  Temporal logics over finite traces have recently seen wide application in a
number of areas, from business process modelling, monitoring, and mining to
planning and decision making. However, real-life dynamic systems contain a
degree of uncertainty which cannot be handled with classical logics. We thus
propose a new probabilistic temporal logic over finite traces using
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 then
study a fragment of the logic with better computational properties. Notably,
formulas in this fragment can be discovered from event log data using
off-the-shelf existing declarative process discovery techniques.
