When Pascal is finally apprehended, he is charged with murder and found guilty by the lower courts as well as on appeal. A hybrid argumentative-narrative theory In this section, we will discuss the argumentative and narrative approaches before proposing our hybrid combination. Additionally, the discussion below will also focus on the use of various types of commonsense knowledge expressed as schemes. Reasoning with evidence involves a large amount of commonsense knowledge about the world around us, which allows us to assume or infer new information in a way that is as safe as is needed in the context.
In this paper, we show that in the argumentative approach commonsense knowledge often takes the form of argumentation schemes Walton et al. Argumentative Approach In the argumentative approach, arguments are constructed by performing consecutive reasoning steps, starting with one or more items of evidence and reasoning towards a conclusion, a fact at issue in the case. The reasoning steps in these arguments have associated generalizations that justify the inferences cf.
This intermediate conclusion can then be used to infer that it was indeed Pascal who was in the car. Thus lines of reasoning can be combined to construct argument trees, which can be rendered as diagrams Freeman ; Reed et al. Take, for example, Figure 1. The argument in Figure 1 uses typical generalizations, such as the above-mentioned generalization about witnesses, to justify the inferences. These generalizations can be rendered as argumentation schemes; for example, consider the scheme for Argument from Witness Testimony Walton et al.
Witness w is in a position to know whether a is true or not. Witness w asserts that a is true false. Therefore , a may plausibly be taken to be true false. In addition to these general schemes, more case- specific generalizations are also used as inference licences in Figure 1. In the argumentative approach, the individual facts at issue are supported by the evidence in the case through arguments. The argument-based approach is inherently dialectical: The critical questions associated with the argumentation schemes in the arguments are a useful aid here, as they point to ways in which an argument based on a scheme can be attacked Bex et al.
Take, for example, the critical questions for the Witness Testimony scheme: Was w is a position to know a? Is a consistent with what other witnesses say? These critical questions give pointers on how and where an Argument from Witness Testimony might be attacked. For example, the third question asks if there is an exception to the general scheme i. Question 5 is interesting in that it asks for the inherent plausibility i. We will return to this inherent plausibility when we discuss stories and story coherence below.
The argumentative approach is a dialectical way of reasoning with and about the evidence in a case. Argumentative reasoning has been called atomistic because the various elements of a case i. The approach builds on a significant academic tradition of research on informal and formal argumentation and is well suited for a thorough analysis of the individual pieces of evidence and the inferences that can be drawn from them, using critical questions to probe the arguments for possible weak spots.
However, the atomistic nature of arguments makes them less suitable for giving an overview of the various hypothetical scenarios about what happened in the case. The Narrative Approach In the narrative approach, the facts of the case are organised into one or more stories: In this approach, the evidential data in the case should be causally explained by such hypothetical stories through abductive inference. The basic idea of abductive inference see e. This cause c which is used to explain the effect can be a single state or event, but it can also be a sequence of events, a story.
Take, as an example, the observation that Nadia is dead. The arrows in the story-diagram in Figure 2 represent causal relations whereas the arrows in the argument diagram in Figure 1 represent inferential relations and thus the events in the story causally explain the evidence in the case.
Abductive inference is a creative process, in which we use patterns of commonsense knowledge combined with observed evidence to form a number of hypothetical scenarios. One aid in the abductive process is so-called story schemes , general patterns of events that can serve as a background to particular stories.
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More specific schemes were given by Schank , who defines a number of explanation patterns which may help in explaining events or states by connecting an event to an explanation that has been used to explain similar events before. In the Nadia example, the murder scheme may be used to abduce a possible story from the observation that Nadia is dead. The motive m would then be the disagreement and the weapon w a gun.
Taken by itself, abductive reasoning can seem to take the form of the fallacy of affirming the consequent. However, the apparent fallaciousness disappears if we consider abductive reasoning in the broader context of inference to the best explanation IBE: The choice between these alternative stories depends on how well the individual stories explain the evidence and how coherent Thagard each of them is.
