Did He Jump or Was He Pushed?
Abductive Practical Reasoning
Floris BEX a,1 , Trevor BENCH-CAPON b and Katie ATKINSON ba
Faculty of Law, University of Groningen, The Netherlands.
b
Department of Computer Science, University of Liverpool, UK.
Abstract. In this paper we present an approach to abductive reasoning in law by
examining it in the context of an argumentation scheme for practical reasoning. We
present a particular scheme, based on an established scheme for practical reasoning,that can be used to reason abductively about how an agent might have acted to reacha particular scenario, and the motivations for doing so. Plausibility here depends ona satisfactory explanation of why this particular agent followed these motivations in
the particular situation. The scheme is given a formal grounding in terms of Actionbased Alternating Transition Systems and we illustrate the approach with a runninglegal example.
Keywords. Argumentation Schemes, Abductive Reasoning, Practical Reasoning

1. Introduction
It is by now well-accepted that stories, or sequences of events, play an important part intheories of how people reason with the evidence in criminal cases. In legal psychology,
authors such as Pennington and Hastie [9] and Wagenaar et al. [12] argue that judges,
jurors and police investigators construct and compare stories about ‘what happened’ in acase using the available evidence. This approach has been adopted by researchers in AI(& Law), who model stories as causal networks that explain the evidence; Thagard [11]has applied his connectionist model of inference to the best explanation to legal cases
and Bex et al. [5] propose an approach that combines classical abductive inference to thebest explanation with defeasible argumentation.
A good story of a criminal case should not only be sufficiently supported by evidential data (e.g. testimonies, forensic data) but it should ideally also be plausible, that is,
the story should conform to our beliefs about how things generally happen in the world
around us. This plausibility of a story partly depends on the plausibility of the causal
links between the events in the story, which give a story its coherence. For example, astory where one person died because he was shot by another person is coherent because
we believe that, in general, shooting someone can cause that person to die. Many stories
about crimes involve rational agents. When rational agents are concerned we need to see
events not simply as the result of the operation of physical causal laws – what Dennet[6] terms the physical stance – but also as the result of choices made by the agents –1 Corresponding Author: Faculty of Law, University of Groningen, The Netherlands. E-mail: f.j.bex@rug.nl

what Dennet calls the intentional stance. For the intentional stance, plausibility comesfrom our view of how likely it is that the agent would have made the required choicein the situation, and this in turn depends on the motivational preferences we believe theagent to have. For example, an agent may act in a certain way only if he prefers fame tofortune. If we wish to say he is motivated by fame, we need to explain why we believe
this particular agent has this preference2 .
The formal framework proposed by Bex et al. allows for a careful analysis andcritique of the causal links between the events. The validity of the causal rules can beargued about and exceptions to these rules can be given. However, the model of agent
decision making as regarded from the intentional stance remains something of a ‘blackbox’. In [5] most causal links denote a physical causal relation and while in both [5] and[11] explanations for actions can, in a sense, be given in terms of psychological states,
the agents’ motivations and the question of whether and how the agents act on thesemotivations remains implicit. For example, Thagard explains ‘Claus injected Sunny withinsulin’ with ‘Claus wanted to end his marriage to Sunny’ ([11], pp. 238). Here Claus’reasoning remains implicit and therefore somewhat unbelievable, as one can argue that
there are less drastic ways of ending a marriage. For real plausibility we need a moreelaborate explanation of why the choice was made by Claus at the particular time.
In this paper we will attempt to allow this elaborated conception of the intentional
stance by giving agents’ motives, and the priorities amongst the agents’ motives, a clear
place in evidential reasoning about actions. We do this by using an argumentation scheme
for abductive practical reasoning, based on the normal (non-abductive3 ) practical reasoning scheme as proposed by Atkinson et al. [2]. The abductive scheme is formallygrounded in terms of an Action-based Alternating Transition System, or AATS [15], andallows us to explain a particular situation in terms of the choices made by the agents
involved and their motivations. The resulting explanations, modelled as arguments in a
Value-based Argumentation Framework [3], can then be evaluated by considering theagents’ motivational priorities.
The rest of this paper is organised as follows. In section 2 we will describe the argumentation scheme for abductive practical reasoning and its associated critical questions.
In section 3 we will apply this to an extended example showing how explanations andobjections can be constructed and how conflicts between explanations may be resolved.
In section 4 we discuss related work, and we finish by making some concluding remarks
and identifying areas for future work.

