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Supporting Discussions About Forensic Bayesian Networks
Using Argumentation
Remi Wieten

Department of Information and Computing Sciences,
Utrecht University, The Netherlands
g.m.wieten@uu.nl

Henry Prakken

Department of Information and Computing Sciences,
Utrecht University, The Netherlands
Faculty of Law, University of Groningen, The Netherlands
h.prakken@uu.nl

ABSTRACT
Bayesian networks (BNs) are powerful tools that are increasingly
being used by forensic and legal experts to reason about the uncertain conclusions that can be inferred from the evidence in acase. Although in BN construction it is good practice to document
the model itself, the importance of documenting design decisions
has received little attention. Such decisions, including the (possibly
conflicting) reasons behind them, are important for legal experts
to understand and accept probabilistic models of cases. Moreover,when disagreements arise between domain experts involved in theconstruction of BNs, there are no systematic means to resolve suchdisagreements. Therefore, we propose an approach that allows domain experts to explicitly express and capture their reasons pro andcon modelling decisions using argumentation, and that resolves
their disagreements as much as possible. Our approach is basedon a case study, in which the argumentation structure of an actual
disagreement between two forensic BN experts is analysed.

CCS CONCEPTS• Applied computing → Law; • Computing methodologies→ Knowledge representation and reasoning; • Mathematics ofcomputing → Probability and statistics.

KEYWORDS
Bayesian networks, argumentation support, legal reasoning
ACM Reference Format:
Remi Wieten, Floris Bex, Henry Prakken, and Silja Renooij. 2019. Supporting
Discussions About Forensic Bayesian Networks Using Argumentation. In
Seventeenth International Conference on Artificial Intelligence and Law (ICAIL
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ICAIL ’19, June 17–21, 2019, Montreal, QC, Canada© 2019 Association for Computing Machinery.
ACM ISBN 978-1-4503-6754-7/19/06. . . $15.00
https://doi.org/10.1145/3322640.3326710

Floris Bex

Department of Information and Computing Sciences,
Utrecht University, The Netherlands
Institute for Law, Technology and Society,
Tilburg University, The Netherlands
f.j.bex@uu.nl

Silja Renooij

Department of Information and Computing Sciences,
Utrecht University, The Netherlandss.renooij@uu.nl’19), June 17–21, 2019, Montreal, QC, Canada. ACM, New York, NY, USA,
10 pages. https://doi.org/10.1145/3322640.3326710

1

INTRODUCTION

Bayesian networks (BNs) are powerful tools that are well-suited forreasoning about the uncertain consequences that can be inferredfrom the evidence in a legal case [1]. A BN compactly representsa joint probability distribution by means of a graph-structure andtables with probability parameters. In recent years, forensic andlegal experts have increasingly developed and used BNs for the interpretation of different types of forensic trace evidence [2], such as
glass fragments, finger marks and DNA evidence, as well as entire
legal cases [3]. Although in BN construction it is good practice todocument the model itself, the importance of documenting design
decisions has received little attention. Such decisions, including
the (possibly conflicting) reasons behind them, are important for
legal experts to understand and accept probabilistic models of cases.
Moreover, when disagreements arise between domain experts involved in the construction of BNs, there are no systematic means
to resolve such disagreements.
An example of a tool that does support domain experts in documenting their BN modelling decisions is that of Yet and colleagues[4]. Their tool allows BN developers to document the (clinical)
evidence, including conflicts, underlying the constructed BN in aqueryable OWL ontology, which users can examine through an
automatically generated free text web page. The tool, however, does
not support (domain) experts in recording conflicting reasons, letalone that it provides experts the ability to resolve them. Since thelegal domain is inherently adversarial, we prefer to use an approachfor capturing and resolving such conflicts based on argumentation[5]. Keppens [6] recently proposed such an argumentation-based
approach to criticise and resolve discussions about a probability distribution. Keppens’ approach can be used when discussions abouta BN only concern the parameterisation of a fully specified BN.
However, disagreements also arise regarding partially specified
BNs, and may also concern a BN’s graph-structure.
Accordingly, in this paper we propose an approach that helps tocapture and resolve disagreements among experts concerning any

ICAIL ’19, June 17–21, 2019, Montreal, QC, Canada
BN element. To this end, we allow experts to explicitly express theirreasons pro and con modelling decisions regarding the structure
and parameterisation of a (fully or partially specified) BN using argumentation. Disagreements are then resolved as much as possible
by utilising preferences that are specified over the arguments by theexperts. Our approach is based on a case study, in which we analyse
the argumentation structure of an actual disagreement between two
experts at the Netherlands Forensic Institute about a forensic BN for
the interpretation of finger marks. In a recent case study, Prakken[7] analysed the argumentation structure of actual court discussions regarding Bayesian analyses of criminal cases. However, hemainly concerned himself with establishing the usefulness of argumentation in structuring this kind of discussion, while the current
case study instead serves to identify how disagreements about BNs
are typically expressed and resolved manually by experts, and how
this process can be specified and (partly) automated using formal(computational) argumentation. Such a formal specification allows
us to investigate formal properties of our approach. Moreover, in
future work our formal model can be the basis for developing andimplementing software tools for supporting discussions about BNs
between forensic experts, and for communicating their BNs anddiscussions to judges and prosecutors.
The paper is structured as follows. Section 2 provides somepreliminaries on BNs and argumentation. In Section 3, we present
our case study, on the basis of which we propose our argumentationbased approach to capturing and resolving conflicts about BNs in
Section 4. In Section 5, we discuss related research and summarise
our findings.

2

PRELIMINARIESIn this section, BNs and argumentation are reviewed.

2.1

Bayesian Networks

A BN [8] is a compact representation of a joint probability distribution Pr (V) over a finite set of discrete random variables V.
The variables are represented as nodes in a directed acyclic graph
G = (V, E), where E ⊆ V × V is a set of directed arcs Vi → Vj fromparent Vi to child Vj . Each node V describes a number of mutually exclusive and exhaustive values; we will refer to these values
as the value space of V . The BN further includes, for each node,a conditional probability table (CPT) specifying the conditional
probabilities, or probability parameters, of the values of the nodeconditioned on the possible joint value combinations of its parents.
A node is called instantiated iff it is set to a specific value. Given a
set of instantiations, or evidence, the probability distributions over
the other nodes in the network can be updated using probability
calculus [8]. An example of a BN graph is depicted in Figure 1,
where ovals denote nodes and instantiated nodes are shaded.
The BN graph G captures the independence relation among its
variables. Let a chain be defined as a sequence of distinct nodes andarcs in the BN graph. A node V is called a head-to-head node on achain c if it has two incoming arcs on c. A chain c is blocked iff it
includes a node V such that (1) V is an uninstantiated head-to-headnode on c without instantiated descendants; or (2) V is instantiatedand has at most one incoming arc on c. A chain is inactive if itis blocked; otherwise it is called active. If no active chains exist

R. Wieten et al.
between V1 and V2 given instantiations of nodes in Z, then they are
considered conditionally independent given Z.