The coherence of a story largely depends on whether the story conforms to our general commonsense knowledge of the world, that is, whether we deem the story to be inherently plausible i. Here, story schemes play an important role see Bex For example, a story is not sufficiently coherent if there are parts missing; the murder story scheme mentions motives m and a weapon w and any murder story that does not explicitly mention a motive or a weapon will be incomplete and hence less plausible.
Furthermore, the causal relations in the story scheme can be used to draw out the implicit causal relations in the story based on the scheme; in the murder scheme, the motive causes the action i. Thus, the causal links can then be further examined and questioned. The narrative approach is a causal, dialectical way of reasoning with hypothetical stories that explain the evidence in a case. Clearly, this reasoning is defeasible, since additional evidence might give rise to new explanations.
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Furthermore, the narrative approach has been characterized as holistic as opposed to atomistic , because the stories allow the elements in a case i. An important advantage of the narrative approach is that it is close to how legal decision makers actually think about a case. Experiments by Pennington and Hastie suggest that when reasoning with a mass of evidence, people compare the different stories that explain the evidence instead of constructing arguments based on evidence for and against the facts at issue as is done in the argumentative approach.
Furthermore, it is not always clear how one should reason about the coherence of a story and how stories should be compared. The Hybrid Approach Both the argumentative and the narrative approach concern reasoning about the facts and the evidence: The argumentative approach, which builds on the philosophical tradition of argumentation, is well-suited for an analysis of the individual pieces of evidence, whilst the empirically-tested narrative approach is appreciated for its natural account of crime scenarios and causal reasoning. Conversely, the atomistic nature of arguments makes them unsuitable for giving an overview of the various hypotheses about what happened in the case and not all aspects of causal reasoning can be found in the argumentative approach.
In the story-based approach, the individual evidence does not have a clear place and its credibility and relevance cannot be checked easily. Arguments and stories therefore need to be combined into one hybrid theory , where facts are organised into stories and arguments based on evidence are used to support these stories. In other words, a story such as the one in Figure 2 should be anchored in evidence using arguments such as the one in Figure 1, viz.
In Figure 3 adapted from Wagenaar et al. Thus, both arguments and stories and their respective schemes have a clear place in the hybrid theory. The hybrid approach solves one of the most important issues with the narrative approach as, for example, described by Wagenaar and colleagues , namely that often the connection between the evidence and the stories is not made clear. In the hybrid approach, stories can be firmly anchored or, in other terms, evidentially supported.
Note that stories can also be evidentially contradicted using arguments. For example, an argument based on a witness statement saying that Pascal was in Poland when the shooting took place contradicts the above story. Aside from anchoring stories in evidence, the hybrid approach also makes it possible to reason about the coherence of a story in a dialectical way, as arguments can be given for the in coherence of a particular story or one of its sub-stories.
In the hybrid theory, stories can be used for constructing intelligible hypotheses about what happened in an intuitive way and arguments can be used to connect the evidence to these stories and to reason about the stories and the evidence in greater detail. In the next section, we will discuss how an anchored story i.
Critical questions for the hybrid theory: These critical questions can be used to unearth sources of doubt in a total case i. In this section, we will list these critical questions and give some examples. CQ1 Are the facts of the case made sufficiently explicit in a story? The starting point of a well-supported opinion about the facts is a concrete story about what happened, that is, a clear and sufficiently specific chronological account of what might have happened in a criminal case.
By presenting the story separately from any arguments about its plausibility and the evidence, the coherence of the story can be best appreciated and investigated. In a sense, one can say that this story is the conclusion of the argument about the case-as-a-whole cf. Which stories can be the conclusion of a legal verdict is often restricted by formal constraints; for instance, in the Netherlands the factual account of a conviction should match the indictment presented by the prosecution.
Nadia and Pascal had a disagreement about a washing machine and Pascal decided to kill Nadia. He called his work to report in sick and grabbed his Uzi, a small machine gun he had in his room. Pascal then shot Nadia twice, dragged her to the kitchen and killed her by shooting again at close range. CQ2 Does the story conform to the evidence? Is the story sufficiently supported by the evidence in the case? Is the story contradicted by evidence in the case? A key step is the identification of the evidential support that can be given for the elements of a story, that is, identifying the sources of evidence that support the story.
