Do Petri Nets Provide the Right Representational Bias for Process Mining?

Process discovery is probably the most challenging process mining task. Given an event log, i.e., a set of example traces, it is difficult to automatically construct a process model explaining the behavior seen in the log. Many process discovery techniques use Petri nets as a language to describe the discovered model. This implies that the search space—often referred to as the representational bias—includes many inconsistent models (e.g., models with deadlocks and livelocks). Moreover, the low-level nature of Petri nets does not help in finding a proper balance between overfitting and underfitting. Therefore, we advocate a new representation more suitable for process discovery: causal nets. Causal nets are related to the representations used by several process discovery techniques (e.g., heuristic mining, fuzzy mining, and genetic mining). However, unlike existing approaches, C-nets use declarative semantics tailored towards process mining. 1 Challenges in Process Mining Process mining is an emerging research area combining techniques from process modeling, model-based analysis, data mining, and machine learning. The goal is to extract knowledge about processes from event data stored in databases, transaction logs, message logs, etc. Process mining techniques are commonly classified into: (a) discovery, (b) conformance, and (c) enhancement [2]. In this paper, we restrict ourselves to control-flow discovery, i.e., learning a process model based on example traces. A trace is a sequence of events for a particular process instance (also referred to as case). Events refer to some activity. For example, the trace 〈a, b, c, d〉 refers to a process execution starting with activity a and ending with activity d. An event log is a multiset of traces, e.g., L = {〈a, b, c, d〉, 〈a, c, b, d〉, 〈a, e, d〉} describes the execution sequences of 90 cases. There are dozens of process discovery techniques that are able to construct a process model from such an event log. Many of these techniques use Petri nets as a target representation [4,5,7,12,19,22,23]. Given event log L, these techniques have no problems discovering the Petri net in which, after a, there is a choice between doing b and c concurrently or just e, followed by d. Note that this example is misleadingly simple as process discovery based on real-life event logs is extremely challenging. Generally, we use four main quality dimensions for judging the quality of the discovered process model: fitness (the model should allow for the behavior observed), simplicity (the model should be as simple as possible), precision (the model should not allow for behavior that is very unlikely given the event log), and generalization (the model should not just represent the observed examples and also allow for behavior not yet observed but very similar to earlier behavior).