2. An Argumentation Scheme for Abductive Reasoning
In this section we will define an argumentation scheme for abductive practical reasoning.
This scheme is based on a well-known argumentation scheme for practical reasoning
defined by Atkinson et al. [2]. The original scheme and its critical questions enables
agents to propose, attack and defend justifications for actions: presumptive or prima facie
justifications of actions can be presented as instantiations of an appropriate argument
2 When speaking of persons we might call such a preference ‘character’ and may attempt to explain whatkind of character the person has, cf. Walton [13].
3 We use ‘non-abductive’ instead of ‘deductive’ because deductive implies that normal practical reasoning is
not presumptive/defeasible, which it of course is.

scheme, and then critical questions characteristic of the scheme used can be posed tochallenge these justifications. The original scheme is stated as follows:
In the current circumstances R,
we should perform action A,
which will result in new circumstances S,
which will realise goal G,
which will promote some value V.
The idea is that an agent performs an action to move from one state of affairs toanother, realising his goal in order to promote one of his values. An agent who does not
accept this presumptive argument may challenge elements in the instantiation throughthe application of critical questions and an unfavourable answer to a critical question
will identify a potential flaw in the argument. For example, one of the original criticalquestions (CQ8) is ‘Does doing the action have a side effect which demotes the value’?
Through the critical questions agents can attack the validity of the various elements of
the argument scheme and the connections between them, suggest alternative possible
actions, and draw attention to side effects of the proposed action.
The argumentation scheme for practical reasoning has roughly the same elements
as Pennington and Hastie’s episode scheme, a basic model about intentional actions [9].
In this scheme, some initiating states and events cause the agent to have a set of goals,
which give rise to actions that have consequences. In the argumentation scheme, we havethe current circumstances (the initiating states) in which the value acts as a motive forsome goal, which gives rise to some action that results in the new circumstances (theconsequences). An important difference, however, between an episode and an instantiation of the practical reasoning scheme is that in the argument based on the scheme thevalue that acts as a motivation is explicitly mentioned, whereas in an episode the motive
for the action remains implicit.
Now the argument scheme for abductive practical reasoning can be stated as follows:
The current circumstances S,
are explained by the performance of action A,
in the previous circumstances R,
with motive M.
By combining the normal and the abductive schemes for practical reasoning thiswill allow us to reason about intentional actions predictively as well as explanatorily.
Given this combination, two important questions need to be addressed. Firstly, is theagent reasoning about past actions or is he reasoning about possible future actions andsecondly, is the agent reasoning about his own actions or about the actions of some otheragent? If he is reasoning about his own actions, then he can apply the abductive practicalreasoning scheme to justify with what motives he took certain actions in the past andapply the normal (non-abductive) practical reasoning scheme to guide his future actions
according to his values. If, on the other hand, he is reasoning about some other agent,
then he can apply the abductive practical reasoning scheme to explain why and withwhat motives the other agent took certain actions in the past and apply the normal (nonabductive) practical reasoning scheme to predict what actions this other agent will takein the future to promote his values. The importance of the distinction is stressed in [10].
Agents can combine these different ways of practical reasoning. For example, a policeinvestigator tracking a serial killer can be guided in his actions by predicting what thekiller will do next. Similarly, a judge can be guided in his choice of action (i.e. acquit,
convict) by accepting an explanation of what happened and determining what could havemotivated the suspect in this particular explanation.
In [1], Atkinson and Bench-Capon argued for the necessity of a well-founded formal
model underlying the generation of arguments and critical questions. They provided therequired grounding in terms of an Action-based Alternating Transition System, or AATS
[15]. Essentially, an AATS consists of a set of states and transitions between them, withthe transitions labelled with joint actions, that is actions comprising an action of eachof the agents concerned. To represent the fact that the outcome of actions is sometimes
uncertain, in the scenario we use in this paper we will add a third “agent” which will
determine whether the actions had the desired or the undesired effect. The transitions will
be labelled with motives, corresponding to the values of [3], encouraging or discouraging
movement from one state to the next. A formal definition of the the abductive argument
scheme, and the associated critical questions discussed below, can be found in [4]. We
use a transition system which is a simplified version of the AATS used in [1] to groundthe practical reasoning argumentation scheme, but this will still allow us to hypothesise
the reasoning concerning the events that may have taken place.
Given an AATS and a number of arguments generated from the AATS, a story (asequence of events) is a path through the AATS. An argument explains why that path was
followed, and so gives coherence and hence plausibility to the story. For example, ‘John
wrote a paper, John went to Florence’ is a story, but it has more coherence expressed as‘John went to Florence because he had to present the paper he had written’.
Throughout this paper, we will use a simple example to illustrate our approach.
Picture two people on a bridge. The bridge is not a safe place: the footpath is narrow, thesafety barriers are low, there is a long drop into a river, and a tramline with frequent traffic
passing quite close to the footpath. One of the persons, call him Ishmael, is standing
still, whereas the other, Ahab, is running. As Ahab reaches Ishmael, Ishmael falls into
the river. Did he jump or was he pushed? To answer this we will need a story explaining
either why Ahab chose to push Ishmael, or why Ishmael chose to jump to his doom. If
Ahab is on trial, the story we believe will be crucial: if Ahab intended Ishmael’s death it
will be murder, if there is a less damning explanation for the push it may be manslaughter,and if Ishmael jumped, Ahab is completely innocent. We illustrate the critical questions
by reference to this example scenario.
Providing an explantion involves formulating the problem, generating candidate explanations, and then choosing the best explanation. As in [1] there are critical questions
associated with both problem formulation and choice of explanation. In this paper, forreasons of space, we will discuss only the latter, although the former are also important
here to enable us to critique and refine the underlying AATS, and so reason about andjustify the causal model. The list of problem formulation questions is given in [4].
We now turn to the critical questions relating to the choice of explanation for theabductive scheme. Below each critical question the answer to that question which would
attack the original argument is given, as well as an informal example of how such an
attack would be phrased in the example situation.
Critical questions for choice of explanation:

CQ1 Are there alternative ways of explaining the current circumstances S?
a) Could the preceding state R have been different?
answer: action A was done in a different preceding state R‘You say that Ahab did not have a clear path in the previous state, but actually
Ahab already had clear progress’b) Could the action A have been different?
answer: a different action A′ was done in preceding state R‘You say that Ahab pushed Ishmael, but actually Ishmael jumped’CQ2 Assuming the explanation, is there something which takes away the motivation?
answer: doing action A in R to reach S demotivates M‘Ahab pushing Ishmael to the ground would not provide a clear path so cannot be
motivated by Ahab wanting clear progress’
CQ3 Assuming the explanation, is there another motivation which is a deterrent for
doing the action?
answer: some other motivation M′ deters from doing action A in R to reach S‘Ahab is deterred from pushing Ishmael off the bridge to get progress because hedoes not want to bring Ishmael into danger’
CQ4 Can the current explanation be induced by some other motive?
answer: there is another motivation M′ which motivated doing A in R to reach S‘Ahab pushing Ishmael of the bridge is not motivated by Ahab wanting clear
progress, but by Ahab wanting to revenge himself on Ishmael’
CQ5 Assuming the previous circumstances R, was one of the participants in the joint
action trying to reach a different state?
answer: in R, even though one agent performed his part of A with motive M, thejoint action was actually A′ which led to S′, where A′ =6 A and S′ =6 S
‘Ahab wanted to push Ishmael out of the way of the tram to get him out of danger,
but nature did not cooperate (and Ishmael fell off the bridge)’
In the above critical questions, ‘explanation’ stands for ‘the performance of joint
action A in previous circumstances R’. With this kind of explanation we mean physicalexplanation, how performing an action in R caused the new state of affairs S, as opposed
to a mental explanation, what motivated an agent to do a particular action. So answering
CQ1 by giving an alternative cause of the current circumstances does not require committing to a particular motivation for that alternative cause. Note that it is possible to ask
for an alternative mental explanation by posing CQ4. CQ2 and CQ3 ask if there are any
reasons for not doing the particular action.
CQ5 is actually a critical question that does not apply to the abductive reasoning
step from the current state S to the previous state R, but rather to normal, non-abductive
reasoning performed in R. It asks if it is at all possible that in the previous state R, theagent wanted to perform a different joint action but was somehow hindered by anotheragent (‘nature’ in the example) not cooperating. Typically, this will suggest that he wasacting with a different, perhaps less culpable, motivation. This reasoning with the abductive scheme and CQ5 actually combines multiple reasoning steps into one. First, theprevious circumstances are abduced using the abductive scheme. Then, assuming theseprevious circumstances were the case, we try to justify the action by applying the normal scheme and finally we answer the critical question 17 from the original practicalreasoning scheme ([1], pp. 859) ‘are the other agents guaranteed to execute their part ofthe desired joint action?’ unfavourably. For reasons of space, we have incorporated thesereasoning steps into one new critical question.