In the Nadia case, many events in the story are explicitly supported by evidence: This list of evidence is taken directly from the verdicts, where they are largely listed in chronological story order [v]. In general, not all elements of a story can be supported by evidence. This does not need to be a problem, and is in fact unavoidable as certain story elements must by their nature be indirectly justified. In sum, CQ2 has been satisfactorily answered. The existence of evidential gaps, here conceived of as parts of a story for which no direct evidence [vi] is available, is one reason why a mixed-argumentative narrative perspective can be useful.
The analytical argumentative perspective makes the evidential gaps visible, the narrative perspective shows why the evidential gaps can still be believed in conjunction with other facts. In general, it is a matter of good judgment which elements of a story must be directly supported by evidence and which can be inferred from other facts. This depends in part on the quality of the evidence a story supported by weak evidence can become stronger by providing evidence for more facts , but also on the nature of the crime and the law.
In addition to looking at how much of the story is supported, one should also consider how much of the total evidence in the case supports the story. If, for example, a story is completely supported by 2 witness testimonies but there are 20 more witnesses who state another incompatible story, the story does not sufficiently conform to the evidence in the case even though there are no gaps in it.
Furthermore, one should also take into account the amount of evidence that directly contradicts a story; instead of giving an alternative story see CQ5 below , the opposing party may simply deny elements of the main story. For example, in the Nadia case the defence might have witnesses that state that there was never a disagreement and that Pascal and Nadia were good friends. In this case, however, such arguments were not made and we turn to the next critical question.
CQ3 Is the support that the evidence gives to the story sufficiently relevant and strong? Are the reasoning steps from evidence to events in the story justified by warranting generalizations and argument schemes that are sufficiently strong and grounded? Are there exceptions to the use of the generalizations and schemes that undermine the connection between evidence and fact? In order to determine relevance and probative force of a piece of evidence, the generalizations and schemes warranting the inference steps should be made explicit. Thus it can, for example, become clear that the generalization is false and cannot be the basis for a good reasoning step.
In general it will therefore be important to determine whether and, if so, on which grounds a generalization is considered to be valid i. For example, the witness testimony scheme can be grounded in the law e. Schemes or generalizations can have other sources than the law [vii]: Such generalizations are necessary but also dangerous Twining , as they might express implicit biases or prejudices we hold e.
In the example of the murder of Nadia, we see that most reasoning steps are based on plausible generalizations and schemes. Perhaps the use of scent tests as a basis for drawing conclusions is the most controversial [viii]. If we consider criticism concerning scent tests as a forensic investigative procedure as well founded, then we must conclude that scent tests cannot be used to support conclusions CQ3a. With respect to most of the listed pieces of evidence, we need not assume that there are exceptions to the underlying generalizations or schemes CQ3b and we can infer the events of the story supported by the evidence.
Now that we have considered critical questions 1, 2 and 3, we are in the following position: The argument about the case as-a-whole can be further improved by showing that the story is plausible in itself. CQ4 Has the story itself been sufficiently critically assessed? Is the story sufficiently coherent? Are there required elements missing? Are there implausible events or causal relations? Is the story inconsistent? Have story consequences been used to test the story?
Here coherence has a specific meaning, namely that the story fits our knowledge and expectations about the world we live in. Unexpectedly, a direct match was found, leading to the arrest of a then year-old suspect. The suspect had voluntarily participated in the screening. John was convicted to 18 years imprisonment for rape and murder. By the following properties, the selected case can be used for the comparison of the three normative frameworks for evidential reasoning:.
Probabilistic and non-probabilistic information. During the investigation, both probabilistic and non-probabilistic information is used. During the investigation of the case, different possible scenarios about what has happened are considered. In the selected case, three hypothetical scenarios can be distinguished: Arguments for and against events and scenarios.
In the investigation, events and scenarios are both supported and attacked by arguments based on the evidence. Arguments against the scenarios that one of the two asylum seekers from Iraq and Afghanistan committed the crime were based on DNA evidence that led to the exclusion of the two asylum seeker scenarios. Using elements from the running example, we now illustrate the essence of the three normative perspectives on reasoning with evidence: An argumentative approach starts with the evidence e.
