Explaining Arguments at the Dutch National
Police?
AnneMarie Borg1[0000−0002−7204−6046] and Floris Bex1,2[0000−0002−5699−9656]
12Department of Information and Computing Sciences, Utrecht University
Department of Law, Technology, Markets and Society, Tilburg University{a.borg,f.j.bex}@uu.nl

Abstract. As AI systems are increasingly applied in real-life situations,
it is essential that such systems can give explanations that provide insight into the underlying decision models and techniques. Thus, users canunderstand, trust and validate the system, and experts can verify thatthe system works as intended. At the Dutch National Police several applications based on computational argumentation are in use, with police
analysts and Dutch citizens as possible users. In this paper we show how
a basic framework of explanations aimed at explaining argumentationbased conclusions can be applied to these applications at the police.
Keywords: Explainable AI · Computational Argumentation

1

Introduction

Recently explainable AI (XAI) has received much attention, mostly directed at
new techniques for explaining decisions of machine learning algorithms [21]. However, explanations also play an important role in (symbolic) knowledge-based
systems [12]. One area in symbolic AI which has seen a number of real-world
applications lately is formal or computational argumentation [1]. Two central
concepts in formal argumentation are abstract argumentation frameworks [7] –sets of arguments and the attack relations between them – and structured or
logical argumentation frameworks [2] – where arguments are constructed from aknowledge base and a set of rules and the attack relation is based on the individual elements in the arguments. Common for argumentation frameworks, abstractand structured, is that we can determine their extensions, sets of arguments thatcan collectively be considered as acceptable, under different semantics [7].
The Dutch National Police employs several applications based on structured
argumentation frameworks (a variant of ASPIC+ [20]). One such application
concerns complaints by citizens about online trade fraud (e.g., a product bought
through a web-shop or on eBay turns out to be fake). The system queries thecitizen for various observations, and then determines whether the complaint?

This research has been partly funded by the Dutch Ministry of Justice and theDutch National Police. We thank Daphne Odekerken for her help with designing theexamples and the anonymous reviewers for their valuable comments.

2

A. Borg and F. Bex

is a case of fraud [3,19]. Another related example is a classifier for checking
fraudulent web-shops, which gathers information about online shops and thus
tries to determine whether they are real (bone fide) or fake (mala fide) shops [18].
These applications are aimed at assisting the police at working through highvolume tasks, leaving more time for tasks that require human attention.
Argumentation is often considered to be inherently transparent and explainable. A complete argumentation framework and its extensions is a global explanation [8]: what can we conclude from the model as a whole? Such global
explanations can be used by argumentation experts to check whether the model
works as intended. However, as we have noticed when deploying argumentation
systems to be used by lay-users (e.g., citizens, police analysts) at the police,
more natural and compact explanations are needed. Firstly, we need ways to
explain the (non-)acceptability of individual arguments, that is, local explanations [8] for particular decisions or conclusions. Secondly, explanations should
be compact, and contain only the relevant arguments which are needed in orderto draw a conclusion. Finally, explanation should be tailored to the receiver. For
example, in the case of online trade fraud, for a citizen the system should return
only the observations provided in the report (“this is presumably a case of fraud
because you provided the following facts in your report:...”), but for a police
analyst the system should also show which (legal) rules were applied and why
there were no exceptions in this case (“this is presumably (not) a case of fraud
because the following legal rules are not applicable:...”).
In this paper, we show how a variety of different local explanations canbe derived from an argumentation framework and we provide motivations forthe design options. We start with the basic explanations from [4], which are
based on concepts from formal argumentation (Section 3.1). We then discuss how
explanations can be selected based on sufficiency and necessity (Section 3.2) andhow our explanations can be used to create contrastive explanations (i.e., “whyP rather than Q”) (Section 3.3). Each of the discussed explanations is based onunderlying formal definitions that we cannot introduce here in full detail. We
refer the interested reader to [4], [6] and [5] respectively.
Our informal exploration has clear ties to recent more formal work on methods to derive explanations for specific conclusions [9,10,11,13,22]. We apply andextend the framework from [4] here for several reasons. Often, explanations are
only defined for a specific semantics [9,10] and can usually only be applied to abstract argumentation [10,13,22],3 while our framework can be applied on top of
any argumentation setting (structured or abstract) that results in a Dung-style
argumentation framework. Furthermore, when this setting is a structured one
based on a knowledge base and set of rules (like ASPIC+ or logic-based argumentation [2]), the explanations can be further adjusted (something which is notconsidered at all in the literature). Moreover, explanations from the literature
are usually only for acceptance [9,13] or non-acceptance [10,22], while with this
3

These explanations do not account for the sub-argument relation in structured argumentation. For example, in structured argumentation one cannot remove specificarguments or attacks without influencing other arguments/attacks.

