Formalising Argumentative Story-based Analysis of
Evidence
F.J. Bex

H. Prakken

B. Verheij

Centre for Law & ICT
University of Groningen
the Netherlands
f.j.bex at rug.nl

Centre for Law and ICT,
University of Groningen
Department of Information andComputing Sciences,
Utrecht University

Department of Artificial Intelligence
University of Groningen
the Netherlands

ABSTRACTIn the present paper, we provide a formalised version of amerged argumentative and story-based approach towards theanalysis of evidence. As an application, we are able to show how
our approach sheds new light on inference to the best
explanation with case evidence. More specifically, it will beclarified how the events in a case story that are considered to be
proven abductively explain the otherwise unproven events of thecase story. We compare our approach with existing AI work onmodelling legal reasoning with evidence.

Keywords
Argumentation, Abductive reasoning, Inference to the best
explanation, Legal evidence, Stories

1. INTRODUCTION
We are developing a conceptual and formal framework for the
analysis of reasoning with evidence about the facts of a legal
case. The main reason for this is to provide the formal
foundations of sense-making software for crime investigation.
Such a sense-making system does not contain a knowledge-base,so it does not need domain knowledge. An advantage of this isthat sense-making systems are not subject to the knowledge
acquisition bottleneck; because reasoning with evidence
encompasses a great number of real-world problems, aknowledge based system would need a huge amount of domain
knowledge. A sense-making system does not reason itself, butinstead helps the user make sense out of a case by structuring it.
In the case of a crime investigation it can, for example, structurea case into a timeline and link the different events to police
records or photographs. Sense-making systems also exist as
more general reasoning aids (see [24] for an overview). The
work presented in this paper is part of a larger project in whichsuch a sense-making system is developed for crime investigation
applications. Van den Braak and Vreeswijk [4] have developed
a prototype system; the present paper aims to investigate thetheoretical basis of such systems.
In our formal framework for the analysis of reasoning with
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evidence we attempt to merge two main approaches of analysing
reasoning with evidence: argumentative analysis and story-based
analysis.
The former goes at least back to Wigmore's work in theearly twentieth century [26] and has been elaborated upon byresearchers of the New Evidence Scholarship, such as Anderson,
Schum, Tillers and Twining [1], [20]. Recently, two tools havebeen added to this style of work: argumentation schemes as usedin the field of (informal) argumentation theory [25], andargumentation logics, especially in the style as developed in thefield of artificial intelligence and law [16]. From the start ofapplying these tools to evidence in the law, there have been
attempts to combine the two tools [2], [23].
The story-based perspective has been taken up by legal
psychologists such as Pennington and Hastie [12], which has
been followed up in the anchored narratives approach by
Crombag, Van Koppen and Wagenaar [5]. Thagard [18] hasapplied his connectionist model of abductive inference to thebest explanation to legal cases, claiming that it provides acomputational account of the story approach to legal evidence.
Keppens and Schafer [9] have applied model-based reasoning
with scenarios to automated support for the investigation of
murder cases.
The anchored narratives approach [5] is a starting point of
our research. Interestingly, although Crombag, Van Koppen andWagenaar focus on the story-based perspective in their choiceboth of wording and of research background, several of theircentral claims have a more argumentative than story-based
flavour. Especially the role of generalisations (or anchors),
exceptions to these generalisations and of the dynamics ofdeveloping and refining an analysis of the evidence in a case arecharacteristic for the argumentative slant of the approach by
Crombag, Van Koppen and Wagenaar. As a result, the anchorednarratives approach can be regarded as a beginning of a merged
argumentative and story-based approach. However, as wealready noted in [3], the details of what part generalisations playin a story are left untreated. Also, the exact interplay between
the evidence, a story and the generalisations connecting these
two is not elaborated upon. Accordingly, another aim of thispaper is to provide a thorough analytic account of the elementsof a story and how a story relates to generalisations andevidence.
The outlines of this merged approach were discussed in ourprevious paper [3], where we proposed a combination of two
techniques from AI, namely inference to the best explanation
and argumentation theory. In this paper, we want to extend andfully formalise this combined theory of evidential reasoning. We
do this by proposing a theory that combines abductive
explanations with evidential arguments. To our knowledge,
these two formal theories have so far not been integrated in any
previous work.
The rest of this paper is organised as follows: in section 2
we discuss the typical aspects of evidential reasoning in crime
investigation contexts as far as relevant for this paper. Section 3
informally discusses the two current approaches on which webase our combined theory and argues why these two approaches
should be combined. In section 4 we propose our combined,
formal theory; section 5 contains an extended example ofargumentative, story-based analysis of the evidence using ourformal theory. Finally, in section 6 we discuss related researchconclude with a discussion and ideas for future research.