In the following, the example arguments in Fig. Evidential arguments A 1 , A 2 , A 3 that attack each other. Such an argument is defeasible, and can for instance be attacked in case of a low prior probability cf. Simple arguments can be chained and combined—e. As such, the argumentative approach focuses on how specific, single conclusions are based on the evidence. The inferences in an argument are made using evidential inference rules of the form e is evidence for c , which act as a warrant for the inference cf.
Such inference-warranting rules can range from very general—e. Argumentation schemes can be used to determine whether an argument has all its necessary elements. If we now have an argument based on expert opinion which does not indicate that p was an expert—e. Therefore we can believe x.
Person p is an expert on x. In the argumentation literature, it is understood that arguments based on argumentation schemes are typically subject to exceptions, and do not guarantee the conclusions based on them under all circumstances. It is, therefore, customary to define for each argumentation scheme some typical sources of doubt.
These doubts, when phrased as critical questions, can then be used in the adversarial process of reasoning with evidence to probe and test the arguments. For example, a critical question for the expert opinion scheme is: The critical questions point to an important feature of argumentation, namely that it is adversarial or dialectical: These counterarguments can have an opposite conclusion—we say that two such arguments rebut each other.
Consider the example in Fig. From the premise that an asylum seeker molested Mary we can infer that it was not John who molested Mary assuming that Mary was not molested by both the asylum seeker and John together. Thus, arguments A 1 and A 2 in Fig. Arguments can also be countered by an argument that gives an exception to the evidential rule that was used. However, if the DNA sample was tainted by being handled improperly, we can argue that in this case we have an exception to the general reliability of DNA profiling, and that we cannot reasonably say something about the source of the trace on the basis of this evidence.
In such a case, we say that one argument undercuts another: When arguments can attack each other, it is not always clear which conclusions follow from them. The arguments in Fig. If we only consider A 1 and A 2 , we have a conflict of arguments that is not resolved: No clear conclusion follows about the issue whether John molested Mary or not.
If it now turns out that the DNA sample was tainted A 3 , the conflict is resolved, since A 2 does no longer support that John molested Mary. In that case, given the arguments in Fig. The evaluation of arguments that combine support and attack has been extensively studied in the literature. These formal and computational models build on the influential work by Pollock on defeasible argumentation and Dung on argument attack Pollock, , ; Dung, see van Eemeren et al. The scenario approach to evidential reasoning, also called the story-based or narrative approach, stems from legal psychology Bennett and Feldman, ; Pennington and Hastie, ; Wagenaar et al.
It has only relatively recently been further specified in both a formal setting Bex et al. This approach focuses on scenarios or stories about what happened in a case e. Two scenarios S 1 , S 2 from the example case explaining evidence. Like the argumentative approach, the scenario approach has an adversarial element: Assuming that John and the Iraqi man did not kill Mary together, the alternative scenario contradicts the main scenario in the case.
An alibi scenario e. John could not have been both at home and at the scene of the crime at the same time. As mentioned before, the scenario approach is a kind of inference to the best explanation Josephson and Josephson, ; Pardo and Allen, In addition to the explanatory power of stories, it is also possible to use stories to predict the possible existence of certain evidence.
Thus, the search for evidence is guided by the hypothetical scenarios considered: This shows how causal scenarios can be used to both explain and predict evidence. In inference to the best explanation, the objective is to consider the alternative scenarios and ultimately select the scenario that best explains the evidence. The question to be answered is: Pennington and Hastie provide several criteria for judging scenarios. The most important one, which is also standard in logical definitions of inference to the best explanation Josephson and Josephson, , is evidential coverage: In addition to looking at how well a scenario covers the evidence, it also makes sense to consider what Pennington and Hastie call the plausibility of a scenario irrespective of the evidence: Bennett and Feldman, ; Anderson et al.
