Abstract
In a variety of application domains, (business) processes are intrinsically uncertain. Surprisingly, only very few languages and techniques in BPM consider uncertainty as a first-class citizen. This is also the case in declarative processes, which typically require that process executions satisfy all the elicited process constraints. We counteract this limitation by introducing the notion of probabilistic process constraint. We show how to characterize the semantics of probabilistic process constraints through the interplay of time and probability, and how it is possible to reason over such constraints by loosely coupling temporal and probabilistic reasoning. We then rely on this approach to redefine several key process mining tasks in the light of uncertainty. First, we discuss how probabilistic constraints can be discovered from event data by employing, off-the-shelf, existing algorithms for declarative process discovery. Second, we study how to carry out monitoring, obtaining a setting where a monitored partial trace may be in multiple monitoring states at the same time, though with different probabilities. Third, we handle conformance checking both at the trace and event log level, in the latter case providing a notion of earth mover’s distance that suits with our context. All the presented techniques have been implemented in proof-of-concept prototypes.