3. Representation of the Example
The first stage of our approach is to produce a transition diagram representing the scenario. The objective is to include all that is relevant, but only what is relevant, so as to
avoid complicating the problem beyond what is necessary. Recall that the footpath isnarrow, and that Ahab is running. He may be assumed to desire a clear path, and so ourfirst proposition is “Ahab’s path is clear” (C). Recall also that the bridge is a dangerous
place: a person on the bridge may be in danger by falling into the river (R), or by being
hit by a tram (T). We also introduce a proposition “Ishmael’s life is in danger” (D), which
is true whenever either R or T is true, since this will be useful when we construct ourarguments. In our example we consider only the states which are of interest to us, and forsimplicity’s sake omit the other possible states from the diagram. For example, the statein which both T and C are true is of no interest to us, since no one claims that it was thecase, nor that anyone tried to reach it.
q1: CRTD = 0000 – Ahab’s path is not clear and Ishmael is not in danger from either theriver or the tram. This is the presumed situation before the incident.
q2: CRTD =1101 – Ahab’s path is clear and Ishmael is in danger from the river. This is
the situation immediately after the incident, which we wish to explain.
q3: CRTD = 1000 – Ahab’s path is clear and Ishmael is not in danger from either theriver or the tram.
q4: CRTD = 0011 – Ahab’s path is not clear and Ishmael is in danger from the tram. Thissituation would hold if Ishmael was too close to the tramline and a tram was approaching.
Now consider the actions. Ishmael can jump or do nothing. Ahab can push Ishmaelor do nothing. Pushing and jumping are not simultaneously possible. Since, however,
the effect of a push is uncertain, we add a notional third agent (“nature”) to determine
whether the push sends Ishmael into the river, or simply out of Ahab’s way. Nature isirrelevant here when Ishmael jumps.
There are thus three joint actions which can be performed in states q1 and q4 (seeFigure 1):
j1: Ishmael jumps and Ahab does nothing.
j2: Ishmael does nothing, Ahab pushes Ishmael and Ishmael falls off the bridge into theriver.
j3: Ishmael does nothing, Ahab pushed Ishmael and Ishmael is out of Ahab’s way but
still on the bridge.
We must next label the transitions with motives. Moving from q1 to both q2 andq3 is motivated by Ahab’s progress: in q1 the path was not clear and in q2 and q3 it isclear. Equally the transitions from q1 to q2 demote Ishmael’s safety: in q1 he is in no
danger and in q2 he is. But suppose also Ahab has a reason to seek revenge of Ishmael:this will apply only if q2 is reached from q1 by Ahab pushing Ishmael. Finally suppose
Ishmael wishes to kill himself, then, for him, oblivion will motivate moving from q1 to
q2. Turning to the transitions from q4, we can see that moving from q4 to q3 promotes
both Ahab’s progress and Ishmael’s safety. Moving from q4 by j1, where Ishmael jumps,
promotes Ahab’s progress, but does not affect Ishmael’s safety or his chance of oblivion,
since he dies in either case. Finally the transition from q4 to q2 by j2 can be motivatedeither by Ahab’s progress or by Ahab’s revenge, since it is important to satisfy this motivethat Ishmael is killed by Ahab rather than by the tram.
Our final transition diagram is shown in Figure 1. Of course, there are further transitions such as those between q1 and q4, and those where both do nothing, which leave
the state unchanged, but those play no role in our considerations, and so are omitted.
This model could be challenged using the critical questions relating to problem formulation given in [4]. For example, someone might claim that any push would send Ishmael into the river, so denying that j3 is possible, which would remove the transitions
into q3. For reasons of space, however, let us take our formulation as accepted, and notconsider these questions further here.
q4