Furthermore, elements which are implausible at first sight might warrant further investigation: This is not normal behaviour for a man like John. Finally, judges or jurors are often also forced to fill gaps in the scenario using their own knowledge. For example, except in case of a confession, there is often no direct evidence for the fact that a killing was premeditated. In Dutch law, however, it is often accepted that the action was premeditated if it can be made plausible that, given the circumstances i. A notion related to the plausibility of scenarios is that of scenario schemes—also called story schemes Bex, or scripts Schank and Abelson, —which are stereotypical patterns that serve as a scheme for particular scenarios.
For example, Pennington and Hastie use a general scenario scheme for intentional action: More specific scenario schemes may be instances of such a generic scheme: The double arrows indicate abstraction relations. In the figure, the most abstract scheme is the intentional action scenario scheme; the murder scheme is a specialization of this more general scheme, and the scenario S 1 is an instance of both the murder scheme and the intentional action scheme. While the plausibility of the individual causal generalizations also play a significant part in causal reasoning, scenario schemes are used for capturing the global coherence of scenarios Section 1.
To determine whether a scenario is plausible and coherent, we can see whether it fits with well-known scenario schemes or whether any elements are missing. For example, a murder scenario with a missing motive is incomplete, and therefore less coherent: Influenced by the rise of DNA profiling and by some high profile miscarriages of justice, probabilistic approaches to reasoning with evidence remain a focus of study Dawid et al. Proposals and applications go back to the early days of forensic science Taroni et al. The role of probabilistic reasoning remains an issue of debate, cf.
It was estimated that the probability that the DNA profile of a random male matches the DNA profile of that blood trace was about 1 in billion billion, i. Let us assume that there is a population of other males than John that could have murdered Mary say, the local population , and that each of the males considered has equal probability of being the source of the DNA.
Often, assumptions need to be made about probabilities—resulting in subjective probabilities—to be able to perform the relevant probabilistic computations. For example, we here use the number , as that was roughly the number of men that were asked for a DNA sample, because they were living in the area and were within reasonable age limits. A probability function can be represented as a Bayesian network. A Bayesian network consists of an acyclic directed graph with the variables of the probability function as nodes. Figure 5 shows the graph of a Bayesian network for the hypotheses and evidence discussed above, and Table 2 the associated conditional probability tables for each node.
A choice was made to capture the hypotheses H 1 and H 2 by means of separate boolean nodes in the graphical structure, rather than as values of one single node. Conditional probability tables for the Bayesian network in Fig. The number 0, bottom right in the second table, is the probability P H 2 H 1 that someone else is the source given that John is the source. Some values in the third table concern combinations of parents that cannot occur. We have entered the probability of the outcome given those situations as 0.
From a Bayesian network, any prior or posterior probability of interest can be computed. Various software tools for working with Bayesian networks exists, such as GeNIe dslpitt. In a Bayesian network structure, the arrows contain information on the in- dependencies in the model. From the graph, it can be read whether there is possibly an influence between two variables A and B. However, the existence of such an influence can change as a result of instantiating nodes in the network. In Bayesian network terminology, d-connectedness and d-separation are the terms used to express whether there is a possible influence between nodes A and B.
Whether nodes are d-connected or d-separated depends on whether there is an active chain between these nodes. Variables are d-connected when there is an active chain and when there is no active chain, the variables are d-separated. Suppose three variables A , B and C are connected via a serial connection: This is an active chain, and A and B are d-connected. However, as soon as C is observed, the chain is blocked and if no other active chains remain, A and B are d-separated.
Similarly, when A and B are connected via C with a diverging connection: As soon as C is instantiated, the chain becomes blocked and when there are no other active chains between A and B , they are d-separated. A special situation arises when A and B are connected via C with a converging connection: This is also called a head-to-head connection.
As opposed to the previous situations, this chain is inactive as long as C and all descendants of C have not been observed. When there are no other active chains between A and B , this means they are d-separated. As soon as C or a descendant of C is instantiated, the chain becomes active and A and B are d-connected.
As an example of a converging connection, consider a structure with only three nodes in which A and B are alternative causes for a shared effect C. For example, let A , B and C be as follows: As long as C wet grass has not been observed, the two causes are d-separated and they have no influence on each other.
