Contrastive Explanations for Argumentation-Based Conclusions
Extended Abstract
AnneMarie Borg

Floris Bex

Utrecht UniversityUtrecht, The Netherlands
a.borg@uu.nl

Utrecht UniversityUtrecht, The Netherlands
Tilburg University
Tilburg, The Netherlands
f.j.bex@uu.nl

ABSTRACTIn this paper we discuss contrastive explanations for formal argumentation – the question why one argument (the fact) can beaccepted, whilst another argument (the foil) cannot be accepted. We
show under which conditions contrastive explanations in abstract
argumentation are meaningful, and how argumentation allows us
to make implicit foils explicit.

KEYWORDS
Formal Argumentation; Explainable Artificial Intelligence
ACM Reference Format:
AnneMarie Borg and Floris Bex. 2022. Contrastive Explanations for Argumentation-Based Conclusions: Extended Abstract. In Proc. of the 21stInternational Conference on Autonomous Agents and Multiagent Systems(AAMAS 2022), Online, May 9–13, 2022, IFAAMAS, 3 pages.

1INTRODUCTION

Explainable AI (XAI) has become an important research direction inAI [10]. AI systems, including formal argumentation [1], are being
applied in a variety of real-life situations and therefore require
an explanation method. A number of methods for determining
explanations for the (non-)acceptability of arguments have been
proposed [4]. What is still lacking, however, is an argumentationbased interpretation of contrastive explanations.
Contrastiveness is central to explanations [6–8]: when people
ask ‘Why P?’, they often mean ‘Why P rather than Q?’ – here 𝑃
is called the fact and 𝑄 is called the foil [6]. The answer to thequestion is then to explain as many of the differences between factand foil as possible. However, in formal argumentation the existing
work focuses on ‘Why is argument A (not) acceptable?’ instead of thecontrastive question ‘Why is argument A acceptable and argument
B not?’ (or vice versa) and no work on contrastiveness exists.
In this paper we extend the basic framework from [2] with which
explanations for accepted and non-accepted arguments or formulas
can be formulated in a variety of ways. The introduced contrastive
explanations return the common elements of the acceptance explanation of the fact and the non-acceptance explanation of thefoil. We show that in almost all situations these explanations aremeaningful, i.e., that such common elements exist. Additionally weProc. of the 21st International Conference on Autonomous Agents and Multiagent Systems(AAMAS 2022), P. Faliszewski, V. Mascardi, C. Pelachaud, M.E. Taylor (eds.), May 9–13,2022, Online. © 2022 International Foundation for Autonomous Agents and Multiagent
Systems (www.ifaamas.org). All rights reserved.

show that we can provide contrastive explanations when the foil is
not explicitly known.12PRELIMINARIES

We focus on explanations for conclusions derived from Dung-style
argumentation frameworks.
An abstract argumentation framework (AF) [5] is a pair AF =⟨Args, Att⟩, where Args is a set of arguments and Att ⊆ Args ×Args is an attack relation on these arguments. An argumentation
framework can be viewed as a directed graph, in which the nodes
represent arguments and the arrows represent the attacks.

