Reasoning and querying bounds on differences with layered preferences

Artificial intelligence largely relies on bounds on differences (BoDs) to model binary constraints regarding different dimensions, such as time, space, costs, and calories. Recently, some approaches have extended the BoDs framework in a fuzzy, \u201cnoncrisp\u201d direction, considering probabilities or preferences. While previous approaches have mainly aimed at providing an optimal solution to the set of constraints, we propose an innovative class of approaches in which constraint propagation algorithms aim at identifying the \u201cspace of solutions\u201d (i.e., the minimal network) with their preferences, and query answering mechanisms are provided to explore the space of solutions as required, for example, in decision support tasks. Aiming at generality, we propose a class of approaches parametrized over user\u2010defined scales of qualitative preferences (e.g., Low, Medium, High, and Very High), utilizing the resume and extension operations to combine preferences, and considering different formalisms to associate preferences with BoDs. We consider both \u201cgeneral\u201d preferences and a form of layered preferences that we call \u201cpyramid\u201d preferences. The properties of the class of approaches are also analyzed. In particular, we show that, when the resume and extension operations are defined such that they constitute a closed semiring, a more efficient constraint propagation algorithm can be used. Finally, we provide a preliminary implementation of the constraint propagation algorithms

Temporal Reasoning with Layered Preferences

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