2. EVIDENTIAL REASONING
In this section we aim to give an overview of the typical aspects
and elements of reasoning with evidence. For this overview, wedraw on our earlier work [3], which was in turn based on thework on Anchored Narratives [5]. Note that here we take a static
viewpoint: we assume that once the analysis starts, all theavailable evidence and stories are at hand. In this paper, we do
not concern ourselves with dynamic aspects of evidential
reasoning like, for example, the search for new evidence and the
updating of stories in light of new evidence. We will clarify thisoverview by means of an example, which we will also use in
section 5.
The example concerns a simplified version of the
Rijkbloem case ([5], pp. 78). Danny Rijkbloem is a 23-year old
man from Surinam. He has a considerable list of sentences(theft, robbery) starting when he was 15 years old. Nicole
Lammers is a 20-year old baker’s daughter who had arelationship with Rijkbloem and lived together with him. At
some point Nicole decided, under pressure of her parents that itis best to break up with Rijkbloem and she leaves him. A few
days after the break-up, Nicole and her parents went to
Rijkbloem’s house to pick up some of Nicole’s stuff, and a fightdeveloped between Rijkbloem and Nicole’s father. From thispoint onwards, the two women (Nicole and her mother) andRijkbloem tell a different story. According to the two women,
Rijkbloem pulled out a gun with which he shot father Lammers
through the head from a distance of about 2 meters. Rijkbloem,
however, gives a different account of the events. He said thatduring the fight, Mrs. Lammers pulled a gun out of her purse
and threatened to shoot Rijkbloem with it. Rijkbloem pushed thehand holding the gun away and in the struggle the gun went off
and the bullet hit father Lammers in his head.
In both crime investigation and legal decision making, theinvestigators or decision makers are faced with a number ofstories. Such a story is usually a set of states and events1
structured in a chronological order. Sometimes this story
presents itself through the victim’s testimony. In other cases theinvestigators will have to construct a possible story by means of1

It can be argued that an occurrence of an event is also a state.
For a discussion of this issue, see [8]. In this paper, a state is astate of affairs in the world, and an event is something thatcauses a change in the obtaining states of affairs.

the physical evidence that is presented to them. In the Rijkbloem
case, the police was presented with two stories: The account of
the mother and daughter that Rijkbloem shot the father andRijkbloem’s account, that it was the mother who accidentally
shot the father. Stories are often used to “fill the gaps”: notevery part of a story follows directly from evidence, but thestory as a whole is plausible, so we can more or less safely
assume that the events in the story that do not follow fromevidence also happened.
The second important element of evidential reasoning isevidence. Evidence can be physical evidence, like a knife or abody, or testimonial evidence (this classification of types ofevidence is taken from [26]). In the Rijkbloem case, the police
had as physical evidence the father’s body. Note that a forensics
report on the father's cause of death is considered testimonial
evidence. Other testimonial evidence in the Rijkbloem case was
the mother and daughter’s testimony and Rijkbloem’s testimony.
Once the stories and the evidence are gathered, the analysisof the case can start. The first thing that has to be done isdeciding which events are to be explained, the explananda. The
main explananda are usually the observations that give rise to
the investigation or the legal case in the first place, for example,“how did this man die?” or “who robbed the bank?” Often, newexplananda appear during the investigation or treatment of acase, for example, “why was this man acting suspiciously near
the crime scene?” Explananda usually follow from the evidence
in a case. In the Rijkbloem example the most important
explanandum is the father’s dead body; what caused the father todie?
Often, there are only a few stories or scenarios that explain
the most important explananda. In the Rijkbloem example, there
are two stories that explain the father’s death. For each of thesestories, the investigator or decision maker should look which of
the events in the separate stories are supported by evidence andwhich events are not supported by evidence. So, for example,
the father’s body supports the fact that he is dead and theforensics report supports that the father was shot from a distanceof 50 centimetres. Rijkbloem’s testimony supports, of course,
most of the events in his version of the story while the women’s
testimonies support their own story. Other testimonies by, forexample, acquaintances of the Lammers family support the facts
that Nicole and Rijkbloem had a relationship.
When the different stories and their supporting evidence
are identified, the generalisations must be analysed, as thegeneralisations are the “anchors” of the different stories. Thereare (at least) two distinct types of generalisations, namely causal
and evidential.
The causal generalisations are the glue of a story; they givea story its coherence. For example, the fact that “Rijkbloem shot
the father so the father died” is a coherent part of the women’sstory is because we believe the causal generalisation “if x shootsy, this can cause y to die”. The evidential generalisations
concern the connection between the elements of a story and thesources of evidence. In order for a forensics report to support the(story) event that the father was shot from a distance of 50
centimetres, we have to believe that “usually, a forensics report
describing event e is evidence for the fact that event e really
happened”.

When all these elements have been thoroughly analysed, it
is up to the investigator(s) or decision maker(s) to decide whatstory to believe. Ideally, this will be the story that is best
supported by evidence and contains no dubious generalisations.

3. ARGUMENTATIVE AND STORYBASED ANALYSIS
In this section we first informally discuss two dominant
approaches to reasoning with legal evidence in AI and Law,
namely argumentation and inference to the best explanation or
abductive-causal reasoning. Then, in section 3.2, we will discuss
some of the advantages and disadvantages of the two approaches
and argue that a combined approach best captures the aspects ofevidential reasoning as discussed in section 2.

In the argumentation approach, different arguments like theone shown in Figure 1 are built, supporting the propositions thathave to be proven, and other arguments are also built to attack
these arguments. In the example, the prosecution has to provethat Rijkbloem killed the father. In order to do this, arguments
will have to be constructed for, for example, “Rijkbloem and thefather were in the same house”, “Rijkbloem had a gun which heused to shoot the father”. The defense will try to attack thesearguments by saying, for example, that it was not Rijkbloem but
the mother who shot or by arguing that the testimonies of thetwo women cannot be trusted.
In story- or explanation-based approaches, a story (alsoreferred to as a scenario) is modelled as a causal network. Figure
2 depicts a small part of the prosecution’s story in the Rijkbloem
case.

3.1 Current approaches to reasoning withlegal evidence
In logics for argumentation (see [16] for an overview), the rulesof classical logic are augmented with rules for defeasible
inference. Associated with a defeasible inference is anunderlying generalisation that acts as a warrant [21] (cf. anchor[5], rule [7] and scheme [25]). Arguments can be constructed bychaining applications of inferences and thus one ends up with atree of arguments akin to a Wigmore graph [26], [1]. Each tree
has as its premises the pieces of evidence and the generalisations
and as its ultimate conclusion one of the explananda (in aWigmore graph, the generalisations are contained in the links).
In Figure 1, an example of an argument tree is given, where the“E” nodes are the pieces of evidence, the “G” nodes areevidential generalisations and the arrows are inferences. The
other nodes are (intermediate) conclusions.

