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, “noncrisp” 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 “space of solutions” (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-defined 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 “general” preferences and a form of layered preferences that we call “pyramid” 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.