Explaining Arguments at the Dutch National Police

3framework both acceptance and non-acceptance explanations can be derived ina similar way.4 Finally, to the best of our knowledge, this is the first approach
to local explanations for formal argumentation in which necessary, sufficient andcontrastive explanations are considered.
The paper is structured as follows: in the next section we recall some of themost basic and important concepts from formal argumentation. Then, in Section 3, the internet trade fraud scenario and the different possible explanations
for the derived conclusions are discussed. We conclude in Section 4.

2

Argumentation Preliminaries

We focus in this paper on the intuition behind the explanations introduced
in [6,4] and the motivation for some of the choices that can be made in thederivation of these explanations. We therefore keep the formal definitions andresults limited, leaving more space for an informal discussion.
An abstract argumentation framework (AF) [7] is a pair AF = hArgs, Ai,
where Args is a set of arguments and A ⊆ Args × Args is an attack relation onthese arguments. An AF can be viewed as a directed graph, in which the nodes
represent arguments and the arrows represent attacks between arguments (see,e.g., Figure 1 on page 6). Dung-style semantics can be applied to an AF, todetermine what combinations of arguments can collectively be accepted.
Definition 1. For AF = hArgs, Ai, A ∈ Args attacks B ∈ Args if (A, B) ∈ A
and S ⊆ Args attacks B if there is some C ∈ S such that (C, B) ∈ A; A defends
B if A attacks an attacker of B and S defends B if it attacks every attacker of
B;5 S is conflict-free if there are no A1 , A2 ∈ S such that (A1 , A2 ) ∈ A; and S
is admissible if it is conflict-free and it defends all of its arguments.
A ⊆-maximal admissible set is a preferred extension (Prf) of AF. The setof all preferred extensions of AF will be denoted by Prf(AF).
There are different ways in which the conclusions can be drawn from theextensions of a framework. At the police, when drawing a definite conclusion(e.g., someone is guilty) it is important to be completely certain. This means thatthe application uses a very skeptical approach towards drawing conclusions: only
arguments that are part of every complete set are considered conclusions (i.e.,
the grounded semantics from [7] is used). When considering whether there is thepossibility of the conclusion (e.g., it could be a case of fraud), a more credulous
approach can be taken. We follow the latter approach here: an argument that ispart of some preferred extension can be considered a conclusion or accepted.
4

An exception to this might be [11]. However, we consider our framework more easily
applicable, since it returns sets of arguments rather than sets of dialectical trees,
which might contain many arguments.
5
In [7], attack and defense are defined from a set of arguments to an argument. In
this paper we will mainly rely on attack and defense between arguments, since weare interested in the arguments that defend a certain argument, rather than whether
that argument is defended by the set of arguments.

4

A. Borg and F. Bex

For example, in the AF from Figure 1 we have that all arguments are accepted (while under the grounded semantics only C1 would be accepted). In particular, we have the following preferred extensions: {A1 , A2 , A3 }, {A1 , A2 , A5 },{A1 , A3 , A4 }, and {A3 , A4 , A6 }.
In abstract argumentation, as defined above, the arguments are abstract
entities and the attack relation is pre-defined. In contrast, in structured argumentation, the arguments are derived from a knowledge base and a set of rules
and the attack relation is based on the structure of the arguments. Each of theapplications that is in use, is based on a variation of ASPIC+ , one of the bestknown approaches to structured argumentation [20]. In particular, the notionsof a language, axioms and defeasible rules are taken from ASPIC+ . See [19] forthe formal details.6 In this paper we only provide the preliminaries that are necessary for the explanations. As we will show in the next section, the AF from
Figure 1 is based on a structured setting.
Argumentation frameworks in ASPIC+ are constructed from an argumentation theory: AT = hAS, Ki, where AS = hL, R, ni, an argumentation system, isa triple of a formal language, a set of defeasible rules and a naming function forthese rules, and K = Kn ∪ Kp is the knowledge base containing the disjoint setsof axioms (Kn ) and ordinary premises (Kp ). Arguments are constructued froman argumentation theory as follows:
Definition 2. An argument A on the basis of an argumentation theory AT =hAS, Ki, where AS = hL, R, ni is:– φ if φ ∈ K, where Prem(A) = Sub(A) = {φ}, Conc(A) = φ and TopRule(A) =undefined;– A1 , . . . , An ⇒ ψ, if A1 , . . . , An are arguments such that there is a rule
Conc(A1 ), . . . , Conc(An ) ⇒ ψ ∈ R.
Prem(A) = Prem(A1 ) ∪ . . . ∪ Prem(An ), Sub(A) = Sub(A1 ) ∪ . . . ∪ Sub(An ) ∪{A}, Conc(A) = ψ, TopRule(A) = Conc(A1 ), . . . , Conc(An ) ⇒ ψ additionally, we denote Ant(TopRule(A)) = {Conc(AS 1 ), . . . , Conc(An )}. Moreover,where S is a set of arguments Prem(S) = {Prem(A) | A ∈ S}.
Attacks between arguments are based on the premises and conclusions ofthese arguments.
Definition 3. An argument A attacks an argument B iff, (where φ = −ψ iff
φ = ¬ψ or ψ = ¬φ)– Conc(A) = ¬n(di ), where there is some B 0 ∈ Sub(B) such that TopRule(B 0 ) =di , it denies a rule; or– Conc(A) = −φ, where there is some B 0 ∈ Sub(B) such that Conc(B 0 ) = φ,it denies a conclusion; or– Conc(A) = −φ, for some φ ∈ Prem(B) \ Kn , it denies a premise.
6