𝐴2

𝐵3

𝐴4

𝐵6

𝐵1

𝐵2

𝐵4

𝐵5

Figure 1: Graphical representation of the AF AF 1 .
Example 2.1. Figure 1 represents the argumentation frameworkAF 1 = Args1, Att1 where Args1 = {𝐴2, 𝐴4, 𝐵 1, 𝐵 2, 𝐵 3, 𝐵 4, 𝐵 5, 𝐵 6 }and Att1 = {(𝐴2, 𝐵 3 ), (𝐴4, 𝐵 6 ), (𝐵 2, 𝐵 1 ), (𝐵 2, 𝐵 4 ), (𝐵 3, 𝐴2 ), (𝐵 3, 𝐵 2 ),(𝐵 5, 𝐵 4 ), (𝐵 6, 𝐴4 ), (𝐵 6, 𝐵 5 )}.
Dung-style semantics [5] can be applied to an AF, to determine
the sets of arguments (called extensions) that can be accepted. In
this abstract we will work with preferred semantics. An argument
is accepted if it is part of a preferred extension and it is not accepted
if there is a preferred extension without that argument.
We will require that the explanation for an argument 𝐴 is relevant(i.e., the arguments in the explanation (in)directly attack or defend𝐴), in order to prevent that explanations contain arguments that
do not influence the acceptance of 𝐴. We will say that an argument
𝐵 is conflict-relevant for 𝐴 if 𝐵 (in)directly attacks 𝐴.
In what follows we assume that we have an acceptance and a
non-acceptance explanation for arguments, as introduced in [2].
In particular, given an argument 𝐴, the acceptance explanation(denoted by Acc(𝐴)) collects the arguments from an extension that
defend 𝐴 against some attack and the non-acceptance explanation(denoted by NotAcc(𝐴)) collects the arguments that attack 𝐴 andto which an extension does not provide a defense.
Example 2.2. For AF 1 we have that Acc(𝐵 2 ) = {𝐴2 }, Acc(𝐵 4 ) ={𝐵 3, 𝐵 6 }, NotAcc(𝐵 2 ) = {𝐵 3 } and NotAcc(𝐵 4 ) = {𝐴2, 𝐴4, 𝐴2, 𝐵 5 }.
1 See [3] for the full version of this paper.

3CONTRASTIVE EXPLANATIONS

A contrastive explanation explains 𝐴 by explaining why 𝐴 ratherthan 𝐵. Important in contrastive explanations is that the difference
between fact (i.e., 𝐴) and foil (i.e., 𝐵) is highlighted. In this paper
we assume that fact and foil are not always compatible: 𝐴 and 𝐵
are not always part of the same extension. Intuitively, we makethis assumption since otherwise there is no contrastive question
for fact and foil (i.e., why both 𝐴 and 𝐵 is not contrastive).
Contrastive explanations are modeled by comparing the elements of the basic explanations that explain the acceptance of thefact and, at the same time, explain the non-acceptance of the foil.
Definition 3.1 (Contrastive explanations). Let AF = ⟨Args, Att⟩
be an AF, let 𝐴 ∈ Args (the fact) and let S ⊆ Args (a set of foils)
such that there is no preferred extension E in which 𝐴, 𝐵 ∈ E forallexplanations are then defined as Cont(𝐴, S) =( 𝐵 ∈ S. ContrastiveÐÐAcc(𝐴) ∩ 𝐵 ∈S NotAcc(𝐵) if Acc(𝐴) ∩ 𝐵 ∈S NotAcc(𝐵) ≠ ∅Ð⟨Acc(𝐴), 𝐵 ∈S NotAcc(𝐵)⟩ otherwise.
In words, when there are arguments that cause the fact to be accepted and the foil to be non-accepted, the contrastive explanationis the set of such arguments, the first case. If there are no common
causes for the acceptance of the fact and the non-acceptance of thefoil, the explanation is a pair of the respective explanations, thesecond case.
Example 3.2. For AF 1 we have the following: Cont(𝐵 4, 𝐵 2 ) ={𝐵 3 }, Cont(𝐵 4, 𝐵 5 ) = {𝐵 6 } and Cont(𝐵 4, {𝐵 2, 𝐵 5 }) = {𝐵 3, 𝐵 6 }.
Recall (Example 2.2) that the acceptance of 𝐵 4 can be explainedby 𝐵 3 and 𝐵 6 , when compared to the non-acceptance of 𝐵 2 [resp.
𝐵 5 ] the acceptance of 𝐵 4 is explained by 𝐵 3 [resp. 𝐵 6 ] alone.
One could consider these explanations more meaningful when
they return a set, rather than a pair. This is the case since thenthere are arguments that influence both the acceptance of the fact
and the non-acceptance of the foil. The next proposition showsthat in most cases the explanation is a set. Only when the accepted
argument is not attacked or fact and foil are not conflict-relevant isthe intersection empty.
Proposition 3.3. Let AF = ⟨Args, Att⟩ be an AF and 𝐴, 𝐵 ∈Args. If Acc(𝐴) ∩ NotAcc(𝐵) = ∅ then Acc(𝐴) = ∅; or 𝐴 is notconflict-relevant for 𝐵.
In view of the above result, the following conditions are introduced on the fact and foil. By requiring these conditions to hold,meaningful contrastive explanations can be obtained. For this let
AF = ⟨Args, Att⟩ be an AF and let {𝐴}∪S ⊆ Args. Then Cont(𝐴, S)
can be requested when, for each 𝐵 ∈ S:
• 𝐴 is at least accepted and 𝐵 is at least not accepted;• for each preferred extension E it never holds that {𝐴, 𝐵} ⊆ E;
• 𝐴 is conflict-relevant for 𝐵 or 𝐵 is conflict-relevant for 𝐴.
These conditions ensure that fact and foil are incompatible, but still
relevant for each other: it is explained what makes the fact accepted
and, simultaneously causes the foil to be non-accepted. This prevents contrastive explanations for arguments that are not related orconflicting. These conditions are not exhaustive, depending on, e.g.,
the application, a user might wish to enforce further conditions onfact or foil.