2.2

Argumentation

Throughout this paper, a simplified version of the ASPIC+ framework for structured argumentation [5] is assumed. We only semiformally specify ASPIC+ in this section, where the defined concepts
will become clear through the examples discussed throughout thispaper; for the formal definitions, we refer the reader to [5]. The
ASPIC+ instance assumes a logical language L containing the basic
elements that can be argued about, a knowledge base K ⊆ L ofpremises and a set of inference rules R that can be chained into
arguments. Specifically, L is a non-empty propositional languagewith ordinary negation symbol ¬. Two propositions are each other’scontradictories if one of them negates the other or if they are explicitly declared as contradictories by a contrariness function overthe language (for example, being a bachelor and being married
can be declared contradictories). Knowledge base K consists of
two disjoint subsets Kn and Kp of axiom and ordinary premises,
respectively. Inference rules in R are defined over L and are either
strict or defeasible in that the consequent of the rule holds either
deductively or tentatively given its antecedents. Arguments arethen iteratively constructed from knowledge base K by chaining
inference rules in R.
Arguments can be attacked in three ways: on the conclusion ofa defeasible rule (rebuttal), on a defeasible rule itself (undercutting
attack), or on an ordinary premise (undermining attack). The conclusion of a strict rule or a strict rule itself cannot be attacked. To
allow for undercutting attacks, L contains a well-formed formula
corresponding to the name of every defeasible rule. Defeasible rules
can be used to express argument schemes [9], which capture stereotypical non-deductive patterns of argumentation in a given domain
as a scheme with a set of premises and a conclusion, plus a set ofcritical questions that need to be answered before the scheme canbe used to derive conclusions. Critical questions then correspondto undercutters of the rule. Examples of argument schemes arepresented in Section 3.2.
In ASPIC+ , attack is resolved into defeat on the basis of a binary
preference relation over the arguments, where undercutting attack
is preference-independent. ASPIC+ thus induces abstract argumentation frameworks [10], which consist of a set of arguments alongwith a binary defeat1 relation, and which can be used to evaluate
the acceptability of the arguments. The theory of abstract argumentation frameworks is built around the notion of an extension,
which is a set of arguments that is internally coherent and defends
itself against attack. Dung precisely defined different types of extensions and conditions under which arguments belong to these
extensions. For our current purposes, we only define the terms“justified”, “overruled”, and “defensible” argument, which are basedon the notion of an extension. Informally, an argument is justified if
it survived the competition, while an argument is called defensible
if it is involved in a tie. An argument is justified iff it is a memberof all extensions. An argument is overruled iff it is not justified
and it is defeated by an argument that is justified. An argument
1 Note that Dung [10] called his relation “attack”. In ASPIC+ , the term attack is reserved

for the basic notion of conflict, which is resolved into defeat using preferences.

Supporting Discussions About Forensic Bayesian Networks Using Argumentation
is defensible iff it is not justified and not overruled. The status ofa conclusion ϕ ∈ L of an argument is then defined as follows. ϕ
is justified iff there exists a justified argument with conclusion ϕ,
ϕ is defensible iff ϕ is not justified and there exists a defensible
argument with conclusion ϕ, and ϕ is overruled iff ϕ is not justified
or defensible and all arguments with conclusion ϕ are overruled.
Throughout this paper, arguments are depicted informally inargument graphs; an example of an argument graph is depicted in
Figure 2. Nodes in argument graphs denote propositions ϕ ∈ L,
where shaded nodes denote propositions in Kn . Every applicationof a rule in R is indicated with a solid (hyper)arc in the graph thatis directed from the nodes corresponding to the antecedents of therule to the node corresponding to the consequent of the rule. Everyarc is annotated with the name of the applied inference rule (where
di and si indicate a defeasible and a strict rule, respectively). A
dashed arc directed from node N 1 to N 2 indicates that N 1 rebuts N 2 .
A dashed hyperarc directed from node ¬d 1 to a solid arc labelled
d 1 indicates that ¬d 1 undercuts d 1 .

3CASE STUDY - DISAGREEMENTS ABOUT A
FORENSIC FINGER MARK BN

In this section, we perform a case study to identify where disagreements about BNs can arise and how such disagreements are resolved
by experts. Doekhie and colleagues [11, 12] constructed a BN for
the interpretation of two finger marks2 , described in Section 3.1.
Doshi [13] criticised this BN and proposed adjustments that address
the supposed shortcomings. In Section 3.2, we analyse the argumentation structure of Doekhie’s modelling decisions and Doshi’s
criticism on these decisions. While the main objective of this casestudy is to identify where disagreements about BNs typically occur
and how such disagreements are resolved by experts, we also analyse the extent to which the constructed arguments can be classified
as instances of existing or newly proposed argument schemes or as
applications of critical questions of these schemes.

3.1

BN for Two Finger Marks at Finger Level

The BN that Doekhie and colleagues [11, 12] constructed is used
to evaluate from which fingers two marks found at a crime scene
originated, where the assumption is made that these marks areleft behind by two consecutive fingers of the same hand in theact of a single touch. Specifically, if the fingers on the hands of aperson are labelled 1 through 10, then the BN is used to assign a(posterior) probability that the two marks originated from a specificconfiguration of consecutive fingers. In a police investigation, afingerprint expert enters the marks into a software system that
automatically compares them to a fingerprint database. Knowing
beforehand from which finger a mark most probably originatedcan considerably narrow down the search and, in turn, speed up
the matching process. It should be noted that the constructed BN
cannot be used to evaluate from which person the finger marks
originated; BNs at person level are used for this purpose.
In Figure 1, Doekhie and colleagues’ BN is depicted. FingerCombinations is the variable of interest for which we wish toobtain a posterior distribution. This variable describes eight values,
2 A finger mark is a mark recovered from a crime scene. A fingerprint is a print takenfrom a suspect at the police station.

