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It can be easily seen from Theorem 6 together with its argumentation procedure that, when (Vert nabla u^{0} Vert _{0}) and (Vert nablasigma^{0} Vert _{0}) are small enough, the conditions (N_{0} Vert nabla{boldsymbol {u}}_{h}^{i} Vert _{0}le 1/4) ((i=1, 2, ldots, N)) of Theorem 9 are tenable.
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If followed by both parties to the disagreement, the rules constrain the argumentation decision procedure such that any resolution reached will be deemed reasonable, and "every violation of any of the rules of the discussion procedure for conducting a critical discussion" will be a fallacy (2004, 175).
Although comparatively simple, Brewka's protocol is thus representative of a wide range of other more complex argumentation and dispute resolution procedures that have been proposed.
The "Python Abstract Argumentation Library" implements labeling-based procedures for determining the justification status of arguments and for enumerating the labelings for many semantics (see Section 4.1).
We also prove that in the case of p-acyclic assumption-based argumentation frameworks (a variant of) the procedure of [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114 159] for the admissible semantics is complete.
A key point to note about the four techniques, relating back to the principle that we "accept and propose on the basis of kinds," is that all are specifically procedures for analogical argumentation, aimed at distinguishing similarities and differences between kinds of things and assertions about them.
But what about implementing procedures for abstract argumentation from scratch?
A popular approach for obtaining proof procedures for abstract argumentation is based on so called dialogue games (see, e.g., [35,39]).
The procedures are adapted from (variants of) corresponding procedures for computing the credulous admissible semantics for assumption-based argumentation, proposed in [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114 159].
The central role of abstract argumentation frameworks also boosted research on efficient procedures for this particular formalism.
This study proposed how collective argumentation could be developed through students' questions, cognitive procedures (reasoning and knowledge) as well as argument constructions.
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