Two limitations of abstract argumentation frameworks: (i) irrelevance is acceptable and (ii) the last one wins

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I often review or otherwise comment on research publications which build on abstract argumentation frameworks to develop some novel formalism, typically for modeling specific kinds of decisions.

By abstract argumentation, I mean a Phan Minh Dung abstract argumentation framework [1], defined as a pair of sets, (i) a set of arguments, and (ii) a set of attack relations over arguments. The two sets give you a graph of arguments and attack relations. You can label each argument as accepted or not by ensuring these are satisfied by the labels on the graph: (a) any argument which is not attacked is accepted, (b) if an argument is attacked by an accepted argument, then the former is not accepted, (c) an argument is defended if every argument which attacks it is attacked by an accepted argument.

There are two problems that you inherit by building on top of an abstract argumentation framework.

One, an argument can point to, or refer to any proposition. Because all that matters for acceptability are attack relations, it does not matter how the argument actually reads. Hence, there is no notion of relevance in an argumentation framework. By “relevance”, I mean something like what Wilson and Sperber say in the following:

“When is an input relevant? Intuitively, an input (a sight, a sound, an utterance, a memory) is relevant to an individual when it connects with background information he has available to yield conclusions that matter to him: say, by answering a question he had in mind, improving his knowledge on a certain topic, settling a doubt, confirming a suspicion, or correcting a mistaken impression. In relevance-theoretic terms, an input is relevant to an individual when its processing in a context of available assumptions yields a POSITIVE COGNITIVE EFFECT. A positive cognitive effect is a worthwhile difference to the individual’s representation of the world – a true conclusion, for example. False conclusions are not worth having. They are cognitive effects, but not positive ones.” [2]

This is often difficult for many people to understand, that you can have acceptable arguments which are, so to speak, non-sensical, or irrelevant. the confusion is due to a poor choice of terms, as acceptability of arguments obtains a technical definition in an argumentation framework, while that same term probably has a very different intuitive interpretation for you. It is, however, not strange at all. The formalism of argumentation frameworks is not designed to address this. But if you want to use it to do something where relevance matters, the argumentation framework cannot help you – you can use it, but you have to deal with relevance with something else in your own method or formalism that builds on top of it.

The second interesting limitation is this: if you ask for people to provide arguments, and you set a deadline by which they can do so, the last person can determine fully which arguments end up being acceptable. Since irrelevance is acceptable (see above), it only matters that they provide an argument – regardless of what that argument is. Again, this is counterintuitive, because how could someone possibly determine the outcome of potentially complex arguments and attacks being put forward, simply by being last. If you understood the former point about irrelevance, and how acceptability is computed in the graph, this should be obvious, even it may remain odd.

Despite being an elegant and attractive seemingly all-purpose formalism, argumentation frameworks should be used with caution.

[1] Dung, Phan Minh. “On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games.” Artificial intelligence 77.2 (1995): 321-357.

[2] Deirdre Wilson, Dan Sperber. Relevance Theory. G. Ward, L. Horn. Handbook of Pragmatics, Blackwell, 2002.