In a variety of application domains, (business) processes are intrinsically uncertain. Surprisingly, interest in uncertain process models has increased only recently, with a main focus in process mining. This calls for understanding, at the foundational level, how uncertainty and behavior interact with each other. On the one hand, imperative process models have a long tradition grounded in variants of stochastic Petri nets, which however misses techniques that match key process-related requirements, such as duplicate labels and silent transitions. On the other hand, little is known about uncertainty in declarative processes, due to the lack of studies on uncertainty in temporal logics over finite traces.
In this talk, we report on some of our recent advancements in this fascinating area, with a broad focus that spans from model-driven to data-driven analysis. We start with declarative processes, considering in particular the Declare language and its formalization in linear temporal logic over finite traces. To deal with uncertainty, we formally define the notion of probabilistic process constraint and show how it is possible to reason over probabilistic Declare specifications by loosely coupling reasoning on behaviors through finite-state automata, and reasoning on probabilities through analytical methods. We then turn to imperative processes, describing how reasoning on stochastic processes with repeated labels and silent transitions can be conducted by leveraging techniques from qualitative model checking of Markov chains, paired with automata-based techniques to handle silent transitions. This allows us to combine the two streams, in particular to check whether a stochastic imperative process conforms to a probabilistic declarative specification. We close by discussing the implication of the introduced techniques to process mining, considering in particular discovery, conformance checking, and monitoring.