Excellent description in 'Computing Arguments and Attacks in Assumption-Based Argumentation' (2007, Dorian Gaertner, Francesca Toni) of the five types of choices that need to be made in any implementation of the structured AB-dispute derivation algorithm, i.e.
- Choice of player (P or O);
- Choice of argument (in P or O);
- Selection function (a sentence from the chosen argument);
- Choice of (inference) rule (if chosen sentence is not assumption);
- Choice to ignore (if the opponent is selected and the selection function returns an assumption).
It is stated in this paper that the 'choice of argument' does not apply to AB-dispute derivations, since arguments aren't explicit in AB-dispute derivations. I don't think this is correct. If the opponent is selected in an AB-dispite derivation, the choice of 'S in Oi' is like a 'choice of argument' and the choice of 'sigma in S' is determined by the 'selection function'.
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