ICAIL ’19, June 17–21, 2019, Montreal, QC, Canada
HAND

FINGER A

FINGERCOMBINATIONSFINGER B

GENERALPATTERN AGENDER

GENERALPATTERN B

Figure 1: BN for the interpretation of two finger marks atfinger level, constructed by Doekhie and colleagues [11, 12].
corresponding to the eight possible configurations of fingers fromwhich the two marks originated. Specifically, these values are 1
and 2, . . . , 4 and 5, 6 and 7, . . . , 9 and 10, where the first number
denotes the finger number from which finger mark A originatedand the second number indicates the finger number from which
finger mark B originated. The Finger A and Finger B variables
themselves describe ten values, corresponding to the ten possible
fingers from which a mark can originate.
The GeneralPattern A and GeneralPattern B variables each
describe a number of different values corresponding to the general patterns which are typically observed in finger marks andfingerprints, such as loops, whorls and arches. When using the BN
in practice in a given case, these variables are instantiated to thegeneral patterns observed in marks A and B to obtain a posterior
distribution over the FingerCombinations variable.
The Hand variable accounts for the hand from which the twomarks originated. This variable describes two values, namely Lefthand and Right hand. The Gender variable accounts for the gender of the donor from which the two marks originated. According
to Doekhie and colleagues, this variable describes three values:
Male, Female and Unlabelled. The CPT for this variable is filledusing frequency statistics obtained from a fingerprint database (D 1 ).
This database contains information on every subject’s gender andthe finger from which each subject’s print originated, as well as
the general pattern of each fingerprint as labelled by a fingerprint
examiner. In some cases, information regarding gender was not
documented in the database and the prints were classified as “unlabelled”. Frequency statistics from D 1 are also used to fill the CPTs
for the GeneralPattern A and GeneralPattern B variables.
The CPTs for the Hand, Finger A and Finger B variables arefilled using frequency statistics from a finger mark database (D 2 ).
This database contains similar information as D 1 , except that thedata is obtained from a large number of finger marks found at crime
scenes instead of from fingerprints. As noted by Haraksim andcolleagues [12], frequency statistics provide for a more informed
prior than a uniform prior, which assigns equal prior probabilities
to each finger or hand. From D 2 , it can, for instance, be seen thatmarks of the thumb and index finger are found more often on crime
scenes than marks originating from other fingers.
The CPT for the FingerCombinations variable is filled using
frequency statistics from D 1 . The exact manner in which thesefrequencies are chosen by Doekhie is not further discussed in thispaper, as the parameterisation of the FingerCombinations variable
is not criticised by Doshi.

ICAIL ’19, June 17–21, 2019, Montreal, QC, Canada¬d1
d3

R. Wieten et al.
Variable HAND should be
included in the BN

d1

The non-uniformness of the distribution of the
HAND variable is already captured in the distribution
over the FINGER A and FINGER B variables

d4

d2
The value of the HAND variable is directly
determined by the values of the FINGER A andFINGER B variables

Variable HAND should not be
included in the BN

Finger mark database D2 is adatabase that concerns
variable HAND

Frequency statistics fromfinger mark database D2
indicate that the probability
distribution over the HAND
variable is non-uniform

Removing the HAND variable
and its incoming andoutgoing arcs makes the BN
more simple and compact

Figure 2: Argument-based analysis of Doekhie’s modelling decision for including the Hand variable and Doshi’s criticism.

3.2

Doshi’s Criticism on Doekhie’s BN

In this section, we analyse the argumentation structure of Doekhie’smodelling decisions (Section 3.1) and Doshi’s criticism on thesedecisions. In the argument graphs depicted throughout this section,
propositions corresponding to Doekhie and colleagues’ claims areindicated by plain boxes and propositions corresponding to Doshi’s
claims are indicated by thick boxes.
3.2.1 Relevance of the Hand Variable. Doekhie and colleagues [12,p. 102] state that frequency statistics from D 2 indicate that theprobability distribution over the Hand variable is non-uniform,
from which they conclude that this variable should be included in
the BN and that this non-uniform distribution should be used forthe parameterisation of this variable. This can be interpreted as anargument from data set (defined below): as D 2 implies a propertyof the Hand variable, a probability distribution (or BN) over a setof variables including the Hand variable should be constrained bythis property. Doekhie and colleagues’ arguments are depicted in
the centre of Figure 2 (inference d 1 ).
The argument scheme from data set we propose is a generalisation of the scheme originally proposed by Keppens [6, p. 260].
Keppens’ scheme can only be used to reason about the source of a
specific parameterisation. We generalise this scheme such that it
can also be used to reason about general properties of a BN, suchas whether a variable should be included in the BN or not or what
its value space should be:
S is a data set that includes variable(s) V1 , . . . , Vn .
S implies a property Prop of a subset V of V1 , . . . , Vn .
Therefore, a BN with variables V may be constrainedby property Prop.
Critical questions corresponding to this scheme include (adaptedfrom Keppens [6, p. 261]): (1) (Relevance) Does data set S cover all
variables and values of variables necessary to identify the relevant
circumstances covered by property Prop?; (2) (Representativeness)
Is the population considered in data set S representative for the
population under investigation in the present case?; (3) (Precision)
Is the volume and precision of data set S consistent with the precision of property Prop?; and (4) (Consistency) Is the observation ofproperty Prop in data set S consistent with other data sets?
Doshi criticises Doekhie and colleagues’ modelling decision bystating that the value of the Hand variable is directly determinedby the value of the Finger A and Finger B variables. Specifically,knowing from which finger a mark originated implies that weknow from which hand the mark originated. From this claim it
follows that the non-uniformness of the distribution of the Hand
variable is already captured in the distribution over the Finger A
and Finger B variables. This can be interpreted as an undercutterof the argument from data set as posed by Doekhie and colleagues;
it is depicted on the left-hand side of Figure 2. We note that thisundercutter cannot be categorised as any of the critical questionsas proposed by Keppens. Instead it can be considered a variant ofcritical question (1), where the word “necessary” is replaced by theword “sufficient”. We denote this critical question by (1 ′ ).
Doshi provides additional reasons for not including the Hand
variable by claiming that this makes the BN more simple and compact. To capture this, we propose the following argument scheme
for reduced complexity:
V is a variable in BN B.
Removing variable V and its incident arcs from B makes B
less computationally and representationally complex.
Therefore, variable V should be removed from B.
We propose the following corresponding critical questions for thisscheme: (1) Is variable V relevant for computing the posterior distribution of variables of interest in B?; and (2) Does the complexity
gain from removing V compensate for the loss of accuracy andcompleteness of B?
Doshi’s arguments are depicted on the right-hand side of Figure
2. Weighing the reasons pro and con, Doshi concludes that theHand variable along with its incident arcs should be removed.
3.2.2 Independence of the GeneralPattern A and GeneralPattern B Variables. On discussing this with fingerprint examiners,
Doshi found that these examiners believe that there exists no significant correlation/dependency between the general patterns thatexist on different fingers. Doshi criticises Doekhie’s BN by statingthat the GeneralPattern A and GeneralPattern B variables are
possibly dependent in her BN. The fingerprint examiners’ claimthat the GeneralPattern A and GeneralPattern B variables are
independent can be interpreted as an argument from expert opinion.
The argument scheme for arguments from expert opinion which
we present below is taken from Prakken [7], who adapted it from
Walton and colleagues [9]:Supporting Discussions About Forensic Bayesian Networks Using Argumentation
The arcs between FINGER A and
GENERALPATTERN A and between
FINGER B and GENERALPATTERN B
should not be reversedd3
Reversing the direction between
FINGER A and GENERALPATTERN A andbetween FINGER B and
GENERALPATTERN B is not inagreement with the perceived directionof causality between these variables

d4

Reversing the direction between
FINGER A and GENERALPATTERN A andbetween FINGER B and
GENERALPATTERN B makes the CPTs of
FINGER A and FINGER B more complex

