In many real-world scenarios, processes naturally define partial orders over their constituent tasks. Partially ordered representations can be exploited in process discovery as they facilitate modeling such processes. The Partially Ordered Workflow Language (POWL) extends partially ordered representations with control-flow operators to support modeling common process constructs such as choice and loop structures. POWL integrates the hierarchical nature of process trees with the flexibility of partially ordered representations, opening up significant opportunities in process discovery. This paper presents and compares various approaches for the automated discovery of POWL models. We investigate the effects of applying varying validity criteria to partial orders, and we propose methods for incorporating frequency information to improve the quality of the discovered models. Additionally, we propose alternative visualizations for POWL models, offering different approaches that may be useful in various contexts. The discovery approaches are evaluated using various real-life data sets, demonstrating the ability of POWL models to capture complex process structures. • Employing different validity requirements in the discovery of POWL models. • Incorporating frequency-based filtering in the discovery of POWL models. • Enhancing the visualization of the discovered models. • Proving the soundness of the discovered models.

Many real-life processes naturally define partial orders over the activities they are composed of. Partial orders can be used as a graph-like representation of process behavior, allowing us to model concurrent and sequential dependencies. The Partially Ordered Workflow Language (POWL) combines block-structured modeling notations with partially-ordered graph representations. A POWL model is a hierarchical model where sub-models can be combined into a new model either using a control-flow operator or as a partial order. The application of POWL models in process mining remains a challenge due to a lack of scalable approaches for the discovery of POWL models. In this paper, we address this gap by proposing an approach for the discovery of POWL models that leverages large data sets and ensures high conformity with the input data. Our approach provides formal guarantees on the uniqueness, existence, and quality of discovered partial orders. The evaluation of our approach underscores its scalability with large data sets and its ability to generate high-quality models.