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Many native ASP solvers exploit unfounded sets to compute consequences of alogic program via some form of well-founded negation, but disregard itscontrapositive, well-founded justification (WFJ), due to computational cost.However, we demonstrate that this can hinder propagation of many relevantconditions such as reachability. In order to perform WFJ with low computationalcost, we devise a method that approximates its consequences by computingdominators in a flowgraph, a problem for which linear-time algorithms exist.Furthermore, our method allows for additional unfounded set inference, calledwell-founded domination (WFD). We show that the effect of WFJ and WFD can besimulated for a important classes of logic programs that include reachability.This paper is a corrected and extended version of a paper published at the 12thInternational Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR2013). It has been adapted to exclude Theorem 10 and its consequences, butprovides all missing proofs.

Efficient Approximation of Well-Founded Justification and Well-Founded Domination (Corrected and Extended Version)