ICAIL ’19, June 17–21, 2019, Montreal, QC, Canada

The arcs between FINGER A and
GENERALPATTERN A and between
FINGER B and GENERALPATTERN B
should be reversedd2
Variables GENERALPATTERN A and
GENERALPATTERN B are independent

Variables GENERALPATTERN A
and GENERALPATTERN B canbe dependent

d1
Fingerprint examiners:“Variables GENERALPATTERN A and
GENERALPATTERN B are independent”

Figure 3: Argument-based analysis of Doshi’s criticism on the possible dependency between the GeneralPattern A andGeneralPattern B variables.
E is an expert in domain D.
E asserts that P.
P is within D.
Therefore, presumably, P.
This scheme includes the following critical questions: (1) How credible is E as an expert source?; (2) Is E personally reliable as a source?;(3) Is P consistent with what other experts assert?; and (4) Is E’sassertion of P based on evidence?
The claim that the GeneralPattern A and GeneralPattern
B variables are independent and the claim that these variables canbe dependent rebut each other. Note that the latter claim is not
explicitly made by Doekhie; it is, however, implied by the structureof the BN she constructed. Doekhie’s implicit argument, as well as
Doshi’s counter-argument, are depicted in Figure 3.
Doshi notes that the GeneralPattern A and GeneralPattern
B variables can be made independent in Doekhie’s network by
reversing the directions of arcs between GeneralPattern X andFinger X, for both X = A and X = B. However, this would (1) not
be in agreement with the perceived direction of causality between
these variables (inference d 3 ); and (2) would increase the number ofprobabilities that need to be estimated in the CPTs for the Finger
A and Finger B variables and, therefore, make these CPTs more
complex (inference d 4 ). The latter argument can be interpreted as
an instance of a variation on the argument scheme for reduced
complexity presented in Section 3.2.1. Instead of concerning theremoval of a variable, this variation concerns the reversal of an arc
between two variables. Specifically, if reversing an arc between two
variables makes the BN less computationally and representationallycomplex, this arc should be reversed. We replace critical question(1) by “Does reversing arc E change the independence relation
represented by the BN graph?”. Critical question (2) can be directly
applied to this scheme by replacing the words “removing V ” by thewords “reversing E”.
Doshi’s arguments for reversing the arc directions, as well as
those for keeping the original arc directions, are depicted in Figure
3. These conclusions then rebut each other.
3.2.3 Conditional Independence of the FingerCombinations Variable and the Finger A and Finger B Variables. Doshi notes that,
hypothetically, the FingerCombinations variable is conditionallyindependent from the Finger A and Finger B variables given Z= {Hand, GeneralPattern A, GeneralPattern B} (its Markov
blanket). Doshi criticises this modelling decision by stating that,knowing from which two fingers the marks originated, we should
also be able to derive the combination of fingers that was used.
Therefore, the FingerCombinations variable and the Finger A
and Finger B variables should not be conditionally independent
given Z. An argumentation-based analysis of Doshi’s criticism isshown in Figure 4. Note that the argument on the left-hand side was
not explicitly made by Doekhie and colleagues. Instead, it follows
implicitly from the structure of Doekhie’s BN. Its conclusion andthe ultimate conclusion of Doshi’s argument then rebut each other.
3.2.4 The Value Space of the Gender Variable. Doekhie and colleagues base their design choice for using values Male, Female andUnlabelled as the value space of the Gender variable on the observation that the Gender variable can take on these three valuesin D 1 . This can be interpreted as an argument from data set; it isdepicted in the centre of Figure 5 (inference d 1 ). Doshi criticises thisdecision by arguing that in reality people are either male or female,and that “unlabelled” merely refers to the fact that data is missing
with respect to this variable in D 1 . Therefore (inference d 2 ), Doshi
concludes that values Male, Female and Unlabelled are not mutually
The FINGERCOMBINATIONS
variable should be conditionallyindependent from the FINGER A
and FINGER B variables given Z ={HAND, GENERALPATTERN A,
GENERALPATTERN B}

The FINGERCOMBINATIONS
variable should not be
conditionally independent
from the FINGER A andFINGER B variables given Z

d1
Knowing from which two
fingers the marks originated,
we should also be able toderive the combination of
fingers that was used

Figure 4: Argument-based analysis of Doshi’s criticism on
the independence between the FingerCombinations variable and the Finger A and Finger B variables given Z ={Hand, GeneralPattern A, GeneralPattern B}.

ICAIL ’19, June 17–21, 2019, Montreal, QC, Canada

R. Wieten et al.
BN variable GENDER should
describe values Male,
Female and Unlabelled

¬d1

d1

d3
Values Male, Female
and Unlabelled are notmutually exclusive

BN variable GENDER
should describe values
Male and Female

The values of BN
variables should bemutually exclusive

Fingerprint database D1 isa database that concerns
variable GENDER

d5
In fingerprint database D1, variable
GENDER can take on values Male,
Female and Unlabelled

Values Male andFemale are mutually
exclusive

The values of BN
variables should bemutually exclusived4

d2
In reality, people are
either male or female

Value “unlabelled” only
refers to missing data in D1

In reality, people are
either male or female

Figure 5: Argument-based analysis of Doekhie’s modelling decision regarding Gender’s value space and Doshi’s criticism.
The CPTs for the FINGER A and FINGER B
variables can be filled using frequency
statistics from finger mark database D2

A uniform distribution should be
used for the CPTs for the FINGER A
and FINGER B variables

d4

¬d1
d2

d1

Finger mark database D2
contains no information
regarding consecutivenessof finger marks

Finger mark database D2 isa database that concerns
variables FINGER A,
FINGER B and HAND

The CPTs for the FINGER A andFINGER B variables should be
uninformative
Frequency statistics of
FINGER A given HAND and
FINGER B given HAND canbe calculated from finger
mark database D2

d3
No databases currently exist that
contain information regarding
consecutiveness of finger marks

