To bind or not to bind? Discovering Stable Relationships in Object-centric Processes (Extended Version)

TL;DR

This paper explores how to formally identify and represent stable relationships between objects in object-centric process models, bridging the gap between informal models and formal synchronization approaches.

Contribution

It introduces a formal mapping from object-centric Petri nets to object-centric Petri nets with identifiers, capturing stable many-to-one object relationships.

Findings

Formal mapping from OCPNs to OPIDs for stable relationships

Proof of equivalence for executions satisfying relationships

Implementation of the mapping process

Abstract

Object-centric process mining investigates the intertwined behavior of multiple objects in business processes. From object-centric event logs, object-centric Petri nets (OCPN) can be discovered to replay the behavior of processes accessing different object types. Although they indicate how objects flow through the process and co-occur in events, OCPNs remain underspecified about the relationships of objects. Hence, they are not able to represent synchronization, i.e. executing objects only according to their intended relationships, and fail to identify violating executions. Existing formal modeling approaches, such as object-centric Petri nets with identifiers (OPID), represent object identities and relationships to synchronize them correctly. However, OPID discovery has not yet been studied. This paper uses explicit data models to bridge the gap between OCPNs and formal OPIDs. We identify the implicit assumptions of stable many-to-one relationships in object-centric event logs, which implies synchronization of related objects. To formally underpin this observation, we combine OCPNs with explicit stable many-to-one relationships in a rigorous mapping from OCPNs to OPIDs explicitly capturing the intended stable relationships and the synchronization of related objects. We prove that the original OCPNs and the resulting OPIDs coincide for those executions that satisfy the intended relationships. Moreover, we provide an implementation of the mapping from OCPN to OPID under stable relationships.