ion but at best as a partial validation method, and that a full validation of abstract accounts of argumentation should include theorybased validation. A case study of the `standard' theory of bipolar frameworks reveals that it is to a large extent still awaiting validation as a good theory of rational argumentation.
When a formal or computational theory of argumentation is proposed, an
important question is why it is a good theory of argumentation. In this paper I
discuss several ways of answering this question for abstract theories of
argumentation. By `abstract' I mean theories that leave the nature of arguments and
their relations unspeci ed. With `goodness' I do not mean whether the theory is
empirically adequate as a theory of how humans actually argue. Rather I mean
whether itis a good theory of rational reasoning and argumentation, that is,
of how people (or machines) should argue. I will in particular focus on bipolar
argumentation frameworks (BAF s, frameworks with both attack and support
relations between arguments), since these have recently been the subject of two
detailed validation studies [
The rst attempt to validate an abstract theory of argumentation was made
by Dung in his seminal paper [
tation in its full generality. This is done in two steps. In the rst step,
a formal, abstract but simple theory of argumentation is developed to
capture the notion of acceptability of arguments. In the next step, we
demonstrate the \correctness" (or \appropriateness") of our theory. It is
clear that the \correctness" of our theory cannot be \proved" formally.
The only way to accomplish this task is to provide relevant and
convincing examples. Two \examples" are provided. The rst one shows how our
theory can be used to investigate the logical structure of many human
economic and social problems. The second one shows that many
major approaches to nonmonotonic reasoning in AI and logic programming
(. . . ) are in fact di erent forms of our theory of argumentation.
Interestingly, as regards reasoning and argumentation, Dung did not instantiate
his abstract theory with concrete natural-language examples but with logical
systems, namely, default logic [
The style of my paper will be largely informal, paraphrasing rather than stating formal results and observations, and assuming that the reader is familiar with the discussed works. Nevertheless, for ease of reference I will start with a brief recapitulation of the main de nitions of the theories of AF s and BAF s. 2
In this section the basics of Dung's theory of abstract argumentation frameworks and the main theories of bipolar frameworks are reviewed.
An abstract argumentation framework (AF ) is a pair hA; Ci, where A is a set of arguments and C A A is a relation of attack. Dung's theory of AF s identi es sets of arguments (called extensions ) which are internally coherent and defend themselves against attackers. An argument A 2 A is defended by a set by S A if for all B 2 A: if B attacks A, then some C 2 S attacks B. Then relative to a given AF , E A is admissible if E is con ict-free and defends all its members; E is a complete extension if E is admissible and A 2 E i A is defended by E; E is a preferred extension if E is a -maximal admissible set; E is a stable extension if E is admissible and attacks all arguments outside it; and E A is the grounded extension if E is the least xpoint of operator F , where F (S) returns all arguments defended by S. It holds that any preferred, stable or grounded extension is a complete extension. Finally, for T 2 fcomplete, preferred, grounded, stableg, X is sceptically or credulously justi ed under the T semantics if X belongs to all, respectively at least one, T extension.
Bipolar frameworks add a binary support relation S to AF s. Thus BAF s
are a triple (A; C; S). In [
To the best of my knowledge, only two works following Dung's validation strategy
for bipolar argumentation frameworks exist: my own preliminary research in [
Cohen et al. take ASPIC + [
Cohen et al. rst de ne four ways in which ASPIC + arguments can support each other. The rst is the ASPIC + proper subargument relation between arguments. The second notion of support is a notion of argument accrual: two di erent arguments A and B conclusion-support each other if they have the same nal conclusion. A third notion is premise support. Argument A premisesupports another argument B if A's nal conclusion is a premise of B. Fourth, a variant of conclusion support is intermediate support: if A conclusion-supports a proper subargument of another argument B that does not equal a premise of B, then A intermediate-supports B.
Cohen et al. then consider three semantics for BAF s in terms of the AF s
generated by sets of attack constraints. A BAF , is for general support i its
attack relation is closed under supported and secondary attack. As in [
Cohen et al. then investigate whether their four notions of support in ASPIC + can be related to these three BAF semantics. They do this for each of the three ASPIC + attack relations separately. Like in the present paper they assume that all ASPIC + attacks succeed as defeats. For each AF = (A; C) induced by an ASPIC + instantiation and a particular ASPIC + attack relation (undermining, rebutting or undercutting attack), they rst consider the BAF = (A; C; Ss) where Ss is the support relation on A according to ASPIC + support type s (proper-subargument, conclusion, premise or intermediate support). Then for each of the three BAF semantics x (general, deductive or necessary) they consider BAFx = (A; Cx; Ss), where Cx is the closure of C under the attack constraints of semantics x. They then compare for each ASPIC +-induced BAF = (A; C; Ss) and each corresponding BAFx = (A; Cx; Ss) the sets C and Cx. The semantics x is an abstraction of support type s just in case C = Cx.