Figure 6: Argument-based analysis of Doekhie’s modelling decision regarding the parameterisation of the Finger A and Finger B variables and Doshi’s criticism.
exclusive. By furthermore stating that the values of variables in
a BN should be mutually exclusive, Doshi poses (inference d 3 ) an
exception to the argument from data set as posed by Doekhie andcolleagues. Doshi’s exception can be interpreted as an instance of
critical question (1 ′ ) of this argument scheme; his arguments are
depicted on the left-hand side of Figure 5.
In addition, Doshi claims that the Gender variable should instead
describe values Male and Female. First, he claims that values Maleand Female are mutually exclusive, which is based on the fact that, in
reality, people are either male or female. This argument is depictedon the right-hand side of Figure 5 (inference d 4 ). From this claim,and by again stating that the values of BN variables should bemutually exclusive, Doshi concludes that Gender should describe
values Male and Female (inference d 5 ). This argument and Doekhie
and colleagues’ argument then rebut each other.
Based on his criticism, Doshi proposed to adjust the BN of
Doekhie and colleagues by removing the Unlabelled value from thevalue space of the Gender variable.
3.2.5 Parameterisation of the Finger A and Finger B Variables.
Doekhie’s motivation for using frequency statistics from D 2 for theparameterisation of the Finger A and Finger B variables can beconsidered an argument from data set. This argument is depicted in
the centre of Figure 6 (inference d 1 ). Doshi criticises this modelling
decision by stating that D 2 cannot be used for establishing therelevant frequencies for these variables, as this database contains
no information regarding consecutiveness of finger marks. Thiscan be interpreted as an undercutter of Doekhie’s argument fromdata set; specifically, it is an instance of critical question (1) of thisargument scheme. Doshi’s argument is depicted on the left-handside of Figure 6 (inference d 2 ).
Doshi instead proposes to use uniform distributions for both
values of the Hand variable for the CPTs for these variables. His
reason for using uniform distributions is that no databases currently
exist that contain information regarding consecutiveness of finger
marks and that the CPTs for the Finger A and Finger B variables
should, therefore, be uninformative (for now). These arguments are
depicted on the right-hand side of Figure 6; its ultimate conclusion
and the conclusion of Doekhie’s argument then rebut each other.

4

AN ARGUMENTATION-BASED APPROACH
TO SUPPORTING DISCUSSIONS ABOUT BNSIn this section, we propose an argumentation-based approach thatcan be used to capture and help resolve conflicts about BNs. Thisapproach is based on observations from our case study of Section
3. Our approach consists of two phases that are iteratively run
through. In the first phase, domain experts are allowed to constructarguments pro and con the outcomes of modelling decisions underlying a given partially or fully specified BN, as well as preferences
over these arguments. Arguments can be constructed regarding theinclusion or exclusion of different types of BN elements (described
below) which may or not be in the existing BN. In the second
phase, conflicts are then resolved by using the dialectical status of
the constructed arguments to derive probabilistic and structural
constraints on the BN (Sections 4.1 and 4.2).
Our sub-division of BN elements is inspired by our case studyof Section 3, by the work of Pitchforth and Mengersen on theSupporting Discussions About Forensic Bayesian Networks Using Argumentation
validation of expert-elicited BNs [14] and by the work of Yet andcolleagues [4]:• Arguments regarding the existence of variables (Section 3.2.1).
Conclusions of such arguments are of the form ϕV = “Include
V in the BN” and ¬ϕV = “Exclude V from the BN”.
• Arguments regarding whether a variable is observable or not.
Typically, a fixed set of variables O is observed and instantiatedwhen using the BN in practice in a given case. Conclusionsof such arguments are of the form ϕV
O = “Include V in O” and¬ϕV=“Exclude
V
from
O”.
O
• Arguments regarding (conditional) (in)dependencies (Sections
3.2.2 and 3.2.3). Arguments of this type are constructed for agiven (possibly empty) subset of variables Z ⊆ V. Conclusionsof such arguments are of the form ϕVI 1,V2,Z = “Variables V1 andV2 should be conditionally independent given Z” and ¬ϕVI 1,V2,Z =“Variables V1 and V2 should be conditionally dependent given Z”.
• Arguments regarding the existence of arcs (Section 3.2.2). Conclusions of such arguments are of the form ϕVE1 →V2 = “Include
E = V1 → V2 in the BN” and ¬ϕVE1 →V2 = “Exclude E = V1 → V2from the BN”. Arguments for arc reversal can then be indirectly
constructed by constructing arguments with both conclusions¬ϕVE1 →V2 and ϕVE2 →V1 .
• Arguments regarding the value spaces of variables (Section
3.2.4). Conclusions of such arguments are of the form ϕV
S1 =“Use value space 1 for variable V ”. Such arguments may either be
attacked by constructing an argument for its negation ¬ϕV
S1 =“Do not use value space 1 for variable V ” or by constructing anargument for an alternative value space ϕV
S = “Use value space 22

V
for variable V ”, where ϕV
S 1 and ϕ S 2 are declared contradictories
of each other in L.
• Arguments regarding the parameterisation of variables (Section
3.2.5). Conclusions of such arguments are denoted by ϕVP ar andare similar in form to arguments regarding value spaces ofvariables, and can be attacked similarly, by replacing the words“value space” by the word “parameterisation”. Here, we assume
that a conflict concerns part of the CPT for V . Specifically, let
V1 , . . . , Vn be the parents of V . Then conflicts regarding theparameterisation of V concern a specific distribution Pr(V |V1 = v 1 , . . . , Vn = vn ) for given values v 1 of V1 , . . . , vn of Vn .
We note that probabilities Pr(V = v | V1 = v 1 , . . . , Vn = vn )should sum to 1 when summing over all possible values v of V ;conflicts regarding the parameterisation of a variable, therefore,
never concern a single value of its CPT.

It should be noted that we do not propose a dialogue protocol.
Instead, we first allow domain experts to construct arguments regarding all the different types of BN elements specified above alongwith a preference relation over those arguments, after which a priority ordering over the arguments corresponding to the different
types of BN elements is applied to establish which conflicts, if any,
should be resolved first.

4.1

Priority Ordering for Conflict Resolution

The idea of a priority ordering is based on the observation that
BN elements from different types are dependent on one another.

ICAIL ’19, June 17–21, 2019, Montreal, QC, Canada

For instance, it only makes sense to resolve conflicts regarding
the value space of V iff V ’s existence is justified. We propose thefollowing priority ordering over the types of BN elements:
P1 . Existence of variables.
P2 . Inclusion of variables in O.
P3 . Conditional independencies between variables given Z = O.
P4 . Conditional independencies between variables given subsets
Z ⊆ V, Z , O.
P5 . Existence of arcs between variables.
P6 . Value spaces of variables.
P7 . Parameterisation of variables.
A BN graph, by means of its arcs and their directions, represents an
independence relation, so the (conditional) independencies impliedby the graph should be verified. We note that, upon constructing
BNs, arcs are typically added first, after which the implied independence relation is verified. In our approach, we instead prioritise theresolution of conflicts regarding independencies (P3 and P4 ) overthose concerning arc directions (P5 ), as arguments of the former
type should generate new arguments for the existence of arcs andtheir directions at P5 that together realise the conditional independence relation implied by the arguments at P3 and P4 . Since anunjustified independence assumption can affect the behaviour of
the BN, independencies exploited in deriving conclusions in an
actual case are most important to verify. As such, we prioritise
arguments regarding conditional independencies given O (P3 ) overconditional independencies given subsets Z ⊆ V, Z , O (P4 ).
After obtaining a fully specified BN graph, conflicts regarding
the value spaces of variables are considered (P 6 ). Finally, at P7
conflicts regarding the parameterisation of variables are resolved.
Specifically, the parameterisation of a variable V can be considered
iff V ’s existence, V ’s value space, the existence of V ’s incoming
arcs, and the value spaces of V ’s parents are justified.
We introduce the following notation. With APi we denote the setof arguments whose conclusions concern BN elements at priority
level Pi , i ∈ {1, . . . , 7}. We assume that APi divides into disjoint
subsets of arguments AeP concerning BN element e at priorityilevel Pi . For example, AVP only contains those arguments with1
conclusions ϕV and ¬ϕV for the inclusion/exclusion of variable V .

