving translation into workflow nets.

References

Section~\ref{subsec:open-problems} collects four open problems. It asks which series-parallel-poset languages a process tree can define, whether process trees admit a canonical form covering the loop operator, in what precise sense the BPMN normal form is faithful to its OR-gateway original, and whether POWL fits as a further instance of the general framework.

— String Diagrams for Process Mining  (2609.20478 - Lee et al., 17 Sep 2026) in Section 4.5, subsection “Open problems,” item 4; discussed also in Section 4.4