The corresponding demo of [19], demonstrating the argumentation-based
part of the application, is available at https://nationaal-politielab.sites.uu.nl/
estimating-stability-for-efficient-argument-based-inquiry/.

Explaining Arguments at the Dutch National Police

5Dung-style semantics can be applied to argumentation frameworks based onargumentation theories as defined in Definition 1. We will say that a formula
φ in an argumentation framework AF(AT) is accepted if there is some E ∈Prf(AF(AT)) with A ∈ E such that Conc(A) = φ and non-accepted if there issome E ∈ Prf(AF(AT)) such that there is no A ∈ E with Conc(A) = φ.
These basic preliminaries on formal argumentation are enough to illustrate
the different possibilities for explaining argumentation-based conclusions derived
from the internet trade fraud application at the police.

3

Deriving Explanations

Suppose that the following knowledge base is provided: a citizen has ordered a
product through an online shop, paid for it and received a package. However, itis the wrong product, it seems suspicious as if it might be a replica, rather thana real product. Yet an investigation cannot find a problem with the product.
Still, the citizen wants to file a complaint of internet trade fraud.
While the citizen provides the information from the described scenario, thesystem constructs further arguments from this, based on the Dutch law.7 In
particular, the following rules are applied:
R1 If the complainant paid then usually the complainant delivered ;R2 If the wrong product was received then usually this is not a case of fraud ;R3 If the wrong product was received then usually the counter party has delivered ;R4 If the product seem suspicious then usually the product is fake;R5 If the product is fake then usually the counter party did not deliver ;R6 If an investigation shows that there is no problem with the product thenusually the product is not fake;R7 If the complainant delivered and the counter party did not deliver it is usuallya case of fraud.
From this we obtain arguments for:8
C1 :
A1 :
A2 :
A3 :
A4 :
A5 :
A6 :
7

the complainant paid + R1 ⇒ the complainant delivered
the wrong product was received + R2 ⇒ it is not a case of fraud
the wrong product was received + R3 ⇒ the counter party has delivered
the product seems suspicious + R4 ⇒ the product is fakeA3 + R5 ⇒ the counter party did not deliver
an investigation shows no problems + R6 ⇒ the product is not fakeC1 + A4 + R7 ⇒ it is a case of fraud.

In order to make the argumentation framework and corresponding explanations moreinteresting the rules that are applied here are only inspired by the law. The realapplication is based on slightly different rules [19].
8
We do not state the arguments based on the knowledge base explicitly, since theseneither attack other arguments nor can be attacked themselves and do therefore notinfluence the acceptability of other arguments.

6

A. Borg and F. Bex

Note that the argument A5 which has conclusion not fake will attack any
argument with the conclusion fake (and vice versa), as well as any argument
based on the conclusion fake (i.e., A5 and A3 attack each other and A5 attacks A4
and A6 because they have fake as a sub-conclusion). The graphical representationof the AF, which we will refer as AF 1 = hArgs1 , A1 i can be found in Figure 1.

C1

A1

A6

A2

A4

A5

A3

Fig. 1. Graphical representation of the argumentation framework AF 1 constructedbased on information provided in the complaint.

As the aim of the system is to determine whether a particular situation is acase of fraud, we will focus here on the arguments A1 (not fraud ) and A6 (fraud ).
Note that, from an argumentative perspective, both arguments can be accepted,
though not simultaneously. For A1 this is the case since A1 attacks any argument
by which it is attacked (i.e., (A1 , A6 ) ∈ A). For A6 additional conclusions haveto be accepted as well. In particular, one can accept the argument for fraud when
also accepting the arguments for the counter party did not deliver (A4 ) and thatthe product is fake (A3 ). This follows since {A3 , A4 , A6 } is a preferred extension
and A3 and A4 attack attackers of A6 that A6 would otherwise not be defended
against. In what follows we will consider for both A1 and A6 explanations forwhy one could (not) accept them.
3.1

Basic explanations

In [4] skeptical and credulous acceptance and non-acceptance explanations for
abstract and structured argumentation were introduced. These explanations aredefined in terms of two functions: D, which determines the arguments that are in
the explanation and F, which determines what elements of these arguments the
explanation presents. For the basic explanations in this paper, we instantiate
D with the following functions, let A ∈ Args and E ∈ Prf(AF) for some AF
AF = hArgs, Ai:– Defending(A) = {B ∈ Args | B defends A} denotes the set of argumentsthat defend A and Defending(A, E) = Defending(A) ∩ E denotes the set ofarguments that defend A in E.
– NotDefAgainst(A, E) = {B ∈ Args | B attacks A and E does not defend A
against this attack} denotes the set of all attackers of A that are not defended
by E.
The explanations are defined for arguments and formulas.