q3

j3
Pa+ Si+

0011

1000

j1
Pa+

Pa+

j3
Pa+

j2
Ra+

j2
0000

Pa+ Si− Ra+ Oi+

q1

j1
Pa+ Si− Oi+

1101
q2

Figure 1. State transition diagram for the scenario
We now turn to the arguments that can be produced on the basis of Figure 1. Recall
that we are trying to explain how we reached q2 and say that first we assume that theprevious state is q1. There are two transitions from q1 to q2, one promoting three values
and one promoting two. We therefore have five possible instantiations of our abductive
argument scheme.
A1: q2 is explained by Ahab pushing Ishmael in q1 to reach q2 motivated by progress.
A2: q2 is explained by Ahab pushing Ishmael in q1 to reach q2 motivated by revenge.
A3: q2 is explained by Ahab pushing Ishmael in q1 to reach q2 motivated by oblivion.
A4: q2 is explained by Ishmael jumping in q1 to reach q2 motivated by progress.
A5: q2 is explained by Ishmael jumping in q1 to reach q2 motivated by oblivion.
These arguments can be now be the subject of critical questioning. CQ1 applies, attacking
all five of the above arguments. Answering CQ1a, we can say that it is possible that thepreceding state was q4 rather than q1. Thus we have:
Obj1a: The preceding state was q4, not q1.
This objection can be met with the following rebuttal:
Reb1: The preceding state was indeed q1.
Notice that here, we label the answer to the critical question as an objection. It is also
possible to answer critical questions that ask for another explanation (CQs 1, 4 and 5)
by providing an instantiation of the argument scheme, an alternative explanation. If wetake, for example, A1 as the current explanation, A4 and A5 are answers to CQ1b and if