4.2

Constraint Table and Default Values

In Figure 7, the second phase of our approach, concerning conflict
resolution, is summarised in pseudocode; throughout this section,
we will explain and refer to the lines in this pseudocode. As input forthis phase, either a fully or partially specified BN is used, along witha set of arguments and preferences constructed according to the firstphase of our approach (lines 2 and 3 of the pseudocode). The processof conflict resolution at priority level Pi starts by calculating thedialectical status of conclusions in AeP for each BN element e (line 7
iof the pseudocode). Conflicts are then resolved by consulting Table
1, which throughout this paper will be referred to as a constraint
table (line 8 of the pseudocode). Depending on the priority level,
different rows of the constraint table are used. At priority levels P1- P5 , the set of arguments AeP can either contain arguments withiultimate conclusions ϕ e only, ¬ϕ e only, or both. For these priority
levels, rows 1−3 of the constraint table are used. At priority levels P6

works Using Argumentation
ICAIL
June 17–21,
Montreal, Canada
ICAIL ’19, June 17–21,
2019,’19,
Montreal,
QC,2019,
Canadawith Bayesiann Networks for
Wiley, 2014.
ew of Statistics

nce framework
117–143, 2017.
th preferences.

kelihood ratio
22(3): 239–290,

porting discusntelligence andaphs. Springer,

bridge Univer-

al role in nonrtificial Intelli-

1 function ConflictResolution(BN, Args):
2
3
4
5
6
7
8
9
10
11
12
13
14
15

Input: Partially or fully specified BN
Input: Set of arguments Args with preferences
Output: Partially or fully specified BN
for i ∈ {1, . . . , 7} doforeach BN element e at priority level Pi do
Calculate dialectical status of arguments in AePi
Consult constraint table:
if constraint table states “Include e” thenInclude e
endelse if constraint table states “Exclude e” thenExclude e
Retain documentation regarding e
Disregard arguments in AeP for j > i
jan network. In
onal Models of
106. IOS press,end
17else if constraint table states “No constraint” then18
Ask expert to further specify AeP :i
19
if AeP is further specified theni20goto line 7
21
end
22
else
23
Resort to default choice
24
end
25
end
26
end
27
end
28 endn constructing
gal Knowledge
erence, volume

Figure 7: Pseudocode of our argumentation-based approachto resolving conflicts about BNs.

hich finger left
ds, 2012.
Assignment ofesian network.
nal Conference. GI, 2012.
erprint general013.
ork for expert
0(1): 162–167,

n. In B. Verheij,
nt: Proceedings. A two-phaseworks. Interna-sian networks.

16

and P7 , claims can also be constructed for alternative value spaces
or parameterisations, indicated by ϕ e ′ ; row 4 is also used at thesepriority levels.
The second column of the constraint table indicates the possible
configurations of dialectical status of the claims in the first column.
The third column then indicates the corresponding constraints on
the BN for each configuration. Entries indicated with an asterisk
indicate BN constraints at priority levels P 6 and P 7 , whereas forthe same dialectical status configurations at priority levels P1 − P5 ,entries without an asterisk are used.
Depending on the entry in the third column of the table, different actions should be taken. If the entry in the constraint table
reads “Include e” or “Exclude e”, the BN element should be includedin the BN, respectively excluded (lines 9-11 respectively 12-16 of
the pseudocode). In the latter case, the arguments regarding thisvariable should still be retained for documentation purposes inorder to keep a “chain-of-evidence” of the changes made to the
BN. If a domain expert wishes to provide further argumentation as
to why this element should still be included, they can review theexisting arguments regarding this BN element and supplement itwith additional arguments or preferences. Furthermore, arguments
of inferior priority which concern the excluded BN element should
be disregarded in that these arguments should not be evaluated or

R. Wieten et al.
used in conflict resolution. For instance, if a variable V is removed
from the BN at priority level P1 , arguments in AP j for j > 1 thatconcern this variable should be disregarded. Arguments for a conditional independency at P3 and P4 should be disregarded in case
V is an element of the set of variables Z ⊆ V under consideration
or if V takes on the role of V1 or V2 in the argument.
For some configurations of dialectical status, a (univocal) constraint on the BN cannot be derived. Considering priority levels
P1 − P5 , two BNs are then possible: one in which e is included and
one in which e is excluded. One possible approach would be toretain two BNs at this point, one including e and one excluding e,
and to continue resolving conflicts for both BNs by considering all
BN elements at all priority levels. Following this approach, a list
(or tree) of candidate BNs is obtained after attempting to resolve
all conflicts, from which the domain expert can choose one BN tocontinue with. However, for larger BNs the space of candidate BNs
corresponding to a set of arguments would quickly become large.
Moreover, if a large list of candidate BNs is provided to the domain
expert, the differences between these BNs also need to be explained
and presented to the domain expert in order for him to understandthe differences between the presented BNs and to choose, which
would require additional machinery.
We opt for an alternative approach in which the domain expert is asked to further specify his/her arguments every time a
univocal constraint cannot be derived (line 18 of the pseudocode).
Specifically, the domain expert is asked to provide additional arguments to supplement AeP , or (further) specify a preference relationiover AeP . In case the expert opts to not further specify his arguiments, a default choice is made by the approach (lines 22-24 of thepseudocode). What this default choice entails differs per priority
level and per configuration of dialectical status. We note that, informally, the more complete the specification of the arguments andTable 1: Constraint table for including BN element e. Entries
indicated with an asterisk indicate BN constraints at priority levels P6 and P7 , whereas for the same dialectical statusconfigurations at priority levels P1 − P5 entries without anasterisk are used.
Proposed Claims

Dialectical Status

BN constraint

ϕe and ¬ϕe

ϕe justified, ¬ϕe overruled
ϕe overruled, ¬ϕe justified
ϕe defensible, ¬ϕe defensible
ϕe overruled, ¬ϕe overruled

Include e
Exclude e / No constraint*
No constraint
Further specification needed

ϕe onlyϕe justified
ϕe overruled
ϕe defensible

Include e
Exclude e / No constraint*
No constraint¬ϕe only¬ϕe justified¬ϕe overruled¬ϕe defensible

Exclude e / No constraint*
Include e
No constraint

ϕe and ϕe’

ϕe justified, ϕe’ overruled
ϕe overruled, ϕe’ justified
ϕe defensible, ϕe’ defensible
ϕe overruled, ϕe’ overruled