Explaining Arguments at the Dutch National Police

7

Definition 4. Let AF = hArgs, Ai be an AF and suppose that A ∈ Args [resp.
φ ∈ L] is accepted. Then:
Acc(A) = {Defending(A, E) | E ∈ Prf(AF) and A ∈ E}.
Acc(φ) = {F(Defending(A, E)) | E ∈ Prf(AF) such that A ∈ E and Conc(A) = φ}.
An acceptance explanation, for an argument or formula, contains all the arguments that defend the argument (for that for that formula) in an extension. If it
is an explanation for a formula explanation, the function F can be applied to it.
Definition 5. Let AF = hArgs, Ai be an AF and suppose that A ∈ Args [resp.
φ ∈ L] is non-accepted. Then:[
NotAcc(A) =NotDefAgainst(A, E).
E∈Prf(AF ) and A∈E/

NotAcc(φ) =[[A∈Args and Conc(A)=φE∈Prf(AF ) and A∈E/

F(NotDefAgainst(A, E)).

A non-acceptance explanation contains all the arguments that attack the argument [resp. an argument for the formula] and to which no defense exists in some
preferred extension. For a formula F can be applied again.
The function F can be instantiated in different ways. We recall here some ofthe variations introduced in [4]. These will be motivated in the discussions on
the different explanations.
– F = id, where id(S) = S. Then explanations are sets of arguments.
– F = Prem. Then explanations only contain the premises of arguments (i.e.,knowledge base elements).
– F = AntTop, where AntTop(A) = hTopRule(A), Ant(TopRule(A))i. Then explanations contain the last applied rule and its antecedents.
– F = ConcSub, where ConcSub(A) = {Conc(B) | B ∈ Sub(A), Conc(B) ∈/K ∪ {Conc(A)}}. Then the explanation contains the sub-conclusions thatwere derived in the construction of the argument.
We can now turn to a discussion on explanations for the (non-)acceptance of(not) fraud.
It is a case of fraud (acceptance of A6 /non-acceptance of A1 ). The
basic explanation here is that A6 can be accepted, when A3 and A4 are accepted
as well. In terms of the conclusions of the arguments, we say that it is a caseof fraud (A6 ), because the product is fake (A3 ) and the counter party did notdeliver (A4 ). When considering the variations of F, further explanations can beconsidered. For example, it is a case of fraud, because:– the complainant delivered (C1 ) and the counter party did not deliver (A4 )and there is a rule (R7 ) that states that from these conclusions it can bederived that it is a case of fraud (A6 ), i.e., F = AntTop. Such an explanation
can be used by an analyst at the police, who is familiar with the rules andwants to understand what parts of the law were applied.

8

A. Borg and F. Bex– the complainant paid and the product seems suspicious, i.e., F = Prem. At
the moment, the system returns this type of explanation, which can be usedby the complainant, to understand what parts of the report made the systemderive this conclusion.
– the complainant delivered (C1 ), the counter party did not deliver (A4 ) andthe product is fake (A3 ), i.e., F = ConcSub. Explanations like this provide
insight into the reasoning process of the system: it shows the sub-steps thatwere taken. It might be useful for an analyst at the police, who wants moreinsight into the reasons than only the last step, but also for the complainant,
who might not be convinced by an explanation that only contains information provided in the complaint itself.
Similar explanations can be given for not(it is not a case of fraud ), i.e.,that A1 is not accepted. This follows since the main reason that A1 cannot be
accepted is the fact that A6 is accepted.
It is not a case of fraud (acceptance of A1 /non-acceptance of A6 ).
While A1 can be explained by the acceptance of A1 (since it can defend itself
against the attack from A6 ), additional arguments defend A1 as well (i.e., A2
and A5 defend A1 against the attack from A6 as well). To give an overview ofthe possible explanations, we consider here the most extensive set of arguments:
A1 , A2 and A5 . In terms of the conclusions of the arguments, it follows that it
is not a case of fraud, because the counter party has delivered and the productis not fake. Similarly as above, we can also consider other explanations based onelements of arguments: It is not a case of fraud, because:– the wrong product was delivered and there is a rule (R2 ) that states thatusually, when the wrong product is delivered, it is not a case of fraud, i.e.,
F = AntTop. Note that this explanation is the same, whether we consider
A1 to be an explanation for its own acceptance, or the arguments A2 andA5 are considered as well.
– the wrong product was delivered and an investigation shows that there is
no problem with the product, i.e., F = Prem. If A5 is not a part of the
explanation, then this explanation only contains the information that thewrong product was delivered.
– the counter party has delivered (A2 ) and the product is not fake (A5 ), i.e.,
F = ConcSub. Note that, in the case A1 is its own acceptance explanation,no sub-conclusions are derived in the process.
Like in the case above, the explanations that it is not(a case of fraud ) is similar to the explanations for not a case of fraud. This follows since the argument
for a case of fraud (A6 ) is attacked by each of the arguments considered here
(i.e., A6 is attacked by A1 , A2 and A5 ).
The suggested explanations above are not too extensive for the given example. However, a rule might have many antecedents, a conclusion might be basedon many knowledge base elements or the derivation might be long, resulting inExplaining Arguments at the Dutch National Police