we take A4 as our explanation, A1 – A3 are answers to CQ1b. So in virtue of CQ1b we
can see that A1 – A3 attack A4 – A5 and vice versa.
CQ2 does not apply because none of the transitions has a motive which both encourages
and discourages it at the same time.
CQ3 is important: the threat to Ishmael’s safety could be sufficient to deter Ahab frompushing and Ishmael from jumping. Thus we have Obj3a attacking A1 – A3 and Obj3b
attacking A4 and A5.
Obj3a: In q1 Ahab should not push Ishmael to reach q2 since it demotes Ishmael’s safety.
Obj3b: In q1 Ishmael should not jump to reach q2 since it demotes Ishmael’s safety.
CQ4 applies in that if we take, for example, A1 as the current explanation, A2 and A3
are answers to CQ4. So in virtue of CQ4 we can see that A1 – A3 all attack one anotherand A4 and A5 mutually attack.
CQ5 also can be posed. If, for example, the critical question is targeted at A1, the answer
to this question could be an argument that Ahab did indeed push Ishmael motivated byprogress, but hoped he would not fall off the bridge.
Obj5a: Ahab pushed Ishmael in q1 to reach q3 motivated by progress, but nature did notcooperate.
Obj5a attacks (and is attacked by) A1 – A5 because, even though it does not directly
explain q2, it does provide us with a reason for believing things went differently than is
postulated in A1 – A5.
We have one final objection to consider, which can be made if we accept Obj1a,
rather than taking it to be refuted by Reb1. Suppose that Ahab saw the situation as q4
rather than q1, perhaps because he thought a tram was about to hit Ishmael. He therefore
might have pushed Ishmael out of the way, hoping to reach q3, but unfortunately Ishmael
went off the bridge. Now Ahab’s claim would be:
Obj5b: Ahab pushed Ishmael in q4 to reach q3 motivated by safety, but nature did notcooperate.
This objection is a combination of CQ1 and CQ5, where first CQ1 is answered positively
and then CQ5 is also answered positively. Similar to Obj5a, Obj5b attacks A1 – A5, andalso attacks Obj5a.
We have identified a set of arguments and attacks between them, with each argument
associated with a motivating value. We now need to evaluate the status of the arguments.
To do this we form the arguments into a Value Based Argumentation Framework (VAF),
introduced in [3]. A VAF is an extension of the argumentation frameworks (AF) of Dung[7]. In an AF an argument is admissible with respect to a set of arguments S if all of its
attackers are attacked by some argument in S, and no argument in S attacks an argument
in S. In a VAF an argument succeeds in defeating an argument it attacks only if its value
is ranked as high, or higher, than the value of the argument attacked. In VAFs audiences
are characterised by their ordering of the values. Arguments in a VAF are admissible
with respect to an audience A and a set of arguments S if they are admissible with respect
to S in the AF which results from removing all the attacks which do not succeed withrespect to the ordering on values associated with audience A. A maximal admissible setof a VAF is known as a Preferred Extension (PE).

