Controllability of Temporal Problems with Preferences and Uncertainty

In real-life temporal scenarios, uncertainty and preferences are often essential, coexisting aspects. It is desirable to be able to handle events with uncertain duration while taking into account the user’s preferences on the timing of events. This also applies to many problems of space application domains. The two aspects have been dealt with separately, extending in two ways Temporal Constraint Satisfaction Problems (TCSPs), a well-known framework for handling temporal information, widely used in space mission planners (Dearden et al. 2002; Muscettola et al. 1998). First, to account for uncontrollable events, Simple Temporal Problems with Uncertainty (STPU) have been introduced, and second, more recently, to account for soft temporal preferences, Simple Temporal Problems with Preferences (STPP) have been defined. In this paper we propose a unifying framework We present a formalism where temporal constraints with both preferences and uncertainty can be defined. We show how three classical notions of controllability (strong, weak and dynamic), which have been developed for uncertain temporal problems, can be generalised to handle also preferences. We then propose algorithms that check the presence of these properties and we prove that, in general, dealing simultaneously with preferences and uncertainty does not increase the complexity beyond that of the separate cases. In particular, we develop a dynamic execution algorithm, of polynomial complexity, that produces plans under uncertainty that are optimal w.r.t. preference.