Figure 1: an argument tree
Notice that the inferences in such an argument are all of anevidential nature: a piece of evidence e and the evidential
generalisation “e is evidence for p” allows us to infer p. For
example, the evidence that “Nicole saw that Rijkbloem shot her
father” and the generalisation that “if a witness sees an event,
this is evidence for the occurrence of that event” allow us toinfer that “Rijkbloem shot the father”.
Arguments can also be attacked. They can be rebutted withan argument for the opposite conclusion and they can beundercut with an argument for why an inference is not allowed(usually because a generalisation does not apply in the given
circumstances). In the example, an argument for “Rijkbloem did
not shoot the father” rebuts “Rijkbloem shot the father” and anargument for “Nicole wants to protect her mother” undercuts thegeneralisation “if a witness testifies that an event happened, thisis evidence for the occurrence of that event” as applied to
Nicole's testimony. When these attack-relations are known, it
can be determined which arguments “win”, which arguments“lose” and which are “undecided”.

Figure 2: a small causal network
The nodes in this graph are events in the story and the links
represent causal relations between the events: Rijkbloem
shooting the father causes the father to die.
Such a causal network can be used as a causal theory, inwhich observations are explained by hypothesised events orstates through abductive inference to the best explanation (IBE).
The basic idea of abductive inference (for an overview see [10])is that if we have a general rule cause → effect and we observe
effect, we are allowed to infer cause as a possible explanation of
the effect. This cause which is used to explain the effect can be asingle state or event, but it can also be a sequence of events, astory. In the example, the observation that has to be explained is“father dies”. This can be explained by the causal theory
consisting of the generalisations “If person X wants to hurt
person Y and person X has a gun, this will (usually/sometimes)
cause person X to shoot person Y” and “Person X shooting
person Y (usually/sometimes) causes person Y to die” together
with the assumptions that “Rijkbloem wants to hurt father” and“Rijkbloem has a gun”. The theory together with these initialcauses is then a hypothesis which explains the observation“father dies”.
Taken by itself the abductive scheme is nothing but thefallacy of affirming the consequent. However, in a setting where
alternative abductive explanations are generated and compared,
it can still be rational to accept an explanation if no better otherexplanation is available. Clearly, such reasoning is defeasible,
since additional facts might give rise to new explanations. In
sum, the idea of abductive inference to the best explanation isthat there are different explanations which have to be compared.

Figure 3: two explanations

In the Rijkbloem case, we have two different stories: theprosecution’s story that it was Rijkbloem who shot the father,and Rijkbloem’s story that it was the mother who (accidentally)
shot the father. This is visualised in Figure 3.
In the literature there are different ways of comparing the
explanations. The simplest way is choosing a subset-minimal
explanation that explains all the observations. Thagard [18]computes the activation of the individual propositions: (causal)
coherence between two units functions as an excitatory link
between the units. Acceptance or rejection of an explanation isrepresented by the degree of activation of the individual
propositions in the explanation.

3.2 Why combine the two approaches?
In this section we argue why we think a combination of the two
approaches discussed in the previous sections best captures theconcepts expressed in section 2. We will do this by briefly
discussing the advantages and disadvantages of the two
approaches when applied to reasoning with evidence.
Advantages of the argument-based approach are that it isbased on simple principles of reasoning and that it istransparent: the generalisations and the evidence are mentioned
explicitly in the arguments and the reasoning from the evidence
to the conclusion is easy to follow. A disadvantage of theargument-based approach is that it does not provide a complete
overview of the case, as the original stories about “whathappened” are cut into pieces to become conclusions of different
arguments and counter-arguments. It may be possible to reason
abductively within a purely argument-based approach by using
the abductive scheme (if cause → effect and effect then usuallycause) as a warrant for making the inference. However, this kindof abductive reasoning is evidential in nature (see last paragraphof this section), so by using the purely argument-based approach
one loses the causal information and the causal reasoning
inherent to explanations.
An important advantage of the IBE approach is that it
perhaps is closest to how legal decision makers actually think
about a case. Experiments by Pennington and Hastie [12]suggest that when making a decision, people often compare thedifferent stories from which the explananda follow instead of
constructing complex arguments for and against the explananda.
Choosing the best explanation is closer to this ‘holistic’
approach to reasoning with events, where an event is evaluatedby looking at how well it fits a coherent story (see [22], pp. 241
for a short discussion on holistic and atomistic reasoning withevidence).There are also indications that fact investigators workwith causal structures and timelines [15].
However, the IBE approach is arguably less natural in its
treatment of sources of evidence. In IBE approaches, pieces ofevidence are modelled as effects. So a witness testimony, forexample, must be abductively explained by its possible causes,
which are other states or events. An obvious explanation is thatthe testimony was caused by the fact that the event described in
the testimony happened. However, there may be otherexplanations, such as that the witness tried to protect a suspector that the witness’s senses or memory are at fault. In a purely
abductive approach all such explanations always have to beconsidered. However, in reality the ‘truthful’ explanation isconsidered the normal one and alternative explanations are