When C is observed the grass is wet , the two causes become d-connected, which can be understood as follows: Even though Bayesian networks need not be causally interpretable in general, such an effect between parents of a common child is referred to as an inter-causal interaction. This particular example is a very common type of inter-causal interaction called explaining away. Our thinking about the connections between different approaches to evidential reasoning started by comparing and connecting scenarios and arguments.
In the research on legal theory and legal philosophy, there seemed to be two clear, competing approaches. The second is the narrative approach Pennington and Hastie, ; Wagenaar et al. Both the argumentative approach and the scenario-based approach can be separately applied to a case, and each of the two has their own advantages and disadvantages, as was also shown in Table 1.
The argumentative approach is positioned in a formal dialectical framework Dung, for adversarial reasoning and it is expressive enough to capture the different aspects of evidential reasoning Bex et al. Furthermore, it has been argued that when given e. The scenario approach captures the causal elements of a case e.
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While a standard formalization of scenario-based reasoning is perhaps lacking, this type of reasoning can be captured by logical formalizations of model-based abductive reasoning see, for instance, Josephson, Such formalizations use causal rules to model the scenarios, which are then compared on basic criteria such as the minimum number of assumptions. Because these frameworks were originally intended for automatic diagnosis within bounded and pre-defined domains, they are less suited for modelling more open-ended and complex large criminal cases Prakken and Renooij, ; Bex, For example, in purely scenario-based approaches, it is not possible to critically discuss the elements of the scenarios themselves; while in argumentation one can give a reason for an inference warrant, it is impossible to give a reason for a causal relation in a scenario.
Because both the scenario- and the argument-based approach have their own advantages and disadvantages, a combination of the two seems to be an intuitive and analytically useful perspective. Hence, in Bex et al. In the hybrid theory, causal-abductive scenario-based reasoning is combined with a general argumentation framework for evidential reasoning. Furthermore, arguments also allow us to draw further legal conclusions from scenarios. Below, we will briefly discuss the formal hybrid theory Bex et al. Arrows with open arrowheads stand for evidential inferences, and arrows with closed arrowheads stand for causal relations.
The hybrid theory consists of a set of evidence E , a set of hypotheses H and a set of inference rules R of the form r i: Note how these rules are specific in the way in which they force any scenario based on them to be about Mary. This is not a problem, as the identity of the victim and what happened to her were not an issue in this case.
The issue was exactly who the perpetrator person p was: We can now define how arguments and scenarios can be combined. We say that an argument supports a scenario, if the conclusion of the argument is an element of the scenario and the argument itself is not defeated by another argument.
An argument attacks a scenario, if the conclusion of the argument is the negation of an element of the scenario and the argument itself is not defeated by another argument. To this end, scenario schemes are defined that can be used for the construction of hypothetical stories. As an example, take the scenario scheme for murder ss 1 which was also mentioned in Fig. Even though the causal links are left implicit, we still have a fairly coherent if overly generic scenario. Recall from Section 2. These same abstraction links, which are of the form r i: Using these rules we can infer e.
Notice how the evidential arguments support the relevant sub-scenarios, including the application of the causal rule r 5 c. Given alternative scenarios such as S 1 and S 2 , the question is now how to compare them. In Bex , a number of criteria for comparing scenarios are given. An important one is evidential coverage , the portion of the evidence in a case that supports the scenario see also Section 2.
In the example in Fig. Related to evidential coverage is evidential contradiction , which is the portion of the arguments based on evidence that contradict a scenario. Note that the two evidential criteria do not give an absolute measure of how good or strong a scenario is. However, the coverage and contradiction can be used as relative measures to compare scenarios and guide the search for further evidence; if a plausible position has low evidential coverage it might make sense to search for evidence that supports the position.
Another way to compare scenarios is by looking at their coherence irrespective of the evidence in a case. In other words, is the scenario plausible given our general knowledge about the world? Here, scenario schemes play an important part, as we have to look whether the scenario fits a particular scheme, and whether that scheme is a plausible generalization of how things normally happen in the world. In the example case, some could say that the asylum seeker scenario is prima facie more plausible than the scenario about John: John is known as a family man in the village, whereas the asylum seekers came from conflict areas and might be traumatized, causing them to act out violently.