9many sub-conclusions. It is therefore useful to consider how we can reduce thesize of explanations. To this end, it has been argued that humans select their
explanations in a biased manner. Selection happens based on e.g., simplicity,
generality, robustness – see [17] for an overview on findings for the social sciences on how humans come to their explanations and how this could be appliedin artificial intelligence. In the next section we will consider two ways of reducing the size of explanations. Given the space restrictions and since the basic
explanations were similar for acceptance and non-acceptance, we only discuss
acceptance explanations.
3.2

Necessity and Sufficiency

Necessity and sufficiency in the context of philosophy and cognitive science are
discussed in, for example, [14,15,23]. Intuitively, an event Γ is sufficient for ∆ if
no other causes are required for ∆ to happen, while Γ is necessary for ∆, if inorder for ∆ to happen, Γ has to happen as well.9
Sufficiency. In terms of arguments, one could say that a set of arguments issufficient for the acceptance of some argument, if by accepting those arguments
the argument can also be accepted (i.e., that the set of arguments defends theargument against all its attackers). For example, in the cases above:– it was already mentioned that the acceptance of A1 (that it is not a caseof fraud ) can be explained by the argument itself, but also by {A1 , A2 },by {A2 , A5 } and by {A1 , A2 , A5 }. Each of these sets is sufficient for theacceptance of A1 . If one were interested in minimal sufficiency, then theargument itself would be enough.
– for the argument A6 (that it is a case of fraud ) the arguments A3 and A4
have to be accepted. Thus there is only one sufficient set: {A3 , A4 , A6 }.
Formally, given AF = hArgs, Ai and accepted argument A ∈ Args:– S ⊆ Args is sufficient for the acceptance of A if for each B ∈ S, there is anattack-path from B to A,10 S is conflict-free and S defends A against all its
attackers.
We denote by Suff(A) = {S ⊆ Args | S is sufficient for the acceptance of A} theset of all sufficient sets of arguments for the acceptance of A. With this sufficient
explanations can be defined:
Definition 6. Let AF = hArgs, Ai be an AF and suppose that A ∈ Args is
accepted. Then: Acc(A) ∈ Suff(A).
For minimally sufficient explanations Acc(A) ∈ min Suff(A), where minimality can be taken w.r.t. ⊆ or the number of arguments in a set.
9

See [6] for the technical details, in this paper we focus on the application of necessary
and sufficient explanations.
10
There is an attack path from B to A if there are C1 , . . . , Ck ∈ Args such that
(B, C1 ), (C1 , C2 ), . . . , (Ck−1 , Ck ), (Ck , A) ∈ A.

10

A. Borg and F. Bex

The resulting explanations for AF 1 are as described before the formal definitions.
When the structure of the arguments is known we can again look at explanations in terms of the elements of the arguments. Note that when explanations
should contain minimal sufficient sets of elements (e.g., minimal sufficient setsof premises or sub-conclusions) one should not simply take the elements of theminimal sufficient set of arguments, but rather compare the sets of elements
obtained from each sufficient set and compare those sizes.
Definition 7. Let AF(AT) = hArgs, Ai be an AF, based on an argumentation
theory AT and suppose that φ ∈ L is accepted. Then:[
Acc(φ) ∈ {F(Suff(A)) | A ∈ Args and Conc(A) = φ}.
[
Acc(φ) ∈ min {F(Suff(A)) | A ∈ Args and Conc(A) = φ}.
In our example we have that:– receiving the wrong product is sufficient for that it is not a case of fraud, if
F = Prem and, combined with the rule that usually when the wrong productis received it is not a case of fraud, when F = AntTop.
– the premises that the complainant paid and that the product seems suspicious are sufficient for that it is a case of fraud. When F = AntTop, therules from A3 (if the product seem suspicious then usually the product isfake), A4 (if the product is fake then usually the counter party did not deliver) and A6 (if the complainant delivered and the counter party did notdeliver it is usually a case of fraud) form the explanation, together with
their antecedents that the product seems suspicious, the product is fake, thecomplainant delivered and the counter party did not deliver.
Given the structure of AF 1 , there is not much difference between the basic
explanations and sufficient explanations. Therefore, we introduce the following
example, this time not based on a scenario from the police.
Example 1. Let AT2 = hAS2 , K2 i, where the rules in AS2 are such that, with
K2 = {r, s, t, v}, the following arguments can be derived:11d

