Generalized Temporal Inference via Planning

This paper introduces the Temporal Inference Problem (TIP), a general formulation for a family of inference problems that reason about the past, present or future state of some observed agent. A TIP builds on the models of an actor and of an observer. Observations of the actor are gathered at arbitrary times and a TIP encodes hypothesis on unobserved segments of the actor's trajectory. Regarding the last observation as the present time, a TIP enables to hypothesize about the past trajectory, future trajectory or current state of the actor. We use LTL as a language for expressing hypotheses and reduce a TIP to a planning problem which is solved with an off-the-shelf classical planner. The output of the TIP is the most likely hypothesis, the minimal cost trajectory under the assumption that the actor is rational. Our proposal is evaluated on a wide range of TIP instances defined over different planning domains.