Probabilistic Temporal Logic over Finite Traces (Technical Report)

Temporal logics over finite traces have recently gained attention due to their use in real-world applications, in particular in business process modelling and planning. In real life, processes contain some degree of uncertainty that is impossible to handle with classical logics. We propose a new probabilistic temporal logic over finite traces based on superposition semantics, where all possible evolutions are possible, until observed. We study the properties of the logic and provide automata-based mechanisms for deriving probabilistic inferences from its formulas. We ground the approach in the context of declarative process modelling, showing how the temporal patterns used in Declare can be lifted to our setting, and discussing how probabilistic inferences can be exploited to provide key offline and runtime reasoning tasks, and how to discover probabilistic Declare patterns from event data by minor adjustments to existing discovery algorithms.