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 can understand, trust and validate the system, and experts can verify that the 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.
Recently explainable AI (XAI) has received much attention, mostly directed at
new techniques for explaining decisions of machine learning algorithms [
The Dutch National Police employs several applications based on structured
argumentation frameworks (a variant of ASPIC+ [
National Police.
fraudulent web-shops, which gathers information about online shops and thus
tries to determine whether they are real (bone de) or fake (mala de) shops [
Argumentation is often considered to be inherently transparent and
explainable. A complete argumentation framework and its extensions is a global
explanation [
In this paper, we show in an informal way how a variety of di erent 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 su ciency and
necessity. Moreover, we discuss how our explanations can be used to create
contrastive explanations (i.e., \why P rather than Q"). We do not present the
underlying formal de nitions here, these can be found in [
Our informal exploration has clear ties to recent more formal work on
methods to derive explanations for speci c conclusions [
The paper is structured as follows: in the next section we recall some of the most basic and important concepts from formal argumentation. Then, in Section 3, the internet trade fraud scenario and the di erent possible explanations for the derived conclusions are discussed. We conclude in Section 4. 2
In order to present explanations for argumentation-based conclusions, rst some
basic 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 [
An argumentation framework is then a pair of a set of arguments and an attack relation between those arguments. Formally, an argumentation framework is a pair 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 2 Args, it is said that A attacks B i (A; B) 2 A and A defends B if for some C 2 Args, (A; C); (C; B) 2 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 choices
of the designer of the system. Common requirements are that the set:
{ is con ict-free: there are no attacks between the arguments in the set;
4 An exception to this might be [
There are di erent 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 that
are part of every complete set are considered conclusions (i.e., the grounded
semantics from [
Remark 1. For the interested reader, a note on the actual system used in the
applications. Each of the applications that is in use, is based on a variation of
ASPIC+, one of the best-known approaches to structured argumentation [
These basic notions from formal argumentation are enough to illustrate the di erent possibilities for explaining argumentation-based conclusions derived from the internet trade fraud application at the police. 3
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, it is the wrong product, it seems suspicious as if it might be a replica, rather than a real product. Yet an investigation cannot nd a problem with the product. Still, the citizen wants to le a complaint of internet trade fraud.
While the citizen provides the information from the described scenario, the
system 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 [
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 fake A3 + R5 ) the counter party did not deliver an investigation shows no problems + R6 ) the product is not fake C1 + A4 + R7 ) it is a case of fraud.
Attacks between those arguments can be derived from the con icts 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 vice versa), 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.
As the aim of the system is to determine whether a particular situation is a case 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 by which 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 not deliver (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 C1 A1
A6
A2
A4
A5
A3 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 as well. 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 not deliver (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 be derived 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 the antecedents 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 what parts 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 derivation of 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) and the 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 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 of the 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 product is not fake. Similarly as above, we can also consider other explanations based on elements of arguments: It is not a case of fraud, because: { the wrong product was delivered and there is a rule (R2) that states that usually, when the wrong product is delivered, it is not a case of fraud. This is again the explanation in terms of the last rule applied to derive the argument for not a case of fraud and its antecedents. Note that this explanation is the same, 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 the information that the wrong product was delivered. { the counter party has delivered (A2) and the product is not fake (A5). Here the 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 based
on many knowledge base elements or the derivation might be long, resulting in
many sub-conclusions. It is therefore useful to consider how we can reduce the
size 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 [
Su ciency. In terms of arguments, one could say that a set of arguments is
su cient 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 the
argument against all its attackers). For example, in the cases above:
8 See [
Based on these su cient sets of arguments we can again look at explanations in terms of the elements of the arguments. Note that when explanations should contain minimal su cient sets of elements (e.g., minimal su cient sets of premises or sub-conclusions) one should not simply take the elements of the minimal sufcient set of arguments, but rather compare the sets of elements obtained from each su cient set and compare those sizes. In the case of our example this does not matter. However, it might be that one su cient set contains one argument constructed from many premises, while another su cient set contains several arguments which are constructed from less premises.
