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 [20]. However, explanations also play an important role in (symbolic) knowledge-based
systems [11]. 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 [6] –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 [6].
The Dutch National Police employs several applications based on structured
argumentation frameworks (a variant of ASPIC+ [19]). 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
is a case of fraud [3,18]. Another related example is a classifier for checking?

This research has been partly funded by the Dutch Ministry of Justice and the Dutch
National Police.

2

A. Borg and F. Bex

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 [17].
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 [7]: 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 [7] 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 in an informal way how a variety of different local
explanations can be derived from an argumentation framework. In addition to
explanations based on concepts from formal argumentation (e.g., attack and defense), we discuss how explanations can be selected based on sufficiency andnecessity. Moreover, we discuss how our explanations can be used to create contrastive explanations (i.e., “why P rather than Q”). Each of the discussed explanations is based on underlying formal definitions that we do not present here,
but that are collected in a paper currently under review [4].
Our informal exploration has clear ties to recent more formal work on methods to derive explanations for specific conclusions [8,9,10,12,21]. That we introduce a new framework rather than use or modify an existing one has several reasons. Often, explanations are only defined for a specific semantics [8,9]and can usually only be applied to abstract argumentation [9,12,21],3 while ourframework 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 not considered at all in the literature). Moreover,
explanations from the literature are usually only for acceptance [8,12] or nonacceptance [9,21], while we introduce one framework with which both acceptance3

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

3and non-acceptance explanations can be derived in a similar way.4 Finally, tothe best of our knowledge, this is the first approach to local explanations for formal argumentation in which necessary, sufficient and contrastive 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

In order to present explanations for argumentation-based conclusions, first somebasic concepts from formal argumentation have to be introduced. Reasoning
based on formal argumentation is based on three concepts: arguments, an attack
relation and a notion of defense:– In abstract argumentation, as introduced in [6], arguments are abstract entities. However, in structured (or deductive) argumentation, arguments canbe constructed from a knowledge base and a set of rules.
– Between these arguments an attack relation is defined. Again, in abstract
argumentation, this relation is abstract and pre-defined by the user. But instructured argumentation, the attacks between arguments are determinedby the underlying structure of the arguments.
– From the attack relation a notion of defense can be derived. An argument A
can defend an argument B if it attacks an attacker of B.
An argumentation framework is then a pair of a set of arguments and an attack
relation between those arguments. Formally, an argumentation framework is apair AF = hArgs, Ai, where Args is a set of arguments and A ⊆ Args × Args
is an attack relation on these arguments. Given arguments A, B ∈ Args, it issaid that A attacks B iff (A, B) ∈ A and A defends B if for some C ∈ Args,(A, C), (C, B) ∈ A.5 An argumentation framework can be viewed as a directed
graph, in which the nodes represent arguments and the arrows represent attacks
between arguments. See Figure 1 (on page 5) for an example.
Conclusions are drawn by selecting sets of arguments that can collectively
be considered as acceptable. How such sets are selected depends on the choicesof the designer of the system. Common requirements are that the set:
– is conflict-free: there are no attacks between the arguments in the set;4

An exception to this might be [10]. However, we consider our framework easierapplicable, since it returns sets of arguments rather than sets of dialectical trees,
which might contain many arguments.
5
Our notion of defense, defined between arguments, is different from the one introduced by Dung [6], defined between a set of arguments and an argument. We use thisdefinition since we are 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– defends itself: for any attacker of an argument in the set, there is an argumentin the set that defends against this attacker;– is complete: if an argument is defended against all its attackers by the set,
then it is contained in the set.
There are different ways in which the conclusions can be drawn from the selected
sets of arguments. In the application at the police it is important to only draw
conclusions that one can be certain about. This means that the application uses
a very skeptical approach towards drawing conclusions: only arguments thatare part of every complete set are considered conclusions (i.e., the grounded
semantics from [6] is used). For the purpose of this paper, to illustrate the varietyof possible explanations, we take a more credulous approach: an argument thatis part of some complete set can be considered a conclusion (i.e., the preferredsemantics from [6] is used).
Remark 1. For the interested reader, a note on the actual system used in theapplications. Each of the applications that is in use, is based on a variation of
ASPIC+ , one of the best-known approaches to structured argumentation [19].
In particular, the notions of a language, axioms and defeasible rules are takenfrom ASPIC+ and the conclusions are drawn based on the grounded semantics.
See [18] for the formal details.6
These basic notions from formal argumentation are enough to illustrate thedifferent possibilities for explaining argumentation-based conclusions derived
from the internet trade fraud application at the police.

3

Internet Trade Fraud

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 ;6

The corresponding demo of [18], demonstrating the argumentation-based
part of the application, is available at https://nationaal-politielab.sites.uu.nl/
estimating-stability-for-efficient-argument-based-inquiry/.
7
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.

Explaining Arguments at the Dutch National Police

5

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:
C1 :
A1 :
A2 :
A3 :
A4 :
A5 :
A6 :

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.