Cohen et al.'s ndings on this question are largely negative. They identify
only one full correspondence, between ASPIC + proper-subargument support
and BAF s for necessary support, regardless of the type of ASPIC + attack. A
similar result was earlier proven by me in [
Cohen et al. remain neutral on the methodological implications of their ndings but in my opinion they provide strong support for the claim that the `standard' semantics for BAF s has not yet been validated as a good theory of rational argumentation. Of course, this conclusion presupposes that ASPIC + is itself a good structured account of rational argumentation, although it does not presuppose that ASPIC + is the only such good account; nor does it presuppose that the only theory-based way to validate a theory of BAF s is by instantiating it with ASPIC +. In Section 5 I will return to these issues. 4
In the present section I discuss two main alternative validation approaches that have been employed in the literature: appeals to intuition in concrete examples and comparisons with how humans actually argue. 4.1
An often applied strategy in validating the normative adequacy of theories of reasoning is applying them to concrete examples and checking whether they validate one's intuitions about these examples. In the literature on computational argumentation this is occasionally used but not in a very systematic way. For structured accounts of argumentation (which specify the structure of arguments and the nature of their relations) it can be a useful aspect of validation but it should be used with care. One problem is that it is not obvious whose intuitions should count [21, Ch. I.1]. Those of logicians or argumentation researchers are seriously biased by overexposure to formalism. So should we ask the `average language user', hoping that they are not infected by theoretical bias? Then the problem often arises that their answers reveal a lacking understanding of the reasoning patterns; however, teaching them about these reasoning patterns infects them with the theoretical bias we were hoping to avoid. Also, whether we ask researchers or lay people, intuitions of di erent persons often con ict.
In validating theories of defeasible reasoning another problem is that it is
often hard to distinguish between intuitions that a particular reasoning pattern is
invalid and implicitly assumed additional information that invalidates inferences
that are defeasibly valid in the absence of that information [
When validating abstract theories argumentation there is the problem that
if the theory is validated with natural-language examples of argumentation that
are directly translated into AF s instead of through a theory of the nature of
arguments and attacks, then the resulting modellings may be ad-hoc, so that
the observations made about these modellings have no general validity. Prakken
& Winter [
In conclusion, intuition-based validation can, if used with care, be useful for validating structured accounts of argumentation but they should not be used for validating abstract accounts of argumentation, since directly encoding naturallanguage examples in abstract frameworks, without guidance by theories of the nature of arguments and their relations, risks in yielding ad-hoc modellings. 4.2
Polberg & Hunter [
Their overall conclusion is that the data from their experiments support the need for bipolar approaches. The question arises: the need for bipolar approaches for what purpose? Are they needed to specify how people should argue (the topic of the present paper) or are they needed to model how people actually argue? These things are quite di erent. It is not entirely clear from their paper which of these questions Polberg & Hunter are interested in. Yet it is important to disambiguate, since if their claims are interpreted as being about normative adequacy, then the question arises how empirical ndings on how people actually argue can be relevant at all for a normative theory on how they should argue.
Polberg & Hunter write \Without empirical evidence, we can accidentally increase the gap between applying argumentation and successfully applying argumentation in real life situations" (their emphasis, HP). In my opinion, what this hints at is an empirical constraint on normative theories of reasoning that they should refer to the concepts that people use when reasoning or arguing, on the penalty of not being applicable by people. The principles formulated by the theory may still deviate from how people actually reason, as long as they are stated in terms that are natural to people. Otherwise it may happen that a theory, even if it is normatively adequate, is so foreign to people that they are not able to apply the theory, so that they are left without any useful guidance for their reasoning. It may be that Polberg & Hunter have this kind of empirical naturalness constraint on the usefulness of normative theories of argumentation in mind. When interpreted thus, their results do not inform us about whether a semantics of BAF s is normatively correct but about whether it is stated in terms that are natural to people. Henceforth I will call this kind of validation quasi-empirical validation of (the human naturalness of) normative theories.
