“Note that step (2ia) (the ignoring of assumptions) (in the 'Computing Ideal Sceptical Argumentation' paper) is not needed to guarantee soundness, but it is helpful to guarantee success in finding GB-dispute derivations in many cases…” What is meant here by "success" and "soundness"? How do they differ?
"Success" means that the procedure completes (i.e. doesn't get stuck). "Soundness" means that if an assumption is found to be grounded according to the procedure then that assumption is in the grounded set of assumptions.
As an example (taken from 'Dialectic proof procedures for assumption-based, admissible argumentation', example 7.2), given a set of inference rules as:
¬s <- q
¬q <- r, t
¬t
where the set of assumptions is {q, r, t}, and given a left-most selection function, there exists a derivation for the sentence ¬s of defence set {q} only if one of the outputs of the selection function is ignored (i.e. 'r'). Thus, the ignoring of assumptions is required for the procedure to "succeed".
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