Attacks between those arguments can be derived from the conflicts between
conclusions of the (sub)arguments. For example the argument A5 which has
conclusion not fake will attack any argument with the conclusion fake (and viceversa), as well as any argument based on the conclusion fake (i.e., A5 and A3
attack each other on their conclusion and A5 attacks A4 and A6 because they
have fake as a sub-conclusion). The graphical representation of the argumentation framework, which we will refer as AF 1 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 ).
From an argumentative perspective a credulous reasoner (a reasoner who wants
to accept as many conclusions as possible) can accept both arguments, though
not simultaneously. For A1 this is the case since A1 attacks any argument bywhich it is attacked (i.e., there is an attack from A1 to A6 ). For A6 additional
conclusions have to be accepted as well. In particular, one can accept the argument for fraud when also accepting the arguments for the counter party did notdeliver (A4 ) and that the product is fake (A3 ). This follows since A3 , A4 and A6
together attack all the arguments that attack them: A3 attacks A5 and therefore
defends itself, A4 and A6 from the attacks by A5 ; A4 attacks A2 and therefore

6

A. Borg and F. Bex

defends itself and A6 from the attacks by A2 ; and A6 attacks A1 and therefore
defends itself against that attack. In what follows we will consider for both A1
and A6 explanations for why one could (not) accept them.
It is a case of fraud (acceptance of A6 /non-acceptance of A1 ). The
explanation here is that A6 can be accepted, when A3 and A4 are accepted aswell. In terms of the conclusions of the arguments, we say that it is a case of
fraud (A6 ), because the product is fake (A3 ) and the counter party did notdeliver (A4 ). When considering the individual elements of arguments, further
explanations can be considered. 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 ). Explanations like this take the last
rule that was applied in the construction of the argument as well as theantecedents of that rule. Such an explanation can be used by an analyst at
the police, who is familiar with the rules and might want to understand whatparts of the law were applied to derive the conclusion.
– the complainant paid and the product seems suspicious. This type of explanation looks at the information provided by the complainant (i.e., the knowledge base) and shows which of this information was used in the derivationof the conclusion. At the moment, the system returns this type of explanation, which can be used by the complainant, to understand what parts of
the report made the system derive this conclusion.
– the complainant delivered (C1 ), the counter party did not deliver (A4 ) andthe product is fake (A3 ). In this explanation all the sub-conclusions are returned that were derived from the information provided by the complainant.
Explanations like this provide insight into the reasoning process of the system: it shows the sub-steps that were taken. It might be useful for an analyst
at the police, who wants more insight into the reasons than only the last step,
but also for the complainant, who might not be convinced by an explanationthat 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:

Explaining Arguments at the Dutch National Police

7– 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. This isagain the explanation in terms of the last rule applied to derive the argumentfor not a case of fraud and its antecedents. Note that this explanation is thesame, whether we consider A1 to be an explanation for its own acceptance,or the arguments A2 and A5 are considered as well.
– the wrong product was delivered and an investigation shows that there is
no problem with the product. This explanation is about the information
provided by the complainant: the elements from the knowledge base. If A5
is not a part of the explanation, then this explanation only contains theinformation that the wrong product was delivered.
– the counter party has delivered (A2 ) and the product is not fake (A5 ). Herethe sub-conclusions that were found during the derivation of the argument
form the explanation. 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 inmany 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 [16] for an overview on findings for the social sciences on how humans come to their explanations and how this could be appliedin artificial intelligence. To illustrate some of the findings and how these canbe implemented into our system of explanations, we consider three cases. The
first two are often studied together: necessity and sufficiency.8 In the context ofphilosophy and cognitive science, these are discussed in, for example [13,14,22].
The third are contrastive explanations [13,15,16]: when people ask ‘why P ?’,they often mean ‘why P rather than Q?’ – here P is called the fact and Q iscalled the foil [13]. The answer to the question is then to explain as many ofthe differences between fact and foil as possible. We discuss each of the cases
separately, in the context of our argumentation setting.
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:8

See [5] for the technical details of the necessary and sufficient explanations for abstract argumentation.

8

A. Borg and F. Bex– 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. There is therefore only one set of arguments (minimally)
sufficient: {A3 , A4 , A6 }.
Based on these sufficient sets of arguments we can again look at explanations interms of the elements of the arguments. Note that when explanations should contain minimal sufficient sets of elements (e.g., minimal sufficient sets of premises
or sub-conclusions) one should not simply take the elements of the minimal sufficient set of arguments, but rather compare the sets of elements obtained fromeach sufficient set and compare those sizes. In the case of our example this does
not matter. However, it might be that one sufficient set contains one argument
constructed from many premises, while another sufficient set contains several
arguments which are constructed from less premises.
In our example we have that:– receiving the wrong product is sufficient for that it is not a case of fraud, if
we are interested in the premises and, combined with the rule that usuallywhen the wrong product is received it is not a case of fraud, when we areinterested in the last rule applied in the construction of the argument.
– the premises that the complainant paid and that the product seems suspicious are sufficient for that it is a case of fraud. When looking at the last
rules applied, the rules from A3 (if the product seem suspicious then usually
the product is fake), 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 not deliver it is usually a case of fraud) form the explanation, together
with their antecedents that the product seems suspicious, the product is
fake, the complainant delivered and the counter party did not deliver.
Given the structure of the argumentation framework on internet trade fraud,
there is not much difference between the basic explanations and sufficient explanations. Therefore, we introduce here a second argumentation framework, thistime abstract (i.e., no underlying structure in the arguments and not based ona scenario from the police), with which we can show how sufficient explanations
might differ.
Example 1. Let AF 2 = hArgs2 , A2 i be an argumentation framework whereArgs2 = {A, B, C, D, E, F, G} are abstract arguments and where we define theattacks as follows: A2 = {(B, A), (C, B), (C, D), (D, C), (E, B), (F, E), (F, G),(G, F )}. See Figure 2 for a graphical representation.
As in the case of our running example, each argument can be accepted by acredulous reasoner and no argument is accepted by a skeptical reasoner. In orderto accept A either C or E should be accepted as well and in order to accept E