Include e
Include e’No constraint
No constraint

Supporting Discussions About Forensic Bayesian Networks Using Argumentation
the preference relation, the less the approach will resort to making
a default choice. In the next subsections, the different configurations of dialectical status per priority level and their corresponding
constraints are discussed in more detail.
In case the expert further specifies his arguments, he can recalculate the dialectical status of ϕ e and/or ¬ϕ e and establish thecorresponding constraints. This process reiterates until BN element
e is either included or excluded, or a default choice is made.
Conflicts About Variables. At priority level P1 , conflicts regarding the existence of variables are considered. In case claim ϕVfor including variable V is justified (and ¬ϕV is overruled), thisvariable is included in the BN graph. If ¬ϕV is justified (and ϕV isoverruled), variable V and all its incidents arcs are excluded fromthe BN graph. If ϕV and/or ¬ϕV is defensible, the default choice is toresort to using the original modelling decision, i.e. if variable V wasincluded/excluded in the BN, then it should be included/excluded in
the resulting BN. Lastly, if both ϕ e and ¬ϕ e are overruled, neither
the choice for including nor excluding the BN element as a default
is warranted. In this case, the expert should further specify his arguments to be able to derive a constraint (entry “Further specificationneeded” in the constraint table).
As an example of an application of our approach to resolving
conflicts about variables, we consider the argumentation-based
analysis presented in Section 3.2.1. In Figure 2, Doekhie’s argument
for including the Hand variable in the BN is undercut and is, therefore, overruled, as undercutting attack is preference-independent.
It follows that Doshi’s argument for excluding this variable is justified, as its only attacker is overruled. From the constraint table, it
therefore follows that the Hand variable should not be included in
the BN. In case we consider the set of arguments excluding Doshi’s
undercutter, both conclusions pro and con inclusion of the variable
are defensible and no univocal constraint can be derived in this case.
Doshi could in this case, for instance, specify that his argument
for exclusion of the Hand variable is strictly preferred over theargument for inclusion of this variable. The dialectical status of
the corresponding arguments is then recalculated; the argument
for excluding the Hand variable is now justified, from which aconstraint on the BN to exclude this variable is derived.
After resolving all conflicts at priority level P1 , conflicts at P2 ,regarding the set of observable variables O, are considered. Here,the terms “Include V ” and “Exclude V ”’ now refer to including V inand excluding V from the set O rather than the BN graph.
Conflicts About Independencies and Arcs. At priority levels
P3 and P4 , conflicts regarding (conditional) independencies between
variables are resolved using rows 1−3 of the constraint table. In case
ϕVI 1,V2,Z is justified (and ¬ϕVI 1,V2,Z is overruled), independence constraint I should be included in the set of independence constraints
I to which the BN should adhere to. If ¬ϕVI 1,V2,Z is justified (andϕVI 1,V2,Z is overruled), this independence constraint should not be

included in I. If ϕVI 1,V2,Z and/or ¬ϕVI 1,V2,Z is defensible, the default
choice is to resort to the modelling decision implied by the originalBN, that is, if V1 and V2 are conditionally independent given Z thenI should be included in I and otherwise I can be excluded.
As an example, we consider the argumentation-based analysis
presented in Section 3.2.3. The arguments depicted in Figure 4

ICAIL ’19, June 17–21, 2019, Montreal, QC, Canada

concern priority level P4 , as Doshi considers the conditional independencies represented by the BN graph for a hypothetical set ofvariables Z = {Hand, GeneralPattern A, GeneralPattern B}.
As Doshi does not express an explicit preference, both rebutting
conclusions in Figure 4 are defensible and no univocal constraint
can be derived. In case Doshi expresses a strict preference for eitherof these conclusions, this chosen conclusion will be justified andthe other overruled, in which case a constraint can be derived. We
note that when using the BN of Doekhie and colleagues in an actual
case, typically only the GeneralPattern A and GeneralPattern
B variables are observed and instantiated, while the Hand variable
is typically not instantiated. Doekhie and colleagues could, therefore, possibly counter Doshi’s arguments at P4 by constructing
arguments for O = {GeneralPattern A, GeneralPattern B} atpriority level P2 and arguments at P3 for a conditional dependency
between the Finger A and Finger B variables and the FingerCombinations variable given O. These arguments would then beprioritised over Doshi’s arguments.
After resolving all conflicts at P 3 and P4 , our approach should
generate new arguments for the existence of arcs and their directions at P5 that together realise the conditional independence
relation implied by I. The precise manner in which this can beachieved is outside the scope of this paper; we note that so-called
structure learning algorithms exist that can learn the structure ofa BN graph given a set of independence constraints [8, chapter 7].
For now, we illustrate this part of the approach by means of an
example. We consider the argumentation-based analysis presented
in Section 3.2.2. In Figure 3, both arguments are constructed for theclaims that GeneralPattern A and GeneralPattern B should be
independent and can be dependent. Assuming Doshi strictly prefers
his argument over Doekhie’s implicit argument, his argument isjustified. The corresponding independence constraint is, therefore,
added to the set of independence constraints the BN should adhere
to. Doshi then proceeds by attempting to find a configuration of arc
directions under which GeneralPattern A and GeneralPattern
B are independent, which generates arguments at P5 . The generated
arguments at P 5 and the arguments that were already proposed by
Doshi are then collectively considered, where conflicts at P5 areresolved using rows 1 − 3 of the constraint table.
Conflicts About Value Spaces. To resolve conflicts at priority
level P6 , all rows of the constraint table are used. This table canonly be used if arguments for at most two different value spaces
for a variable V are constructed; similar constraint tables can beconstructed in case more than two value spaces are proposed. In
rows 1 − 3 of Table 1, for entries in which ϕV
S is justified, value
Vspace S should be used for variable V . In case ϕV
S and/or ¬ϕ S is
defensible, no univocal constraint can be derived. In this case, thedefault is to resort to the value space of this variable as specifiedVin the original BN. In case ϕV
S is overruled (and ¬ϕ S is justified),no constraint can be derived, other than that value space S should
not be used. In this case, the default choice is to resort to using a
Boolean variable. However, if ϕV
S already concerns a Boolean value
space, the expert should always further specify his arguments.
In the fourth row of Table 1, the situation is considered in whichVarguments are constructed for both ϕV
S 1 and ϕ S 2 . In case one ofthem is justified, the other is overruled; this results in the choice ofICAIL ’19, June 17–21, 2019, Montreal, QC, Canada
the value space posed in the conclusion of the justified argument.
V
When ϕV
S 1 and ϕ S 2 are both defensible, the default is to resort to thevalue space of this variable as specified in the original BN. If bothVϕV
S 1 and ϕ S 2 are overruled, neither value space should be used. If
possible, the default is to again resort to a Boolean value space.
As an example of our approach to resolving conflicts about value
spaces, we consider the argumentation-based analysis presented in
Section 3.2.4. In Figure 5, arguments for two different value spaces
are proposed, where the argument for Doekhie’s value space isoverruled as it is undercut. It follows that the argument for Doshi’svalue space is justified, as its only attacker is overruled. From thefourth row of the constraint table, it therefore follows that Doshi’svalue space should be used.

as structured arguments [5, 18] to a BN. In other related work,
approaches for explaining the reasoning patterns captured in BNs
in terms of argumentation were proposed by Timmer and colleagues[19] and Keppens [20]. However, these approaches do not allow for
any argumentative discussion about the construction of BNs.
In this paper, we have primarily focused on precisely specifying
our approach using formal (computational) argumentation. Such a
specification allows us to prove formal properties of our approach infuture work. Moreover, in future work our formal model can be thebasis for implementing software tools for supporting discussions
about BNs between forensic experts, and for communicating theirBNs and discussions to judges and prosecutors. Such tools may
then also be used in evaluating our approach in practice.