Obj5b

Obj5a

Ahab:
SafetyAhab:
Progress

Ishmael jumped
A4

A5

Ishmael:Progress

Ishmael:Oblivion

Reb1
state =
q1

A1

A2

Ahab:
Progress

Ahab:
RevengeAhabpushedIsmaelObj3b- Safety

Obj1astate =q4

Obj3a
- Safety

A3
Ahab:
Oblivion

Figure 2. VAF showing arguments, objections and rebuttals
Arrows between nodes denote attack relations. To improve readability, the ‘jumping’(A4 – A5) and ‘pushing’ (A1 – A3) explanations have been grouped together. This isrepresented by a rounded box around the respective arguments; the arrow between, forexample, Obj5a and the box surrounding A4 – A5 means that Obj5a attacks both A4 andA5 and vice versa.
Since we have a number of different orderings on values that yield different PEs, wehave a number of competing explanations which we must choose between. In order todetermine which of the arguments A1 – A5 is in the preferred extension, we must firstprovide an ordering on the motivations of Ahab and Ishmael which will allow one of ourarguments to resist the others. In this case, only the most preferred value is important.
We thus have the following possibilities:
1. ahab ∈ {R > {S, P, O}} (murder)
2. ahab ∈ {P > {S, R, O}} (manslaughter)
3. ahab ∈ {S > {P, R, O}} (he did not push)
4. ahab ∈ {O > {P, R, S}} (mercy killing)
5. ishmael ∈ {O > {S, P,}} (suicide)
6. ishmael ∈ {P > {S, O}} (sacrifice to let ahab pass)
7. ishmael ∈ {S > {P, O}} (he did not jump)
If we commit to such an ordering of motivating values, the arguments or objections
associated with the stronger motivation defeat the arguments and objections that rely on
one of the other motivations. This commitment to motivational orderings is important indifferent ways, depending on the phase of the case. In the investigation phase of a case,the assumed motivations of the actors will direct the search for evidence; in the decisionmaking phase, the assumed motivations can influence the decision of the judge or jury.
Examples of both these ways of using motivational orderings will be given below.
We may well think that the normal priority is 3 and 7. Normally people would notendanger the life of another to make progress, have no strong feelings of revenge andsee oblivion as something to be avoided rather than sought. If we indeed assume that S
is the most important motivation for both actors, the only possible acceptable argument
is Obj5b, because Obj3a and Obj3b would defeat A1 – A3 and A4 – A5, respectively.
For Obj5b to be in the preferred extension, however, we have to suppose that the preceding state was q4 and that Obj1a defeats Reb1. In other words, if there is evidence that
Ishmael’s life was indeed threatened by a rapidly approaching tram, we might believethat Ahab accidentally pushed him in the river in an effort to save him. This would be areasonable explanation, since it needs no unusual preference, but it does require evidence
for the tram, and it is unlikely that this would have been overlooked when the case wasprepared. A variant on Obj5b is saying that Ahab had a false belief: no tram was approaching but Ahab thought that Ishmael’s life was threatened by a rapidly approachingtram. This requires evidence that supplies reasons for why Ahab had the false belief, orvery convincing testimony from Ahab.
If, however, we assume the situation was indeed q1 and that Ahab was not justified
in believing the situation was any different from q1, we have to say that either Ahab or
Ishmael had an abnormal ordering of motivations4 . The question then is which of thethese abnormal orderings is the most plausible, and the role of the story is to explain why
the agent concerned can be thought to have this particular abnormal ordering.
In the example, it could have been the case that Ishmael preferred O to S or P to
S. The latter is implausible in the extreme: it is difficult to think of a story which would
explain why Ishmael would risk his own life in order to expedite Ahab’s progress. But
we are familiar with the fact that, in some exceptional circumstances, people are suicidal
and this does indeed lead them to prefer O to S. So a possible explanation is that Ishmael
preferred O to S and therefore jumped to his death (A5). While this is not an implausible
explanation, we would also want the story to be supported by evidence. So we will investigate further. We might find witnesses who heard Ishmael say that life was not worth
living since his wife left him, or we might find other circumstances, for example, that
Ishmael was bankrupt or terminally ill. Assuming that no such evidence can be found,however, this explanation must be abandoned: we cannot accept A5 with no evidence
for Ishmael’s suicidal state. So if the motivational orderings for Ishmael are not 5 and 6
then he must have the normal ordering 7. A4 and A5, the explanations in which Ishmael
jumped, are now defeated by Obj3b, which means that Ishmael did not jump, since hevalued his own safety.
If Ishmael did not jump, one of the explanations that Ahab pushed Ishmael must betrue. The question is now with which motivation Ahab did push Ishmael? One explanation assumes that both Ahab and Ishmael preferred O to S; so Ishmael wanted to die but
could not bring himself to jump so Ahab pushed him to facilitate his death. The problem
with this explanation – apart from the intrinsic implausibility that anyone would agree tosuch a scheme – is that it would need substantiation for Ishmael’s suicidal state. But thishas already been looked for and not found in connection with A5.
We next consider the ordering for Ahab in which R is preferred to S, that Ahab
pushed Ishmael because he wanted revenge (A2). This explanation is not implausible:
feelings of revenge, although normally of little impact, have been known to increase sufficiently to dominate a person’s thinking. The explanation will, however, have to be supported by evidence: for example, witness testimonies of people who heard Ahab threaten
Ishmael, or evidence that Ahab had been ruined by Ishmael. If no such evidence can befound, we should reject A2 and thus also reject a verdict of murder, which requires Ahab
to have killed Ishmael with murderous intent.
Another option is that Ahab preferred P to S: Ahab cared only about his own
progress and so he pushed Ishmael to his death to clear his way (A1). Again, however, weneed to justify the context. For example, assume that Ahab was in a rush to get to work;
4 The point that crimes invariably involve an abnormal or deviant motivation is made in [14].

