Constraint-based Temporal Reasoning with Preferences

Often we need to work in scenarios where events happen over time and preferences are associated to event distances and durations. Soft temporal constraints allow one to describe in a natural way problems arising in such scenarios. In general, solving soft temporal problems require exponential time in the worst case, but there are interesting subclasses of problems which are polynomially solvable. In this paper we identify one of such subclasses giving tractability results. Moreover, we describe two solvers for this class of soft temporal problems, and we show some experimental results. The random generator used to build the problems on which tests are performed is also described. We also compare the two solvers highlighting the tradeoff between performance and robustness. Sometimes, however, temporal local preferences are difficult to set, and it may be easier instead to associate preferences to some complete solutions of the problem. To model everything in a uniform way via local preferences only, and also to take advantage of the existing constraint solvers which exploit only local preferences, we show that machine learning techniques can be useful in this respect. In particular, we present a learning module based on a gradient descent technique which induces local temporal preferences from global ones. We also show the behavior of the learning module on randomly-generated examples

Learning Solution Preferences in Constraint Problems

Usually, not all the solutions of a finite domain constraint problem (CSP) are equally desirable: some of them may be preferred to others. However, classical CSPs do not allow for this more informative kind of knowledge representation. On the other hand, semiring-based CSPs (SCSPs), where a value is associated with each tuple in each constraint, generate solutions with a corresponding value attached, which can be interpreted as the level of preference of that solution. Sometimes, however, even standard SCSPs are not enough, since one may know his/her preferences over some of the solutions but have no idea on how to code this knowledge into the SCSP. In this paper we consider this situation and propose to address it by first defining a classical CSP and giving some examples of solution preferences, and then learning the corresponding SCSP which behaves as the initial CSP (that is, it has the same solutions) and matches the preferences specified in the examples. In other words, we use th..