Modelling Second-Order Uncertainty in State Machines

Modelling the behaviour of state-based systems can be challenging, especially when the modeller is not entirely certain about its intended interactions with the user or the environment. Currently, it is possible to associate a stated level of uncertainty with a given event by attaching probabilities to transitions (producing ‘Probabilistic State Machines’). This captures the ‘First-order uncertainty’ - the (un-)certainty that a given event will occur. However, this does not permit the modeller to capture their own uncertainty (or lack thereof) about that stated probability - also known as ‘Second-order uncertainty’. In this article we introduce a generalisation of probabilistic finite state machines that makes it possible to incorporate this important additional dimension of uncertainty. For this we adopt a formalism for reasoning about uncertainty called Subjective Logic. We present an algorithm to create these enhanced state machines automatically from a conventional state machine and a set of observed sequences. We show how this approach can be used for reverse-engineering predictive state machines from traces.