  Many native ASP solvers exploit unfounded sets to compute consequences of a
logic program via some form of well-founded negation, but disregard its
contrapositive, well-founded justification (WFJ), due to computational cost.
However, we demonstrate that this can hinder propagation of many relevant
conditions such as reachability. In order to perform WFJ with low computational
cost, we devise a method that approximates its consequences by computing
dominators in a flowgraph, a problem for which linear-time algorithms exist.
Furthermore, our method allows for additional unfounded set inference, called
well-founded domination (WFD). We show that the effect of WFJ and WFD can be
simulated for a important classes of logic programs that include reachability.
This paper is a corrected and extended version of a paper published at the 12th
International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR
2013). It has been adapted to exclude Theorem 10 and its consequences, but
provides all missing proofs.
