This paper contributes in two ways to the aims of this special issue on abstraction. The first is to show that there are compelling reasons motivating the use of abstraction in the purely computational realm of artificial intelligence. The second is to contribute to the overall discussion of the nature of abstraction by providing examples of the abstraction processes currently used in artificial intelligence. Although each type of abstraction is specific to a somewhat narrow context, it is hoped that collectively they illustrate the richness and variety of abstraction in its fullest sense.

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Abstract. While many real-world combinatorial problems can be advantageously modeled and solved using Constraint Programming, scalability remains a major issue in practice. Constraint models that accurately reflect the inherent structure of a problem, solvers that exploit the properties of this structure, and reformulation techniques that modify the problem encoding to reduce the cost of problem solving are typically used to overcome the complexity barrier. In this paper, we investigate such approaches in a geospatial reasoning task, the buildingidentification problem (BID), introduced and modeled as a Constraint Satisfaction Problem by Michalowski and Knoblock [1]. We introduce an improved constraint model, a custom solver for this problem, and a number of reformulation techniques that modify various aspects of the problem encoding to improve scalability. We show how interleaving these reformulations with the various stages of the solver allows us to solve much larger BID problems than was previously possible. Importantly, we describe the usefulness of our reformulations techniques for general Constraint Satisfaction Problems, beyond the BID application.

Consistency properties and algorithms for achieving them are at the heart of the success of Constraint Programming. In this paper, we study the relational consistency property R(*,m)C, which is equivalent to m-wise consistency proposed in relational databases. We also define wR(*,m)C, a weaker variant of this property. We propose an algorithm for enforcing these properties on a Constraint Satisfaction Problem by tightening the existing relations and without introducing new ones. We empirically show that wR(*,m)C solves in a backtrack-free manner all the instances of some CSP benchmark classes, thus hinting at the tractability of those classes.