This reasoning also demonstrates the danger of scenarios and scenario schemes, because they often appeal to certain stereotypes. We should, therefore, be careful with drawing conclusions from scenarios that have no evidence to back them up. While developing the hybrid theory, we saw many similarities to argumentative thinking in the work by Wagenaar et al. Moreover, it was obvious that practitioners in the field investigators, fact-finders, lawyers seemed to naturally combine argumentative and scenario elements in their work. Finally, causal and evidential reasoning are closely entwined: Thus, it seems that causal scenarios and evidential arguments are not two separate approaches, but rather two sides of the same coin.
As an example, consider the different ways in which the inferences and attacks surrounding DNA evidence can be captured. One way to do this is to use an evidential rule, like in Fig. However, we can also say that the DNA match was caused by John being the source of the traces, changing the reasoning from evidential argumentation to causal scenario-based reasoning. The attack is then captured as an alternative explanation of the DNA match evidence: This shows that there is a clear link between alternative explanations and attacking arguments, a link which has recently been formalized in Bex Reasoning about the DNA match evidence modelled as two attacking arguments left or as two alternative conflicting scenarios right.
Above we have summarized a formal model connecting arguments and scenarios in evidential reasoning. Strengths and limitations of the proposal include the following:. The proposal shows how reasoning with arguments can be formally combined with reasoning to the best explanatory scenario.
The formalization is based on argumentation formalisms and these are as yet not standardized nor well connected to standard theories, such as classical logic and standard probability theory. The combination of arguments and scenarios in Section 3 makes it possible to construct arguments to support scenarios and to reason about the internal coherence of scenarios. However, it is impossible to reason about degrees of uncertainty in that approach, whereas due to the importance of DNA evidence such reasoning is needed. For instance, the method from Section 3 does not distinguish between strong evidence and weaker evidence, when comparing alternative scenarios.
In this section, the connection between scenarios and probabilities is discussed. The probabilistic framework of Bayesian networks allows for modelling degrees of uncertainty concerning the evidence, which makes it possible to incorporate the strength of evidence in a decision. In what follows, we will discuss how a scenario can be modelled in a Bayesian network such that the key properties of a scenario are represented probabilistically. The elements of a scenario together form a coherent whole. As a consequence of coherence, scenarios can be used to reason about hypothetical events for which there is no direct evidence Tillers, This needs to be captured probabilistically to model scenarios in a Bayesian network.
Reconsider the scenario about John molesting and killing Mary. Suppose that there is evidence to support that John was the molester, but no evidence to support that he was the killer in the real case this was more or less the situation after the DNA screening but before John confessed. In this situation, John killing Mary is an evidential gap in the scenario.
Despite the evidential gap, this scenario can still be used to reason about the killing. When reasoning with evidential gaps as described above, our degree of belief in one element of the scenario namely, that of John killing Mary increased because other elements of the scenario became more believable as a result of the supporting evidence.
This is called transfer of evidential support , and this is what we aim to capture in a Bayesian network model of a scenario: To capture scenarios and their coherence in a Bayesian network, we have proposed the use of idioms. An idiom is a general structure that can be used as a building block in a Bayesian network, simplifying the task of constructing a network structure. The idea of such recurrent substructures for building legal Bayesian networks was proposed by Hepler et al.
The concept is similar to the concepts of argumentation schemes and scenario schemes Section 3 , in which typical patterns of arguments and scenarios, respectively, are modelled. However, idioms are less context dependent than argument and scenario schemes, and can be used as building blocks throughout various cases. Both idioms were previously described by Vlek et al.
The scenario idiom and the subscenario idiom capture coherence of a scenario, possibly with subscenarios. As discussed in Section 4. In the scenario idiom Fig. Considering that the scenario node itself is never observed, these arrows ensure an influence between elements of the scenario needed to capture the transfer of evidential support as discussed in the previous section via the scenario node.
The scenario idiom a and the subscenario idiom b. Double arrows signify that the underlying probabilities are partially fixed as shown in the table. Dashed arrows show some possible connections. The scenario node represents the scenario as a whole. The probability table of the scenario node thus requires a prior probability for the scenario being true.
