9.1-9.4, Persuasion in Practical Argument Using Value-based Argumentation Frameworks

Notes taken from ‘Persuasion in Practical Argument Using Value-based Argumentation Frameworks’ by Trevor J. M. Bench-Capon (2003)

“… In (many) cases(s) the dispute can only be resolved through choosing a preference…”

1, Introduction

… assent through persuasion rather than intellectual coercion… When a case is brought to court, it is because the two parties disagree about what should be done in the light of some set of particular circumstances… Their arguments may all be sound. But their arguments will not have equal value for the judge charged with deciding the case… A key element in persuasion is identifying the value conflict at the root of the disagreement… Perelman makes much of the fact that an argument is addressed to an audience: in many cases this will be a particular audience with a particular set of values, and a particular ranking of them…

2, Standard argumentation frameworks

2.1-2.5, Definitions of an argumentation framework (AF), acceptable arguments, conflict-free sets of arguments, admissible sets of arguments and preferred extensions are as in Dung’s argumentation framework.

The notion of a preferred extension is interesting because it represents a consistent position within AF, which can defend itself against all attacks and which cannot be further extended without introducing a conflict. We can now view a credulous reasoner as one who accepts an argument if it is in at least one preferred extension and a sceptical reasoner as one who accepts an argument only if it is in all preferred extensions… every AF has a preferred extension (possibly the empty set), and that it is not generally true that an AF has a unique preferred extension. In the special case where there is a unique preferred extension we say that the dispute is resoluble, since there is only one set of arguments capable of rational acceptance.

2.6, If AF = (AR, attacks) where AR is finite and attacks contains no self-attacks, has two (or more) preferred extensions, then the directed graph of AF contains a simple directed cycle of even length.

3, Persuasion in a standard argumentation framework

… From figure 1 we can see that there are two preferred extensions: {P, Q, R, P -> Q, Q -> R} and {~P, Q, R, ~P -> Q, Q -> R}.

We can therefore see that Q and R are sceptically acceptable and P and ~P are credulously acceptable. This means that we should be able to persuade someone to accept Q (and also R). Suppose we assert Q: our interlocutor may challenge this with ~Q. We attack this with P -> Q. He in turn attacks this with ~P. I concede not P, and attack ~Q with ~P -> Q. Now my opponent cannot attack this with P, since this is attacked by the already asserted ~P. Therefore my opponent should be persuaded of the truth of Q.

What of a credulously acceptable argument, such as P? Here I cannot persuade my opponent because he can counter with ~P, and I have no independent way of arguing against ~P. So here I cannot persuade my opponent that P should be accepted, but neither can I be persuaded that it should be abandoned. There is no rational way of choosing between P and ~P; it is an empirical fact which must be determined by observation…

4, Practical reasoning

In practical reasoning an argument often has the following form:

Action A should be performed in circumstances C, because the performance of A in C would promote some good G.

This kind of argument can be attacked in a number of ways:
- It may be that circumstances C do not obtain; or it may be that performing A in C would not promote good G. These are similar to the way in which a factual argument can be attacked in virtue of the falsity of a premise, or because the conclusion does not follow from the premise.
- Alternatively it can be attacked because performing some action B, which would exclude A, would also promote G in C. This is like an attack using an argument with a contradictory conclusion.
- However, a practical argument like the one above can be attacked in two additional ways: It may be that G is not accepted as a good worthy of promotion, or that performing action B, which would exclude performing A, would promote a good H in C, and good H is considered more desirable than G. The first of these new attacks concerns the ends to be considered, and the second the relative weight to be given to the ends…

… if an argument attacks an argument whose value is preferred it can be accepted, and yet not defeat the argument it attacks. Thus we can, for arguments which derive their force from the promotion of a value, distinguish between attack and defeat (a successful attack)…