Let us see whether Polberg & Hunter's results can be seen as quasi-empirical
validation of BAF s in this sense. In my opinion, this is not the case, since Polberg
& Hunter state their claims in absolute terms while their data at best support a
relative conclusion, namely, that using BAF s is more quasi-empirically adequate
than using AF s, since their experiments are designed to compare AF s and
BAF s. However, there are other alternatives, namely, using AF s in combination
with a theory of the structure of arguments and the nature of attack. There are
quite a few such theories, dating back to the seminal work of Pollock in [
What is quasi-empirically more adequate: modelling support relations primarily as relations between arguments or primarily as relations between statements? Polberg & Hunter's experiments are inherently unsuitable for answering this question, since they did not instruct their test subjects to identify support relations between statements in the sense of a structured account of argumentation, so between premises and conclusions inside arguments. In fact, Polberg & Hunter's use of the terms `statement' and `argument' is sometimes ambiguous. They refer to the elements of their persuasion dialogues as \statements". However, most of these \statements" are what argumentation theorists would call arguments, with statements as premises, another statement as a conclusion and a claimed relation of support between premises and conclusion. For example:
would be good for them to receive u shots in order to stay healthy (my emphasis, HP).
On the other hand, some of their `statement' are just claims. For example:
Since Polberg & Hunter do not systematically distinguish between statements as full arguments or as elements of arguments, they also do not systematically distinguish between support relations between and inside arguments. In any case, no conclusion can be drawn from their experiments on the relative quasiempirical adequacy of BAF -style approaches and structured approaches to the modelling of support relations in argumentation. 5
As noted above at the end of Section 3, and as also acknowledged by [11, p.
488], the success of theory-based validation depends on whether the more
concrete theories with which abstract theories are instantiated are themselves valid
as normative theories of reasoning or argumentation (or at least accepted as
valid by a substantial part of the research community). A full treatment of this
issue is beyond the scope of this paper but some observations can be made. Dung
instantiated his theory with one of the best known nonmonotonic logics, default
logic, with two semantics for logic programming, which is a well-established
computational theory, and with a system for defeasible argumentation
(Pollock's system) with foundations in epistemology which has been very in uential
in the study of formal argumentation. Others have instantiated Dung's theory
with, for instance, assumption-based argumentation [
In this paper I have argued that the best way of validating the `correctness' of
an abstract normative theory of argumentation is theory-based validation, that
is, instantiation with more concrete theories of reasoning and argumentation
that have themselves been su ciently validated in other ways. As a case study I
have investigated how current bipolar approaches, which extend Dung's abstract
argumentation approaches with abstract support relations, have been validated
in this way. It turned out that the only two papers that, to my knowledge,
apply theory-based validation to bipolar approaches, [
The largely negative results of [
After applying Dung's validation strategy to bipolar approaches, I
investigated two common alternative validation strategies of abstract approaches. As
regards validation of BAF semantics by intuitions in concrete examples, I
repeated and summarised observations in the literature that this validation
strategy is ad-hoc and unreliable and that modellings of concrete examples should be
guided by accounts of the structure of arguments and the nature of their
relations. As regards validation of BAF s by empirical comparison with how people
actually argue I have made the following contributions. I rst distinguished
several senses of validation and argued that Polberg & Hunter's experiments in [
Next, I argued that Polberg & Hunter's results do not contribute to this kind of quasi-empirical validation, since their paper is silent about the vast body of work in AI on the structure of arguments and the nature of attack and support. I agree with them that support relations are important in argumentation but this has been known for a long time. All informal de nitions of argumentation in the argumentation-theoretic literature and all formal de nitions of the structure of arguments in the AI literature are variations on the theme that argumentation involves supporting claims with grounds. The question is how such support relations can best be modelled. One main issue here is whether support can best be modelled primarily as a relation between arguments or primarily as a relation between grounds and claims inside arguments. Polberg & Hunter do not answer to this question, since they do not consider the latter alternative.
Finally, an interesting question is what is the role of postulate-based
approaches (e.g. [
To conclude, although the the present paper by no means o ers a comprehensive account of validating abstract accounts of argumentation, it provides some arguably useful distinctions between various kinds of validation and some guidelines for how to conduct validation attempts.