regarded as exceptions to the generalisation that witnesses
usually speak the truth, and are investigated only if there isevidence for such exceptions. In [3] we argued that this is better
captured by modelling reasoning with sources of evidence asargumentation with evidential default generalisations. The
witness generalisation would then be modelled as “If a witness
says that “P” then usually P is true”, and the undercutting
exceptions to this generalisation are, for example, “the witness
tries to protect a suspect” or “the witness’ memory is at fault”.
Another problem of the IBE approach as it is usuallymodelled is that it is impossible to reason about the causal
generalisations in the causal theory. When IBE is used in adiagnostics tool, the causal theory is determined by experts in
the relevant field, for example, medicine in the case of a medical
diagnostics system. In that case, it is reasonable to assume acausal theory based on expert consensus and thus the
explanations that are provided for a given explanandum. In thecase of reasoning with evidence, however, we cannot assume
that the causal theory provided is correct or agreed upon; in fact,
in an argumentative story-based proof analysis the analysis andperhaps change of the causal generalisations in the stories is acentral point of focus.
A final issue of the IBE approach is the comparison of
explanations. As Thagard and Shelley [19] noted, the simplest(in terms of subset minimality) and most complete (in terms of
explaining the most observations) explanation is not always thebest. Particularly in reasoning with evidence, a complex
explanation that explains only a few important pieces ofevidence can be better than a simple explanation that explains
many less important pieces of evidence. A more fine-grained
approach to comparing explanations is needed for reasoning
with evidence. The evidential arguments will have a big
influence here; these arguments allow one to decide whichevidence to believe and which evidence is most important, andthus which evidence needs to be explained.
In our opinion, an approach that combines theargumentation approach and the IBE approach best models theconcepts of argumentative, story based analysis of evidence as
discussed in section 2. In this combined approach, the stories are
represented as networks of causally linked events. It should be
noted that we use a naïve interpretation of causality; in our
examples, sometimes a link does not represent a much stronger
relation than temporal precedence. Because we also allow
arguments that causal generalisations in the model are attacked,
this interpretation of causality does not pose a real problem; it is
up to the investigator or the decision maker to change the causal
theory into a correct theory. This approach to causality also
allows for the networks to remain relatively simple, so that theykeep providing a good overview of the case.
In our approach, the sources of evidence are connected toevents by evidential arguments, with pieces of evidence aspremises and events as conclusions, and evidential links,
representing inferences, that connect the evidence to the event.
This gives the evidence a clear and separate place in the theory,something which was lacking in other, the Anchored Narratives
approach [5]. It also solves the problems the IBE approach haswith its treatment of sources of evidence as discussed in section
3.2. A third advantage of adding arguments to reasoning with

explanations is that the validity of the causal generalisations in atheory can be argued about.

⇒C denotes a causal generalisation. In the following subsections
we will elaborate on our approach.

Before we continue with the formal theory, an important
remark should be made. When we talk about evidential links, wemean only the links in the argument that connect the source ofevidence to the event. Other authors, notably Pearl [11] andPoole [14], speak of evidential links or evidential reasoning in a
broader sense. According to them, causal reasoning is reasoning
from cause to effect, where a certain cause predicts an effect,and evidential reasoning is reasoning from effect to cause, wherea cause explains an effect. Evidential reasoning can be done
through abduction, viz. “cause → effect and effect so cause” ordeduction (“modus ponens style reasoning”), viz. “effect →cause and effect so cause”. In this paper, we use both kinds ofevidential reasoning: the causal networks representing thestories abductively explain the pieces of evidence; and sourcesof evidence deductively explain why we should believe thatcertain events happened. Of course, here abductive anddeductive reasoning are both considered defeasible. However,when we refer to evidential reasoning, we mean the deductive
evidential inferences from the sources of evidence to the events.
Our approach respects Pearl’s c-e rules [11], that is, in our
approach it is not allowed to apply an evidential generalisation
to a proposition that has been inferred by application of a causal
generalisation.

4.1 A Logic for Argumentation

4. A FORMAL THEORYIn this section we will present our combined formal theory.
Section 4.1 discusses the argumentation logic and section 4.2
discusses how the causal theories are used to explain the
explananda. In section 4.3 we discuss how different
explanations can be compared by taking into account theevidential arguments.
Combining the causal theories and the evidential
arguments, we can define a framework for argumentative, story
based evidence analysis. This framework is a combination of an
explanation framework and an argumentation framework. An
explanation framework is a tuple AC = (T, H, O, F). Here, T isthe causal theory which contains all the causal generalisations
from the different stories. H is a set of explanantia, propositions
with which we want to explain the explananda. The set ofobservations O contains all the propositions that are supported
by some evidence (through an evidential argument). F ⊆ O isthe set of explananda, which are ideally explained. The idea isthat the explanantia H together with a part of the causal theory T
explain the explananda F. An argumentation framework is a pair
AE = (GE, E), where GE is a set of evidential generalisations andE is a set of evidence. Combining these two frameworks, ourframework for evidential reasoning is a pair ER = (AC, AE) suchthat O ⊆ c(AE), where c(AE) are the conclusions on the basis ofAE.
The generalisations in GC and GE are formalised with a
special conditional connective ⇒ which only satisfies the modus
ponens inference rule.
gi(x): p1 ∧...∧ pn ⇒ q