In our example we have that: { receiving the wrong product is su cient for that it is not a case of fraud, if we are interested in the premises and, combined with the rule that usually when the wrong product is received it is not a case of fraud, when we are interested in the last rule applied in the construction of the argument. { the premises that the complainant paid and that the product seems suspicious are su cient 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 di erence between the basic explanations and su cient explanations. Therefore, we introduce here a second argumentation framework, this time abstract (i.e., no underlying structure in the arguments and not based on a scenario from the police), with which we can show how su cient explanations might di er.
Example 1. Let AF 2 = hArgs2; A2i be an argumentation framework where Args2 = fA; B; C; D; E; F; Gg are abstract arguments and where we de ne the attacks as follows: A2 = f(B; A); (C; B); (C; D); (D; C); (E; B); (F; E); (F; G); (G; F )g. See Figure 2 for a graphical representation.
As in the case of our running example, each argument can be accepted by a credulous reasoner and no argument is accepted by a skeptical reasoner. In order to accept A either C or E should be accepted as well and in order to accept E one should accept G. 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 (and possibly both).
Su cient explanations for the acceptance of A are fCg, fE; Gg, fC; E; Gg, but also fC; F g and fD; E; Gg (since these still include C resp. E and G). Minimally su cient explanations are fCg and fE; Gg when minimality is taken w.r.t. and only fCg when minimality is taken w.r.t. the size of the set. There is only one (minimally) su cient explanation for the acceptance of B: fD; F g.
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) su cient explanation of the non-acceptance of A is fB; D; F g while the su cient non-acceptance explanation for B can be fCg, fE; Gg, fC; E; Gg, fC; F g and fD; E; Gg.
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) su cient sets of arguments are also the necessary arguments: A1 is the only necessary argument for the acceptance of A1, while there are three arguments necessary for the acceptance of A6: A3, A4 and A6.
For an illustration of the di erence between su ciency and necessity, consider the argument A2. Then fA2g is su cient for its own acceptance, but fA5g is also su cient for its acceptance. Therefore, there is no argument that is necessary for the acceptance of A2.
Similar reasoning as in the case of su ciency applies to necessary explanations based on the elements of the arguments. One can collect premises, rules and sub-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 of its su cient sets is empty)9 one could still collect necessary premises, rules and 9 It can be shown formally that there are no su cient sets of arguments when the argument is not attacked at all and that there are no necessary arguments if the intersection of the su cient sets is empty (which is at least the case when there are no su cient sets of arguments). sub-conclusions (e.g., by taking the intersection of the elements of the su cient arguments).
For necessity we can also take a look at the abstract argumentation framework AF 2 introduced to illustrate su ciency. As in the case for our running example on internet trade fraud with the argumentation framework AF 1, when the intersection of the su cient sets is empty, there are no necessary arguments. For the argumentation framework AF 2 we have that for the acceptance of A no argument 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 arti cial intelligence because it comes with an explicit notion of con ict (i.e., the attack relation). This allows us to derive a foil 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 the arguments and take the foil to be arguments with con icting conclusion.
Given an argument of which the acceptance status should be explained (the fact) 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.
In this paper we have discussed how a general framework for explaining
conclusions derived from an argumentation framework can be applied on top of the
argumentation systems in use at the Dutch National Police. As an example we
took the system in use to assist in the processing of complaints on online trade
fraud. 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 [
Recall from the introduction that, unlike other approaches to local
explanations of argumentation-based conclusions [
In future work we will continue our study of integrating ndings from the social sciences into our explanations. For example, we will study the notion of contrastiveness further, we will look into the robustness of explanations and we will consider further selection criteria. Additionally, for the applications at the Dutch National Police, we will implement the framework and conduct a user study on the best explanations for these speci c applications and, possibly, the best explanations for other argumentation-based applications.