Explaining Arguments at the Dutch National Police

A

C

D

E

F

9

B
G

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

one should accept G. In order to accept B, one has to accept both D and F .
Similarly, in order to not accept A, one has to accept B and therefore both D
and F as well, while not accepting B means accepting at least C or E (andpossibly both).
Sufficient explanations for the acceptance of A are {C}, {E, G}, {C, E, G},
but also {C, F } and {D, E, G} (since these still include C resp. E and G).
Minimally sufficient explanations are {C} and {E, G} when minimality is taken
w.r.t. ⊆ and only {C} when minimality is taken w.r.t. the size of the set. Thereis only one (minimally) sufficient explanation for the acceptance of B: {D, F }.
Like in the case of the internet trade fraud example (recall AF 1 ), the nonacceptance explanations are very similar to the acceptance explanations: the only
(minimal) sufficient explanation of the non-acceptance of A is {B, D, F } while
the sufficient non-acceptance explanation for B can be {C}, {E, G}, {C, E, G},{C, F } and {D, E, G}.
Necessity. In terms of arguments, an argument can be understood as necessary
if without that argument, the considered argument could not be accepted. In
the case of our example, the (minimal) sufficient sets of arguments are also thenecessary arguments: A1 is the only necessary argument for the acceptance ofA1 , while there are three arguments necessary for the acceptance of A6 : A3 , A4
and A6 .
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 .
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. But there is more possible. Since
sometimes there might not be a necessary argument (i.e., when the argument
for which the explanation is required is not attacked at all, or the intersection ofits sufficient sets is empty)9 one could still collect necessary premises, rules and9

It can be shown formally that there are no sufficient sets of arguments when theargument is not attacked at all and that there are no necessary arguments if theintersection of the sufficient sets is empty (which is at least the case when there areno sufficient sets of arguments).

10

A. Borg and F. Bex

sub-conclusions (e.g., by taking the intersection of the elements of the sufficientarguments).
For necessity we can also take a look at the abstract argumentation framework AF 2 introduced to illustrate sufficiency. As in the case for our running
example on internet trade fraud with the argumentation framework AF 1 , when
the intersection of the sufficient sets is empty, there are no necessary arguments.
For the argumentation framework AF 2 we have that for the acceptance of A noargument is necessary, while for the acceptance of B both D and F are necessary.
Similarly, for the non-acceptance of A the arguments B, D and F are necessary,
while no argument is necessary for the non-acceptance of B.
Contrastive Explanations. When humans provide a contrastive explanation(they answer the question ‘why P rather than Q?’ when asked ‘why P ?’), the foil
(i.e., Q) 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 artificial intelligence because it comes with an
explicit notion of conflict (i.e., the attack relation). This allows us to derive afoil when none is provided. 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.
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).10 For example:– it is a case of fraud and not of not fraud because of the arguments A3 , A4
and A6 .
– it is a case of not fraud and not a case of fraud because of the argument A1(and possibly A2 and A5 ).
The explanations in terms of the elements of the arguments have been discussed
previously, we will therefore not repeat that discussion here.
10

It can be shown formally that the intersection is empty when the accepted argument
is not attacked or fact and foil are not relevant for each other, i.e., neither does
attack the other.

Explaining Arguments at the Dutch National Police

411Conclusion

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 [6].
Recall from the introduction that, unlike other approaches to local explanations of argumentation-based conclusions [8,9,10,12,21], our explanation framework can capture both acceptance and non-acceptance explanations, is not basedon one specific semantics and allows to take the structure of arguments into account (i.e., explanations can be sets of premises or rules, rather than just setsof arguments). Moreover, we have shown how our framework can be used to
study how findings from the social sciences (those collected in, e.g., [16]) can be
implemented. The presented studies of sufficiency, necessity and contrastivenessare 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 have not been investigated yet.
Future work will first focus on presenting the full technical details of ourframework. Once those details are available, we will continue our study of integrating findings from the social sciences into our explanations. For example, wewill study the notion of contrastiveness further, we will look into the robustnessof explanations and we will consider further selection criteria. Additionally, forthe applications at the Dutch National Police, we will implement the frameworkand conduct a user study on the best explanations for these specific applications
and, possibly, the best explanations for other argumentation-based applications.

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