Here gi is the name of the generalisation, x is a tuple of variables
denoting the terms in the generalisation and p1…pn and q are
predicate-logical literals. The type of generalisation is indicatedwith a subscript: ⇒E denotes an evidential generalisation andSince reasoning about evidence is defeasible, the logic ℒ of oursystem must be a nonmonotonic logic. Following our earlier
work in [2], we augment the inference rules of classical logic
with defeasible inference rules (cf. Pollock [13]). In this paper,
we only need one defeasible inference rule, namely the justmentioned modus ponens rule for the conditional operator ⇒.
The application of this inference rule implicitly assumes that
there is no exception to the generalisation to which the inference
rule is applied and that this generalisation is valid. Such an
application can thus be attacked by arguing that there is an
exception or that the generalisation is not valid. An exception toan evidential generalisation gei is modelled as exc(gei(x)), whereexc(gei(x)) stands for “there is an exception to generalisation
gei(x)”, and ¬valid(gei(x)) means that generalisation gei(x) is not
valid. This modeling of exceptions is related to Hage's [7]approach to rule exceptions and validity.
In his work, Pollock defines specific inference rules
relevant for evidential reasoning, such as perception, memory
and temporal persistence. Moreover, in [2] we formulated
reasons for expert and witness testimonies. In this paper,
however, we will model these reasons using the generalinference rule, but we still retain the option of modelling themas separate inference rules for future work.
The evidence E and the evidential generalisations from GE
allow us to build evidential arguments by taking the evidence aspremises and chaining applications of defeasible modus ponens
into tree-structured arguments. Such an evidential argument is a
finite sequence of lines of argument, where a line is either a
proposition from E or the result of an application of thedefeasible modus ponens to one or more previous lines. Take,for example, the following evidential generalisations
ge1(W, P): W testifies that “P” ⇒E P is truege2(W, P): W saw that P happened ⇒E P happened.

These two evidential generalisations can be used to constructargument AR1 for the conclusion that Rijkbloem shot the father:
1.
2.
3.
4.
5.

e1: Nicole testifies: ”I saw Rijkbloem shoot my father”
ge1 : W testifies that “P” ⇒E P is true
Nicole saw Rijkbloem shoot the father (1, 2, def. MP)
ge2: W saw that P happened ⇒E P happened
Rijkbloem shot the father (3, 4, def. MP)

Note that we will often shorten the name of a generalisation
gei(x) to gei. An argument can defeat another argument by
rebutting or undercutting the other argument. Two arguments
rebut each other if they have the opposite conclusion. An
argument ARi undercuts another argument ARj if there is a line
exc(gei(x)) or ¬valid(gei(x)) in argument ARi and a line Q(x) inargument ARj, which is obtained from some previous lines in
ARj by the application of defeasible modus ponens togei(x): P(x) ⇒ Q(x).

So an argument A1 defeats another argument A2 if A1 rebuts
one of A2’s (sub)conclusions or if A1 undercuts an instance of ageneralisation in A2. As an example of rebuttal, take thefollowing argument AR2:
1. e2: Rijkbloem testifies: ”I did not shoot the father”

2. Rijkbloem did not shoot the father (1, ge1, def. MP)

AR2’s conclusion that “Rijkbloem did not shoot the father”
rebuts AR1’s conclusion that “Rijkbloem shot the father” (andvice versa). Note that in the remainder of this paper, we will not
reproduce the evidential generalisations in a line of argument,
but simply refer to them by their name. To give an example ofan undercutting argument, we first need a generalisation thatpoints to an exception:ge3 (W): ¬(W is trustworthy) ⇒E exc(ge1(W, y))This generalisation expresses that if a witness W is nottrustworthy, generalisation ge1 is not applicable anymore(insofar as ge1 is about W). With new evidence an undercuttingargument AR3 can be built:
1. e3: Rijkbloem testifies that ”Nicole is not trustworthy”
2. exc(ge1(Nicole, y)) (1, ge3, def. MP)

This argument undercuts AR1.
When we have a collection of arguments and their binary
defeat relations, the dialectical status of the arguments must be
defined. In this paper, we assume that our semantics instantiates
Dung’s [6] grounded semantics. In these semantics, arguments
can be either justified, which means that they are not attacked byother justified arguments that are stronger, or overruled, whichmeans that they are attacked by one or more other stronger
arguments that are justified, or defensible, which means that they
are neither justified nor overruled. Note that in the present
paper, we will not discuss the relative strength between
arguments.

4.2 Explanations
The IBE part of our theory is mostly based on standard accounts
of inference to the best explanation and abductive reasoning[10]. The causal theory T is the collection of all causal
generalisations that appear in the different stories. An effect canbe a cause of some other event and thus causal generalisations
can be chained. As an example, take the following causal
generalisations
gc1(x, y) : x shoots y ⇒C y is hit in the headgc2 (y) : y is hit in the head ⇒C y dies

These two generalisations can be chained, and in natural
language this would read as: “if a person (x) shoots anotherperson (y), this may cause the person (y) to be hit in the head
and if someone is hit in the head, this may cause that person todie”.
The set of observations O contains the propositions that
follow from an evidential argument. For example, if there is anargument for the proposition “Rijkbloem shoots father” and gc1
is part of T, then “Rijkbloem shoots father” will be in O.
In standard accounts of IBE the observations are usually
given and they all have to be explained. One of the main ideas in
our formal theory is that the set of observations is not simply
given but is determined by the conclusions of evidential
arguments. Furthermore, not all observations have to be
explained. Instead only the observations which are in the set of
explananda F have to be explained. In the Rijkbloem example,
the event that “Rijkbloem and Nicole broke up” is supported byan argument but it is not a part of F. This is because we are notinterested in an explanation for the fact that they broke up; wewant to know who shot the father. So the set of explananda F isessentially chosen by the investigator or decision maker (withthe restriction that they have to be supported by an evidential
argument). It is possible to divide the explananda into
propositions which have to be explained and additional
evidence which can be explained. Propositions in F which aresupported by a justified argument have to be explained andpropositions which are supported by a defensible argument are
ideally explained, but this is not necessary. Note that there will
always be at least one proposition in F that is supported by ajustified argument; otherwise there is no point in looking for an
explanation.
The explanantia H are also chosen by the investigator ordecision maker. Now the precise definition of explanations canbe given.
Definition (explanations)
Si = Hi ∪ Ti, where Hi ⊆ H and T i ⊆ T, is a proper explanationof the explananda F iff
1.