A : s, t ⇒1 ud

D : v ⇒4 ¬qd

B : p, ¬q ⇒2 ¬n(d1 )dE : r, t ⇒5 ¬pd

C : r, s ⇒3 qd

F : v ⇒6 p

See Figure 2 for a graphical representation of the correspond AF AF 2 . Note
that, like for AF 1 , all arguments can be accepted.
On an abstract level, in order to accept A either C or E should be accepted
as well. To accept B, one has to accept both D and F . Sufficient explanations
for the acceptance of A are {C}, {E}, {C, E}, but also {C, F } and {D, E} (sincethese still include C resp. E). Minimally sufficient explanations are {C} and {E}and {D, F } is the only (minimally) sufficient explanation for the acceptance of B.
11

We ignore again the arguments based on the elements of K2 .

Explaining Arguments at the Dutch National Police

D

C

A

B

E

11

F

Fig. 2. Graphical representation of the abstract argumentation framework AF 2 .

When looking at the structure of the arguments, taking F = Prem, we havethat {r, s}, {r, t} and {r, s, t} are some of the sufficient sets for the acceptanceof u and {v} is sufficient to accept an exception to the rule d1 .
Necessity. In terms of arguments, an argument can be understood as necessary
if without that argument, the considered argument could not be accepted. For
AF 1 , the (minimal) sufficient sets of arguments are also the necessary arguments:
A1 is the only necessary argument for the acceptance of A1 , while there are threearguments necessary for the acceptance of A6 : A3 , A4 and A6 .
Formally, given an AF AF = hArgs, Ai and A ∈ Args an accepted argument:– B ∈ Args is necessary for the acceptance of A if there is an attack-path from
B to A and if B ∈/ S for some admissible set S ⊆ Args, then A ∈/ S.
We denote by Nec(A) = {B ∈ Args | B is necessary for the acceptance of A}
the set of all arguments that are necessary for the acceptance of A. With thisnecessary explanations can be defined:
Definition 8. Let AF = hArgs, Ai be an AF and suppose that A ∈ Args is
accepted. Then: Acc(A) = Nec(A).
For an illustration of the difference between sufficiency and necessity, consider
the argument A2 . Then {A2 } is sufficient for its own acceptance, but {A5 } is alsosufficient for its acceptance. Therefore, there is no argument that is necessary
for the acceptance of A2 (see also Proposition 2).
Similar reasoning as in the case of sufficiency applies to necessary explanations based on the elements of the arguments. One can collect premises, rules andsub-conclusions from the necessary arguments. However, in terms of elements wecan be more detailed. For this we need the following results.
Proposition 1. Let AF = hArgs, Ai and let A ∈ Args be accepted. Then Acc(A) =∅ iff there is no B ∈ Args such that (B, A) ∈ A, where Acc can be defined as in
Definition 4 or 6.
Proposition
2. Let AF = hArgs, Ai and let A ∈ Args be accepted. Then Nec(A) =T∅ if Suff(A) = ∅.
While, in view of the above results, a necessary explanation for arguments
might be empty, one could still collect necessary premises, rules and sub-conclusions. We therefore define:12

A. Borg and F. Bex

Definition 9. Let AF(AT) = hArgs, Ai be an AF, based on an argumentation
theory AT and suppose that φ ∈ L is accepted. Then:\
Acc(φ) = {F(Suff(A)) | A ∈ Args and Conc(A) = φ}.
To illustrate the difference between necessary and sufficient explanations andthe application of the above definition, we return to the AF AF 2 from Example 1.
Example 2. For the AF AF 2 we have that for the acceptance of A no argument
is necessary. But, when F = Prem we have that r is necessary. For the acceptanceof B both D and F are necessary and, when F = Prem, v is necessary.
3.3

Contrastive explanations

Another relevant way in which humans structure and select their explanations
is contrastiveness [14,16,17]: 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 [14]. The
answer to the question is then to explain as many of the differences between fact
and foil as possible.12
When humans provide a contrastive explanation, the foil is not always explicitly stated. While humans are capable of detecting the foil based on context
and the way the question is asked, AI-based systems struggle with this.
When the foil is not explicitly stated, formal argumentation has an advantage
over some other approaches to AI because it comes with an explicit notion of
conflict (i.e., the attack relation). This allows us to derive a foil when none isprovided. For example, given an argument one could take as the foil:– all the arguments that directly attack or defend it;– all the arguments that directly or indirectly attack or defend it.
In the context of structured arguments, one can also look at the claims of thearguments and take the foil to be arguments with conflicting conclusion.
Given an argument of which the acceptance status should be explained (thefact) and a foil, a contrastive explanation contains those arguments that explain:– the acceptance of the fact and the non-acceptance of the foil;– the non-acceptance of the fact and the acceptance of the foil.
Definition 10. Let AF = hArgs, Ai be an AF, let A ∈ Args be the fact andS ⊆ Args be the foil (for example defined by the direct attacking arguments of
A). Suppose that A is accepted [resp. non-accepted] and that each B ∈ S is
non-accepted [resp. accepted]. Then:!
[
Cont(A, S) = Acc(A) ∩NotAcc(B)
B∈S!
ContN(A, S) = NotAcc(A) ∩[Acc(B) .

