Contingent durations in temporal CSPs: from consistency to controllabilities

Temporal Constraint Networks (TCSP) allow to express minimal and maximal durations between time-points. Though being used in many research areas, this model disregards the contingent nature of some constraints, whose effective duration cannot be decided by the system but is provided by the external world. We propose an extension of TCSP in which the classical network consistency property must be redefined in terms of controllability: intuitively, we would like to say that a network is controllable if it is consistent in any situation (i.e. any assignment of the whole set of contingent intervals) that may arise in the external world. Three levels of controllability must be distinguished, namely the Strong, the Weak and the Dynamic ones. This preliminary report mainly stresses the representation and concept issues, discussing their relevance in dynamic application domains, and partially tackles the reasoning issues (complexity, algorithms and tractable subclasses).