∀f : If f ∈ F and f is the conclusion of a justified(sub)argument that follows from AE, then:-2.

Hi ∪ Ti ⊢ f; andHi ∪ Ti is consistent.

There is no justified argument for the conclusion¬valid(gci) or exc(gci), where gci ∈ Ti.

Here ⊢ stands for logical implication according to the set of all
deductive inference rules extended with modus ponens for ⇒.
So the hypothesis Hi (which contains some or all of the
explanantia) together with the (sub)theory Ti should explain all
explananda which are supported by a justified argument. Notethat there should be no justified argument for the conclusions
that one of the generalisations in the (sub)explanation is invalidor that there is an exception to it. The idea behind this second
point in the definition is that we should not be able to explain
propositions using a theory that contains invalid generalisations
or generalisations to which an exception has been provided; thispart of the definition allows us to reason about thegeneralisations in the explanation. However, care must be taken
when dealing with arguments with an exception to a
generalisation or the invalidity of a generalisation as theirconclusion. One of the reasons for this is that at present,
generalisations themselves do not have strengths, so they arealways automatically “defeated” by an argument for the opposite
conclusion. If the causal generalisations have strengths, it can be
imagined that, for example, a “strong” causal rule (e.g. x kicks
rubber ball ⇒C ball moves; most rubber balls move when you
kick them) is less easily declared not valid than a “weak” causal
generalisation (e.g. x has fight with y ⇒C x kills y; not everybody
who has a fight with another person kills the other person).
Because of this subtlety, we allow only justified arguments to“block” an explanation.
As a small example, take T = {gc1, gc2} (see the beginningof this section), H = {Rijkbloem shot father, mother shot father},F = {father died} and suppose that there is a justified argument
for father died. Then there are two explanations, namely Sr ={Rijkbloem shot father} ∪ T and Sm = {mother shot father} ∪ T.
The explanandum follows from both explanations and both
explanations are consistent.

4.3 Comparing explanations
Our combination of two reasoning models makes a morerefined assessment of stories possible than in the two individual
approaches. Not all of the observations have to be explained: themost interesting observations can be chosen as explananda.
Also, in our formal proposal causal links are not just given but
their validity can be argued about and exceptions can be given tocausal generalisations. In this section, we will further discuss
how different explanations can be compared. The criteria
discussed in this section are meant to be guidelines for analysing
explanations. We do not claim that the decision about which
explanation is the best is easily made using these criteria. Other
factors, like the quality of the generalisations in an explanation,
also play a role.
From the definition of explanations in section 4.2 it follows
that an explanation has to explain all the explananda which
follow from a justified argument, but it does not have to explain
all the additional evidence, that is, observations which follow
from defensible arguments. The rationale behind this is that if
the argument is justified, we are more certain the event really
happened, and we are less sure that events which follow fromdefensible arguments happened.
However, the explananda that follow from defensible
arguments are not overruled and thus can provide us with acriterion for the comparison of explanations: an explanation ispreferred (over other explanations) if it explains more
propositions in F which follow from defensible evidential
arguments. As an example, take T = {gc1, gc2, gc3}, where
gc3: x shoots y ⇒C x has gunpowder on his hands. Furthermore,
suppose that H = {Rijkbloem shot father, mother shot father},F = {father died, Rijkbloem has gunpowder on his hands}, theargument for father died is justified and the argument for
Rijkbloem has gunpowder on his hands is defensible. Now there
are still two explanations Sr and Sm (see end of section 4.2), but
Sr also explains Rijkbloem has gunpowder on his hands, making
it a better explanation than Sm.
In addition to there being arguments for the explananda,
there can, of course, also be evidential arguments for otherevents in an explanation. This brings us to the second criterion:
the more propositions in an explanation are supported by a nonoverruled argument, the better an explanation is. Normally, thepropositions in an explanation are inferred abductively from an
observation: if we have the causal generalisations a ⇒C b,
b ⇒C c and an observation c that we want to explain, we canabductively infer first b and then a. Even though abduction is
not logically valid, the idea is that we are safe to assume that a
together with the generalisations is an explanation of c and that
thus a and b will be the case. This is the “gap filling” function ofstories (see section 2) in effect: a and b do not follow fromevidence, but the explanation as a whole is plausible, so we canmore or less safely assume that a and b are the case. If, however,a and b from the above example are also supported by anevidential argument this is, of course, even better; they can not
only be inferred abductively but also follow from evidence.

It is also possible that the conclusion of an evidential
argument contradicts an event in an explanation. This brings us
to the third criterion for comparing explanations: an explanation
is preferred if it contradicts fewer conclusions of non-overruled
arguments. With this criterion it does not matter whether theargument which conclusion contradicts the explanation isjustified or defensible. One could argue that an explanation that
contradicts a defensible conclusion is better than an explanationthat contradicts a justified conclusion; however, in this paper wechoose not to make this distinction. As an example, take thesituation as laid out at the end of section 4.2 together with a
non-overruled argument for Rijkbloem did not shoot the father(AR2 on page 5). This time, explanation Sm is better, because Sr
contradicts the conclusion of argument AR2.

