Approaching the core of unfounded sets

We elaborate upon techniques for unfounded set computations by building upon the concept of loops. This is driven by the desire to minimize redundant computations in solvers for Answer Set Programming. We begin by investigating the relationship between unfounded sets and loops in the context of partial assignments. In particular, we show that subset-minimal unfounded sets correspond to active elementary loops. Consequentially, we provide a new loop-oriented approach along with an algorithm for computing unfounded sets. Unlike traditional techniques that compute greatest unfounded sets, we aim at computing small unfounded sets and rather let propagation (and iteration) handle greatest unfounded sets. This approach reflects the computation of unfounded sets employed in the nomore++ system. Beyond that, we provide an algorithm for identifying active elementary loops within unfounded sets. This can be used by SATbased solvers, like assat, cmodels, or pbmodels, for optimizing the elimination of invalid candidate models.

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