Temporal Reasoning with Layered Preferences

Abstract

Temporal representation and temporal reasoning is a central in Artificial Intelligence. The literature is moving to the treatment of "non-crisp" temporal constraints, in which also preferences or probabilities are considered. However, most approaches only support numeric preferences, while, in many domain applications, users naturally operate on "layered" scales of values (e.g., Low, Medium, High), which are domain-and task-dependent. For many tasks, including decision support, the evaluation of the minimal network of the constraints (i.e., the tightest constraints) is of primary importance. We propose the first approach in the literature coping with layered preferences on quantitative temporal constraints. We extend the widely used simple temporal problem (STP) framework to consider layered user-defined preferences, proposing (i) a formal representation of quantitative constraints with layered preferences, and (ii) a temporal reasoning algorithm, based on the general algorithm Compute-Summaries, for the propagation of such temporal constraints. We also prove that our temporal reasoning algorithm evaluates the minimal network.

Reasoning and querying bounds on differences with layered preferences

“…Luckily, in BoDs both computing the minimal network of constraints of a problem and answering queries using it can be done in polynomial time and space (e.g., using algorithms like the Floyd-Warshall's one [28]). [4] generalizes and extends the 3 Notice that structures similar to the minimal network can be obtained also for other classes of CSPs. However, computing them often requires nonpolynomial space and/or time.…”

“…They showed that, by exploiting c-semirings in the treatment of preferences, it is possible to achieve tractability. The approaches by Andolina et al [60], Anselma et al [4] and Khatib et al [37] are the closest ones to ours: a detailed comparison with such approaches is reported in Section 7 after the description of our approach.…”

“…Finally, the approach in this paper is a substantial extension of the one we have recently proposed in [4]. Indeed, such a work addresses the problems of determining the minimal network and querying it considering BoD constraints with preferences, but only in the context of "pyramid" constraints, and considering the min function to resume preferences and max to extend them (i.e., the approach in [4] constitutes the preliminary version of the "specific" approach presented in Section 5 of this paper).…”

“…However, computing them often requires nonpolynomial space and/or time. 4 Actually, there are also other approaches coping with the more general class of linear inequalities. For instance, the work in [72] proposes an approach coping with fuzzy linear inequalities.…”

“…Given a scale S r and given two PyP_BoDs [10,39], low , [11 ,37], medium , [12 ,36] [11,12], medium high , [12,24], high high } pref pref pref , the ⊕ PyPB operator computes the union ⋃{ [10,11], [11,12], [12,24]} to obtain the AdI for the low preference level, and it computes the union ⋃{ [11,12], [12,24]} for obtaining the AdI to obtain the medium preference level. Finally, to obtain the AdI for the high preference level, it computes the singleton union ⋃{ [12,24]}. Thus, 〈 〈〈 〉 〈 〉 〈 〉〉〉⊕ NA1, NA2, [10,39], low , [11 ,37], medium , [12 ,36] [10,24], low , [11 ,24], medium , [12 ,24], high .…”