his boss told him he would be fired if he was late for work. Ishmael was a co-workerof Ahab’s who for some reason had a score to settle with Ahab. Ishmael then decided
to hinder Ahab’s progress so that Ahab would be fired and Ahab pushed Ishmael to his
death because he did not want to lose his job. Here, Ahab’s culpability depends on therisk he took: if, as in A1, it was virtually certain that Ishmael died, Ahab could still be
prosecuted for murder, even though he did not explicitly wish for Ishmael to die.
It is also possible, however, that Ahab was merely reckless and that he pushed Ishmael to clear his way, not realising that Ishmael would fall from the bridge (Obj5a).
While Obj3a should have been sufficient to defeat Obj5a, it is not entirely implausible
to suggest that Ahab miscalculated the risk, and so this attack failed in practice to influence his reasoning. There were, after all safety barriers, although these proved too low
to be effective. Ahab is clearly at fault in that he did not take due account of the risk toIshmael, but the charge is now one of manslaughter rather than murder.

4. Concluding Remarks
In this paper we have shown how we can use an argument scheme for practical reasoning
abductively in order to generate a set of explanations for a given state of affairs in termsof the motivations of the agents who brought it about. Typically we will have competing
explanations which we can resolve by considering the priorities amongst motives of theagents concerned. If the normal default priorities do not explain the situation, we mustfind an ordering which does, and then justify this by means of a story which explains how
the agent came to have this ordering. This will in turn guide search for further evidence
to anchor this explanatory “back story”. Explanation in terms of motives is important,both to make our chosen story plausible and, in some cases, to determine the degree of
culpability of the agents. We have thus given motivations a clear and separate place in evidential reasoning about actions. This distinction has been recognised in other work suchas [8], where a formal treatment is proposed. There Modgil defines a framework in whichconflicts over value orderings are reasoned about at a separate meta-level. This meansthat conflicts between arguments may be resolved through reasoning about preference
orderings at a different level, resulting in a hierarchical argumentation framework. Fora rule based treatment in the style of [5], the need for meta-level reasoning will require
rules of an additional kind which allows us to conclude that an agent has a particularvalue preference, such as if Ishamael ruined Ahab then Ahab prefers Revenge to Safety.
Our approach is firmly grounded on a formal structure provided by an AATS. The
AATS makes the underlying model of the stories less ad hoc than in previous approaches
which rely on a set of rules. In addition, when compared to [5] the problem formulation
critical questions in [4] give us a better opportunity to reason about the causal model underlying the story. A disadvantage is perhaps that the causal rules are not as explicit as in[5], since the causal relations are now implicit in the transition system. We believe, however, that the possibilities for richer reasoning about motivation more than compensates
for this.
For future work we intend to apply the above analysis to provide a rule based representation so as to facilitate computation. Taking as a starting point the rules found in[5], we will need three kinds of rules: rules describing physical causation, such as “If q1
and Ahab pushes Ishmael then Ishmael is in the river”; rules to describe motivation “Ifq1 and Ahab pushes Ishmael revenge is promoted”; and rules to determine value preferences such as that mentioned above to explain why Ahab prefers revenge to safety. The
first kind can be straightforwardly derived from the AATS: each transition represents one
such rule. The second kind can also be extracted from the AATS: each label on a transition represents one such rule. The third kind of rule is not present in the AATS, sincethese rules belong to the meta-level reasoning associated with the VAF: these rules will
require the kind of analysis we used in determining the appropriate audience to use for
Ahab and Ishmael. An excellent case to which these ideas can be applied is the Claus von
Bülow case which is described by Thagard in [11]. There Thagard gives a full description of the case as well as representations of the cases presented at both the initial trial
and the appeal. Using this example will allow direct comparisons with the Explanatory
Coherence and Bayesian Network approaches used by Thagard, as well as the approachof [5].

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