3.1

Non-Explicit Foil

When humans request a (contrastive) explanation the foil is sometimes left implicit, yet the expected explanation does not provide
all reasons for the fact happening, but should rather explain thedifference between fact and foil. While humans are able to detect
the foil based on, e.g., context, this is a challenge for AI systems,including argumentation. In particular, it is impossible to provide
one strategy, since different applications entail different foils. For
example, if argumentation is applied to determine a yes or no answer for argument 𝐴 (e.g., whether one qualifies for a loan), the foil
would be not A, but if the foil should be chosen from a larger set(e.g., a medical diagnosis), it might be any member of that set.
Since in the definition of contrastive explanations it is necessary
to provide a foil, a way to determine the foil is required. This iswhere one of the advantages of formal argumentation comes in: theexplicit nature of conflicts between arguments makes that the foil
or a set of foils can be constructed from an AF. Since the relation
between arguments is only determined by the attack relation in
our setting, it is impossible to distinguish between attackers. One
example collects all directly attacking arguments.
Definition 3.4. Let AF = ⟨Args, Att⟩ be an AF and let 𝐴 ∈ Args.
Then: Foil(𝐴) = {𝐵 ∈ Args | 𝐵 directly attacks 𝐴}.
Example 3.5. For the framework AF 1 we have that: Foil(𝐵 4 ) ={𝐵 2, 𝐵 5 }; Foil(𝐵 2 ) = {𝐵 3 } and Foil(𝐵 5 ) = {𝐵 6 }.
In what follows it will be assumed that Foil(𝐴) ≠ ∅, for fact
𝐴, i.e., that a foil exists. Note that, by Definition 3.4, for any AF
AF = ⟨Args, Att⟩ and 𝐴 ∈ Args, Foil(𝐴) = ∅ iff there is no 𝐵 ∈Args such that (𝐵, 𝐴) ∈ Att. Hence, any argument without a foil is
not attacked at all. The next proposition shows that the obtained
contrastive explanations are meaningful when the first conditionof the applicability of contrastive explanations is fulfilled and thefoil is defined as in Definition 3.4.
Proposition 3.6. Let AF = ⟨Args, Att⟩ be an AF, let 𝐴 ∈ Args besuch that Foil(𝐴) ≠ ∅. Then a contrastive acceptance explanation canbe requested for 𝐴, when 𝐴 is at least accepted and for all 𝐵 ∈ Foil(𝐴),𝐵 is at least not accepted.
In view of the above proposition we obtain the following corollary from Propositions 3.3 and 3.6.
Corollary 3.7. Let AF = ⟨Args, Att⟩ be an AF, let 𝐴 ∈ Args
be such that Foil(𝐴) ≠ ∅. Then: the explanation Cont(𝐴, Foil(𝐴)) isÐnever of the form Acc(𝐴), 𝐵 ∈Foil(𝐴) NotAcc(𝐵) ;4CONCLUSION

In this paper we have introduced a general approach to derive
contrastive explanations from AFs generated from an abstract setting. In [3] we consider additional semantics, two additional notions of (non-)acceptance, contrastive explanations for structured
settings (i.e., ASPIC+ [9]) as well as a real-life example from anargumentation-based system employed at the Netherlands Police.
To the best of our knowledge this is the first investigation into
contrastive local explanations for conclusions derived from bothabstract and structured argumentation.
Acknowledgements. This research has been partly funded by
the Dutch Ministry of Justice and the Dutch National Police.

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