Abstract. In real-life temporal scenarios, uncertainty and preferences are often essential, coexisting aspects. 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. Research on temporal reasoning, once exposed to the difficulties of real-life problems, can be found lacking both expressiveness and flexibility. To address the lack of expressiveness, preferences can be added to the temporal framework; to address the lack of flexibility to contingency, reasoning about uncertainty can be added. In this paper we introduce a framework to handle both preferences and uncertainty in temporal problems. This is done by merging the two pre-existing models of Simple Temporal Problems with Preferences (STPPs) [5] and Simple Temporal Problems under Uncertainty (STPUs). [12]. We adopt the notion of controllability of STPUs, to be used instead of consistency because of the presence of uncertainty, and we adapt it to handle preferences. The proposed framework, Simple Temporal Problems with Preferences and Uncertainty (STPPUs), represents temporal problems with preferences and uncertainty via a set of variables, which represent the starting or ending times of events (which may be controllable or not), and a set of soft temporal constraints over the variables. Each constraint includes an interval containing the allowed durations of the event or the allowed interleaving times between events, and a preference function associating each element of the interval with a value corresponding to how much its preferred. Such soft constraints can be defined on both controllable and uncontrollable events. Examples of real-life problems with temporal constraints, preferences, and uncertainty can easily be found in several application domains (e.g. [7] ). Here we describe in detail one such problem, arising in an aerospace application domain. The problem refers to planning for fleets of Earth Observing Satellites (EOS) [4] . This planning problem involves multiple satellites, hundreds of requests, constraints on when and how to service each request, and multiple resources. Scientists place requests to receive earth images from space. After the image data is acquired by an EOS, it can either be downlinked in real time or recorded on board for playback at a later time. Ground stations or other satellites are available to receive downlinked images. Each satellite can communicate
Closely related to fuzzy networks are STNUs with preferences, REF studies Simple Temporal Problems with Preferences and Uncertainty.
Controllability of soft temporal constraint problems
In Proc. of CP’04, LNCS 3258
Computer Science