5. EXAMPLE
In this section, we present an example of how different elementsof a case can be analysed using our merged theory ofargumentative, story-based analysis of evidence. It should be
noted that the examples in this section present different time
points in an ongoing analysis of one case. As said, we have notyet defined a dynamic framework for argumentative, story-based
analysis.
We start our analysis with the two stories told by
Rijkbloem and Nicole and her mother (see page 2).
T = { gc1: fight between x and y ∧ x has gun ⇒C x shoots y,
gc2: x shoots y ⇒C y is hit,
gc3: y is hit ⇒C y dies,gc4: fight between x and y ∧ z has gun ⇒C z aims gun at x,
gc5: x aims gun at y ⇒C y tries to push gun away,
gc6: x tries to push y’s gun away
⇒C y’s gun accidentally goes off,
gc7: gun accidentally goes off ⇒C x is hit}
F = {father dies}H = {fight starts between Rijkbloem and father, Rijkbloem has
gun, mother has gun}G = {ge1: W testifies that “P” ⇒E P is truege2: W1 and W2 testify that “P” ⇒E P is truege3: police report that “P” ⇒E P is true}
E = {eR : Rijkbloem testifies that:- fight starts between him and father- mother aims gun at him- he tries to push gun away
- gun accidentally goes off- father is hit in the headeW : Nicole and her mother testify that:- fight starts between Rijkbloem and father- Rijkbloem shoots father- father is hit in the headeP : police report that “Mr. Lammers died”}
O = {fight starts between Rijkbloem and father, mother aims gun
at Rijkbloem, Rijkbloem tries to push gun away, gun
accidentally goes off, Rijkbloem shoott father, father is hit in
the head, father dies}Fight starts between
Rijkbloem and father

Rijkbloem
shoots father

Father is hit
in the head

Fatherdies

Rijkbloem
has gunFight starts between
Rijkbloem and father

Mother aims
gun at R

Rijkbloem tries topush gun away

Gun accidentallygoes off

Father is hit
in the head

Fatherdies

Mother has
gun

Figure 4: the two explanations Sm and Sr
With G and E, evidential arguments can be constructed for the
propositions in O. All these arguments are justified because
none of them is attacked by another argument. With this data,
two explanations can be made. The first explanation is thewomen’s story, that Rijkbloem was the one who shot the father:
Sr = Tr ∪ Hr, where Tr = {gc1, gc2 gc3} and Hr = {fight starts
between Rijkbloem and father, Rijkbloem has gun}. The second
explanation is Rijkbloem’s story that the mother’s gun went off:
Sm = Tm ∪ Hm where Tm= {gc4, gc5, gc6, gc7} and Hm = {fightstarts between Rijkbloem and father, mother has gun}. The
explanations have been represented as graphs in Figure 4. The
two propositions that are not supported by evidence arerepresented as boxes with dotted lines.
It is hard to make a decision which of these two
explanations is better if we follow the criteria from section 4.3;
both explanations are supported by evidence, and in both
explanations there is an important proposition which is notsupported by evidence, namely “Rijkbloem/mother has a gun”.
However, the women’s story seems more plausible: acaring father tries to protect his daughter from a criminal andpays with his life. Fathers want to protect their daughters at all
costs. Likewise, when a problem arises, criminals such as
Rijkbloem resort to violence. Rijkbloem can have made up his
strange story to protect himself; women do not normally carryguns around, and the chance that the bullet hit the father after a“struggle” between Rijkbloem and the mother is low. Thisshows how a “good” story can win over a “bad” story. Below wewill formalise this idea and also show that the most plausible
story is not always better supported by evidence.
First we want to argue that Rijkbloem made up his story inorder to protect himself:
1.
2.
3.
4.
5.

Rijkbloem is a suspect
x is a suspect ⇒E x wants to protect himself
Rijkbloem wants to protect himself(1, 2, def. MP)
x wants to protect himself ⇒E exc(ge1(x, p))exc(ge1(Rijkbloem, p)) (3, 4, def. MP)

This argument undercuts every argument that has eR as its
premise; in other words, Rijkbloem’s story is not believed. This
will make Sr (the story that Rijkbloem shot the father) the
preferred explanation, because all arguments which support Sm
are undercut. It is in this way that the interactions between theevidential arguments have their effect on the explanations.

A new, admittedly prejudiced, generalisation can be added
to Tr in order to make explicit one of the reasons that the
women’s story is more plausible.
ge4: x has previous convictions ⇒E x has gun

Say that there is evidence for the fact that Rijkbloem has
previous convictions. Now the explanation Sr is even better
because now Rijkbloem has gun is supported by an evidential
argument; the abductively inferred part of Sr, the “gap” in thestory so to speak, was Rijkbloem has a gun. This proposition can
now be inferred from evidence using ge4. However, it can beargued that generalisation ge4 is based on based on prejudicesand an argument can be constructed for the conclusion that thegeneralisation is not valid.
Another intuitive reason for the fact that the womens’ story
is more plausible concerns the generalisation gc6. It can beargued that this generalization is not valid, on the grounds that it
is highly improbable
For the sake of the example, we return to the situation fromthe beginning of this section: the two explanations Sr and Sm
from Figure 4 without the undercutting arguments for the factthat Rijkbloem wants to protect himself. We present some newobservations:
On = {Rijkbloem’s gun was of type A,
mother’s gun was of type B,¬(bullet casings on crime scene),¬(gunpowder on Rijkbloem’s hands),
Rijkbloem was 50 centimeters away from father,mother was 2 meters away from father,
the angle at which the bullet entered mr. Lammers is θ2}

These observations all follow from evidence: the women statethat Rijkbloem shot with a “black pistol, similar to the one thepolice carries”. Rijkbloem testifies that the mother’s gun was “asmall, revolver-like pistol”. The police report states that there
were no bullet casings found on the crime scene and that here
was no powder on Rijkbloem’s hands. A forensics report statesthat the angle at which the bullet entered was θ1. Assume that all
the conclusions in On follow from defensible arguments and Ou= O ∪ On. The explananda Fu are now changed into {father dies,
the angle at which the bullet entered mr. Lammers is θ2¬(bullet
casings on crime scene), ¬(gunpowder on Rijkbloem’s hands)}.