B∈S
12See [5] for the technical details, in this paper we focus on the application of contrastive explanations.

Explaining Arguments at the Dutch National Police

13

When Cont(A, S) = ∅ (the caseSfor ContN is similar) the explanation will returna pair: Cont(A, S) = Acc(A), B∈S NotAcc(B) .
Thus, given explanations for the acceptance [resp. non-acceptance] of the fact
and the non-acceptance [resp. acceptance] of the foil the contrastive explanation
returns the intersection of these explanations when it is not empty (otherwise it
would simply return those two explanations). An empty contrastive explanation
rarely happens. In particular:
Proposition 3. Let AF = hArgs, Ai be an AF. Let A ∈ Args and let S ⊆Args be such that for each B ∈ S, (B, A) ∈ A.
S Then Cont(A, S) = ∅ [resp.
ContN(A, S) = ∅] implies that Acc(A) = ∅ [resp. B∈S Acc(B) = ∅].
Intuitively, this shows that a contrastive explanation is only empty if the fact
is not attacked at all [resp. no argument in the set of foils is attacked]. To
illustrate contrastive explanations we introduce another scenario, this time about
a possible malafide webshop, based on the application in [18].
Example 3. Consider a language L3 , containing the atoms cf (a complaint was
filed), m (the webshop is malafide), iw (an investigation is done), sa (the url issuspicious), rc (the complaint is retracted), kp (the webshop owner is known by
the police), ka (the address is registered at the chamber of commerce), rr (theregistration was recently retracted) and their negations.
Let AT3 = hAS3 , K3 i, where the rules in AS2 are such that, with the language
L3 and K3 = {cf, rc, sa, ka, kp, rr}, the following arguments can be derived:
A1 : cf

A2 : rc

A3 : sad1

B1 : A1 ⇒ iw
d3

B4 : B1 , A3 ⇒ m

A4 : ka

A5 : kp

A6 : rrd2

d5

B2 : A2 ⇒ ¬n(d1 )B3 : A5 ⇒ ¬rcd4

B6 : A6 ⇒6 ¬ka.

d

B5 : A4 ⇒ ¬n(d3 )See Figure 3 for a graphical representation of the corresponding AF AF(AT3 ).
As in our previous examples, each of the arguments can be accepted.

A1

A2

B3

A3

B6

B1

B2

B4

B5

A4

A5

A6

Fig. 3. Graphical representation of the AF AF(AT3 ).

To start with, we have the following basic explanation for the acceptanceof m (i.e., the webshop is malafide): the owner of the webshop is known by
the police (kp) and the registration at the chamber of commerce was recently
retracted (rr), from which it follows that no exceptions could be derived.

14

A. Borg and F. Bex

Basic explanations are exhaustive: all the reasons why the webshop is malafide
are provided. With our contrastive explanations, the explanation can focus on an
explicit contrastive question. For example: the webshop is malafide rather thanthat there is an exception to rule d1 , since the owner is known by the police (kp);and the webshop is malafide rather than that there is an exception to rule d3 ,since the registration was recently retracted (rr). Thus, the contrastive explanations are better tailored to one question and result in smaller explanations.

4

Conclusion

In this paper we have discussed how a general framework for explaining conclusions derived from an argumentation framework can be applied on top of theargumentation systems in use at the Dutch National Police. As an example wetook the system in use to assist in the processing of complaints on online tradefraud. The ideas presented in this paper can also be applied to the other systems in use at the police as well as any other system based on argumentation
frameworks as introduced in [7].
Recall from the introduction that, unlike other approaches to local explanations of argumentation-based conclusions [9,10,11,13,22], the framework that
we applied can capture both acceptance and non-acceptance explanations, isnot based on one specific semantics (although we only considered preferred semantics here) and allows to take the structure of arguments into account (i.e.,
explanations can be sets of premises or rules, rather than just sets of arguments).
Moreover, we have shown how our framework can be used to study how findings
from the social sciences (those collected in, e.g., [17]) can be implemented. The
presented studies of sufficiency, necessity and contrastiveness are just the beginning. On the one hand, especially in the case of contrastive explanations, much
more can be said about the individual concepts than we could present here. On
the other hand, there are many other aspects of human explanation that havenot been investigated yet.
In future work we will continue our study of integrating findings from thesocial sciences into our explanations. For example, we will study the notion ofcontrastiveness further, we will look into the robustness of explanations and wewill consider further selection criteria. Additionally, for the applications at theDutch National Police, we will implement the framework and conduct a user
study on the best explanations for these specific applications and, possibly, thebest explanations for other argumentation-based applications.

