We elaborate a uniform approach to computing answer sets of disjunctive logic programs based on state-of-theart Boolean constraint solving techniques. Starting from a constraint-based characterization of answer sets, we develop advanced solving algorithms, featuring backjumping and conflict-driven learning using the First-UIP scheme as well as sophisticated unfounded set checking. As a final result, we obtain a competitive solver for Σ P 2-complete problems, taking advantage of Boolean constraint solving technology without using any legacy solvers as black boxes.

One of the most significant language extensions to Answer Set Programming (ASP) has been the introduction of aggregates. A significant amount of theoretical and practical work on aggregates in ASP has been published in recent years. In spite of these developments, aggregates are treated in a quite straightforward and ad-hoc way in most ASP systems. For the system DLV, several specialized techniques for aggregates have been described in [6], however still leaving a lot of room for improvement. In this paper, we build upon work on look-back optimization techniques done recently for DLV, and extend its reason calculus for backjumping to include reasons from aggregates. Furthermore, we describe how these reasons can be used in order to tune look-back heuristic counters. We present a preliminary experimental analysis, including also other state-of-the-art ASP systems, showing that our approach is promising. 1