Conflicts About Parameterisations. Conflicts at priority levelP7 are resolved similarly as conflicts at P 6 , where the default is toresort to using a uniform distribution in case arguments for specificparameterisations are overruled and the arguments are not further
specified. Although a uniform distribution can easily be criticised,
we opt for this distribution as a more informative choice cannot bemade on the basis of the provided arguments. The default is also
to resort to a uniform distribution even if the original distribution
was uniform, instead of always requiring the expert to further specify his arguments in this case. Arguments in AVP regarding the7parameterisation of a variable V should be disregarded in conflict
resolution if one of V ’s incoming arcs, V ’s value space or one of
V ’s parents’ value spaces is overruled at P5 or P6 . In this case, thedefault choice is to resort to a uniform distribution for V .
As an example, we consider the argumentation-based analysis
presented in Section 3.2.5. In Figure 6, arguments for two different
parameterisations are proposed. Similar to the example discussed
in the previous paragraph, Doshi’s parameterisation is justified
and Doekhie’s parameterisation is overruled; therefore, Doshi’s
parameterisation should be used.

REFERENCES

5

CONCLUSION AND RELATED RESEARCH

In this paper, we have proposed an approach to capturing and resolving conflicts about BNs using computational argumentation.
Our approach allows domain experts to document their reasonspro and con modelling decisions and their preferences in a structured manner using argumentation. The dialectical status of theconstructed arguments is then used to derive probabilistic andstructural constraints on the BN. Our approach always returns apartially or fully specified BN. Starting with a fully specified BN, afully specified BN is returned by resorting to default choices in casea univocal constraint cannot be derived and the arguments andpreferences are not further specified. Our approach can possibly
be extended in future research by making explicit to the expert inwhich ways the arguments/preference relation can be further specified to obtain a univocal constraint. This would be an applicationof research on so-called resolution semantics; see e.g. [15].
As noted in the introduction, the work of Keppens [6] and Yet
and colleagues [4] is related to this paper. In other related work,
Bex and Renooij [16] and Wieten and colleagues [17] also derive
constraints on a BN given arguments. The focus of their work isdifferent from the present paper in that their aim is not to use
arguments to argue about BNs but to map information expressed

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R. Wieten et al.

[1] N. Fenton and M. Neil. Risk Assessment and Decision Analysis with Bayesian
Networks. CRC Press, 2012.
[2] F. Taroni, C.G. Aitken, P. Garbolino, and A. Biedermann. Bayesian Networks for
Probabilistic Inference and Decision Analysis in Forensic Science. Wiley, 2014.
[3] N. Fenton, M. Neil, and D. Berger. Bayes and the law. Annual Review of Statistics
and Its Application, 3: 51–77, 2016.
[4] B. Yet, Z.B. Perkins, N.R.M. Tai, and D.W.R. Marsh. Clinical evidence frameworkfor Bayesian networks. Knowledge and Information Systems, 50(1): 117–143, 2017.
[5] S. Modgil and H. Prakken. A general account of argumentation with preferences.
Artificial Intelligence, 195: 316–397, 2013.
[6] J. Keppens. On modelling non-probabilistic uncertainty in the likelihood ratio
approach to evidential reasoning. Artificial Intelligence and Law, 22(3): 239–290,
2014.
[7] H. Prakken. A new use case for argumentation support tools: supporting discussions of Bayesian analyses of complex criminal cases. Artificial Intelligence andLaw, https://doi.org/10.1007/s10506-018-9235-z.
[8] F.V. Jensen and T.D. Nielsen. Bayesian Networks and Decision Graphs. Springer,
2nd ed., 2007.
[9] D. Walton, C. Reed, and F. Macagno. Argumentation Schemes. Cambridge University Press, 2008.
[10] P.M. Dung. 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.
[11] G. Doekhie. A Bayesian network for assigning probabilities on which finger left
a mark. Master’s thesis. University of Amsterdam, The Netherlands, 2012.
[12] R. Haraksim, D. Meuwly, G. Doekhie, P. Vergeer, and M. Sjerps. Assignment of
the evidential value of a fingermark general pattern using a Bayesian network.
In A. Brömme and C. Busch, eds., Proceedings of the 12th International Conferenceof the Biometrics Special Interest Group, volume 212, pages 99–109. GI, 2012.
[13] V. Doshi. Validation of Bayesian networks with a case study on fingerprint general
patterns. Master’s thesis. Utrecht University, The Netherlands, 2013.
[14] J. Pitchforth and K. Mengersen. A proposed validation framework for expert
elicited Bayesian networks. Expert Systems with Applications, 40(1): 162–167,
2013.
[15] S. Modgil and H. Prakken. Resolutions in structured argumentation. In B. Verheij,
S. Woltran, and S. Szeider, eds., Computational Models of Argument: Proceedingsof COMMA 2012, volume 245, pages 310–321. IOS Press, 2012.
[16] F. Bex and S. Renooij. From arguments to constraints on a Bayesian network. In
P. Baroni, T.F. Gordon, T. Scheffler, and M. Stede, eds., Computational Models of
Argument: Proceedings of COMMA 2016, volume 287, pages 95–106. IOS press,
2016.
[17] R. Wieten, F. Bex, H. Prakken, and S. Renooij. Exploiting causality in constructing
Bayesian networks from legal arguments. In M. Palmirani, ed., Legal Knowledge
and Information Systems. JURIX 2018: The Thirty-first Annual Conference, volume313, pages 151–160. IOS Press, 2018.
[18] F. Bex, S. Modgil, H. Prakken, and C.A. Reed. On logical specifications of theargument interchange format. Journal of Logic and Computation. 23(5): 951–989,
2013.
[19] S.T. Timmer, J.-J.C. Meyer, H. Prakken, S. Renooij, and B. Verheij. A two-phasemethod for extracting explanatory arguments from Bayesian networks. International Journal of Approximate Reasoning, 80: 475–494, 2017.
[20] J. Keppens. Argument diagram extraction from evidential Bayesian networks.
Artificial Intelligence and Law, 20(2): 109–143, 2012.