References
1. Atkinson, K., Baroni, P., Giacomin, M., Hunter, A., Prakken, H., Reed, C., Simari,G., Thimm, M., Villata, S.: Towards Artificial Argumentation. AI magazine 38(3),25–36 (2017)
2. Besnard, P., Garcia, A., Hunter, A., Modgil, S., Prakken, H., Simari, G., Toni, F.:
Introduction to structured argumentation. Arg. & Comp. 5(1), 1–4 (2014)

Explaining Arguments at the Dutch National Police

15

3. Bex, F., Testerink, B., Peters, J.: AI for online criminal complaints: From naturaldialogues to structured scenarios. In: Workshop proceedings of Artificial Intelligence for Justice at ECAI 2016. pp. 22–29 (2016)
4. Borg, A., Bex, F.: A basic framework for explanations in argumentation. IEEE
Intelligent Systems 36(2), 25–35 (2021)
5. Borg, A., Bex, F.: Contrastive explanations for argumentation-based conclusions.
arXiv/CoRR abs/2107.03265 (2021), https://arxiv.org/abs/2107.03265
6. Borg, A., Bex, F.: Necessary and sufficient explanations for argumentation-based
conclusions. In: Proceedings of ECSQARU’21 (2021)
7. Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial Intelligence
77(2), 321–357 (1995)
8. Edwards, L., Veale, M.: Slave to the algorithm: Why a ‘right to an explanation’is probably not the remedy you are looking for. Duke Law & Technology Review
16(1), 18–84 (2017)
9. Fan, X., Toni, F.: On computing explanations in argumentation. In: Bonet, B.,
Koenig, S. (eds.) Proceedings of AAAI’15. pp. 1496–1502. AAAI Press (2015)
10. Fan, X., Toni, F.: On explanations for non-acceptable arguments. In: Black, E.,
Modgil, S., Oren, N. (eds.) Proceedings of TAFA’15. pp. 112–127. Springer (2015)
11. Garcı́a, A., Chesñevar, C., Rotstein, N., Simari, G.: Formalizing dialectical explanation support for argument-based reasoning in knowledge-based systems. Expert
Systems with Applications 40(8), 3233 – 3247 (2013)
12. Lacave, C., Diez, F.J.: A review of explanation methods for heuristic expert systems. The Knowledge Engineering Review 19(2), 133–146 (2004)
13. Liao, B., van der Torre, L.: Explanation semantics for abstract argumentation.
In: Prakken, H., Bistarelli, S., Santini, F., Taticchi, C. (eds.) Proceedings of
COMMA’20. pp. 271–282. IOS Press (2020)
14. Lipton, P.: Contrastive explanation. Royal Institute of Philosophy Supplement 27,
247–266 (1990)
15. Lombrozo, T.: Causal-explanatory pluralism: How intentions, functions, and mechanisms influence causal ascriptions. Cognitive psychology 61(4), 303–332 (2010)
16. Miller, T.: Contrastive explanation: A structural-model approach. CoRR
abs/1811.03163 (2018), http://arxiv.org/abs/1811.03163
17. Miller, T.: Explanation in artificial intelligence: Insights from the social sciences.
Artificial Intelligence 267, 1 – 38 (2019)18. Odekerken, D., Bex, F.: Towards transparent human-in-the-loop classification of
fraudulent web shops. In: Villata, S., Harašta, J., Křemen, P. (eds.) Proceedingsof JURIX 2020. pp. 239–242. IOS Press (2020)
19. Odekerken, D., Borg, A., Bex, F.: Estimating stability for efficient argument-based
inquiry. In: Prakken, H., Bistarelli, S., Santini, F., Taticchi, C. (eds.) Proceedingsof COMMA’20. pp. 307–318. IOS Press (2020)
20. Prakken, H.: An abstract framework for argumentation with structured arguments.
Argument & Computation 1(2), 93–124 (2010)
21. Samek, W., Wiegand, T., Müller, K.R.: Explainable artificial intelligence:
Understanding, visualizing and interpreting deep learning models. CoRR
abs/1708.08296 (2017), http://arxiv.org/abs/1708.08296
22. Saribatur, Z., Wallner, J., Woltran, S.: Explaining non-acceptability in abstract
argumentation. In: Proceedings of ECAI’20. pp. 881–888. IOS Press (2020)
23. Woodward, J.: Sensitive and insensitive causation. Philosophical Review 115(1),1–50 (2006)