The causal theory T is also updated with some newgeneralisations:Rijkbloem 50 cm awayfrom father

angle of bullet entry
theta1
gunpowder on
Rijkbloem’s hands

Fight starts between
Rijkbloem and father

Rijkbloem
shoots father

Father is hit
in the head

Fatherdies

Rijkbloem
has gunRijkbloem’s gun is oftype Abullet casings found at
the crime scenemother 2 m away fromfatherFight starts between
Rijkbloem and father

Mother aims
gun at R

Rijkbloem tries topush gun away

Mother has
gun

Gun accidentallygoes off

mother’s gun is oftype B

angle of bullet entry
theta2Father is hit
in the head

Fatherdiesnot(bullet casings
found at the crime
scene)

Figure 5: the updated explanations Sru and Smu
gc9: x shoots y ∧ x is 50 centimeters away from y⇒C the angle at which the bullet entered y is θ1
gc10: x shoots y ∧ x shoots with gun type A⇒C bullet casings on crime scene
gc11: x shoots y ⇒C x has gunpowder on his hands
gc12: x’s gun accidentally goes off ∧ x is 2 meters away from y⇒C the angle at which the bullet entered y is θ2
gc13: x’s gun accidentally goes off ∧ y’s gun is of type type B⇒C ¬(bullet casings on crime scene)

Note that these generalisations are typically generalisations that
follow from expert statements; for example, an expert on guns
testifies that the semi-automatic pistol with which Rijkbloem
shot ejects its empty casings when fired. Arguments about thevalidity and quality of generalisations can play a big part indetermining the right causal theory. However, in this paper, we
do not discuss this in great detail.
Two new explanations can now be built (Figure 5). The first is
an updated version of the women’s story: Sru = Tru ∪ Hru, where
Tru = {gc1, gc2 gc3, gc9, gc10 gc11} and Hr = {fight started
between Rijkbloem and father, Rijkbloem had gun, Rijkbloem was
50 cm away from father, Rijkbloem’s gun was of type A}. This

explanation explains the explanandum father dies. However, italso explains three propositions which are contradicted bydefensible arguments; the angle at which the bullet enteredfather is θ2 instead of θ1, Rijkbloem did not have gunpowder on
his hands and there were no bullet casings found at the crime
scene. The propositions that contradict an argument’s
conclusion have been rendered in a lighter colour in Figure 5.
The second new explanation is an updated version of
Rijkbloem’s story: Smu = Tmu ∪ Hmu where Tmu = {gc4, gc5, gc6,
gc7, gc12, gc13} and Hm = {fight started between Rijkbloem andfather, mother had gun, mother was 2 m away from father,mother’s gun was of type B}. This explanation does notcontradict any conclusions of arguments. It does explain two
explananda which follow from defensible arguments, about theangle of entry and about the fact that no bullet casings were
found (these propositions have been rendered as dark grey boxes
in Figure 5).

So it seems that, while Rijkbloem’s story fares less well onplausibility, it fares better in light of the evidence. This is not to
say Rijkbloem did not shoot the father. However, the analysis
does show that “good” stories are not necessarily true, and “bad”
stories are not necessarily untrue

6. CONCLUSION
In this paper we have argued for a combined story andargumentative approach to reasoning with evidence. In our
opinion, such an approach solves the problems of the individual
approaches as discussed in section 3.2. When stories are
represented as causal networks, the overview of “whathappened” in the case is retained, and the abductive approach to
explaining the explananda nicely captures the intuitive processof comparing different stories. Also, the role of stories as “gapfillers” is captured by this abductive reasoning.
Adding evidential arguments to connect the sources ofevidence solves the problems the abductive approach has withthese sources, and gives the individual pieces of evidence a
separate place in the theory. The conclusions of the evidential
arguments can be used to define criteria for comparing
explanations, and the evidential arguments are a good tool for
analysing the causal generalisations in a theory.
As for future research, we did not discuss alternative story
structures like intentional structures (such as the one used by
Pennington and Hastie [12]) and content-based structures (suchas the story schemes used by Schank and Abelson in theirseminal work on story understanding [17]). However, theseother story structures also have a causal model as their basis; theschemes are added as an extra layer to this causal structure. So
our basic causal approach allows us to extend our theory, adding
other layers as necessary.
Another limitation of the present work is that we take astatic viewpoint: we provide an analysis framework for thecurrent status of an argumentative and story-based analysis of
the evidence about case facts, and postpone attention to the
dynamics of developing and refining such an analysis. We trustthat our work can be a fruitful basis for further research in whichthe dynamics of proof analysis is given due attention. In our
opinion, our approach can be used to explicate heuristics forpolice investigation into the case facts, using alternative
explanations to steer the further gathering of evidence.

[12] Pennington, N. and Hastie, R. (1993) The story model
for juror decision making. In Hastie, R. (eds.), Inside
the Juror, The Psychology of Juror Decision Making,Cambridge University Press, Cambridge.

ACKNOWLEDGMENTS[13] Pollock, J. (1995) Cognitive Carpentry: A Blueprint for
How to Build a Person, MIT Press, Cambridge, MA.

This research was supported by the Netherlands Organisation for
Scientific Research (NWO) under project number and634.000.429. Henry Prakken was also partially supported by the
EU under IST-FP6-002307 (ASPIC).

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