Furthermore, due to the nature of the scenario node, representing the scenario as a whole, there is a special relation between the scenario node and each element node, signified by double arrows in Fig. The intuition is the following: Because of this, some numbers in the probability table of each element node are fixed: With these probabilities, the transfer of evidential support is captured, since in the absence of other influences an increased belief in one element of a scenario will lead to an increased belief in the scenario node, which in turn yields an increased belief of all other element nodes.
With the scenario idiom, the scenario about John can be modelled as shown in Fig. Due to the structure of the scenario idiom and the probabilities as specified in the table of Fig. This means that, as was described in Section 4.
The subscenario idiom builds upon the same ideas as the scenario idiom, but also captures the internal coherence of a subscenario. To model a coherent subscenario within a scenario, a subscenario node is used to represent the subscenario as a whole, and arrows with probabilities fixed similarly are drawn from the subscenario node to all elements in that subscenario as shown in Fig. Again, transfer of evidential support within a subscenario is guaranteed.
With the scenario and the subscenario idioms, it becomes possible to gradually construct a Bayesian network for a case see Vlek et al. To construct a network, we rely on the concept of unfolding which was already mentioned in Section 3. A scenario can be told at various levels of detail, and elements of a scenario can be unfolded into more specific subscenarios when needed.
The construction process starts with an initial scenario such as the one from Fig. The node itself now serves as a subscenario node, and the events of the subscenario are attached to that subscenario node. This process is repeated to gradually construct a Bayesian network with the required level of detail. To summarize, the approach described in this section has the following strengths and limitations:. We have combined scenarios and their global coherence with degrees of uncertainty by showing how scenarios can be embedded in Bayesian networks, a prominent probabilistic modelling tool.
In the approach, we captured the concepts of coherence and transfer of evidential support probabilistically. The approach inherits a standard criticism associated with Bayesian networks: Bayesian network models including scenarios are large and complex, so explaining their meaning to fact-finders and forensic experts is a further challenge.
We have already seen argumentation and Bayesian networks in two different contexts now. Argumentation has been introduced as a method to support or attack events and causal links in a scenario-based model of evidence. These scenario models have been shown to be useful during the construction of Bayesian networks. There is, however, also a more direct connection between Bayesian and argumentative models of proof.
We will proceed by describing some of the characteristics of both models and how these two formalisms can be used together.
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Specifically, we will show how arguments can be grounded using rules that can be extracted from a Bayesian network. Figure 12 shows a global outline of the approach. We make an automated translation from information in a Bayesian network to arguments that are structured hierarchically.
The constructed arguments could, for instance, be used to support steps in a narrative model but this is not necessarily the only possible application. The following method is based on Timmer et al. To understand how we can extract arguments from a Bayesian network we must first identify what characteristics of probabilistic reasoning we would like to be able to capture.
Bayesian networks represent a joint probability distribution and as such can be a probabilistically accurate representation of the facts in a legal case. However, the structure of a Bayesian network is made to represent independence information through d-separation rather than inferential steps such as in many argumentative models.
This mismatch in interpretation is what makes Bayesian network models less ideal for communication to legal experts such as lawyers and judges. The arrows in the Bayesian network convey statistical correlations and not necessarily causal relations. The directions of the edges contain information on the in- dependencies in the model. As an illustration of the method we apply our argument construction method to the example introduced in Fig.
These two hypotheses can both individually cause a particular outcome of the DNA matching test. Because the two hypotheses are modelled—exactly for this reason—as parents of the evidence, finding one of them to be true explains the other away.
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If John is the source, then, likely, nobody else is and, vice verse, if another person is the source of the sample, John cannot be the source. The use of defeasible reasoning is particularly useful in combination with probability theory because statistical inferences are also not strict but merely suggest an elevated belief in some statements. In particular, the concept of undercutting has a striking resemblance to the concept of explaining away in Bayesian networks. An alternative explanation can provide a context in which the statistical inference is not applicable.
In defeasible reasoning sometimes a rule that is in principle valid can not be applied to a premise, due to some exceptional circumstances. These circumstances are then called undercutters of the rule. In a probabilistic setting, an explaining away provides a similar mechanism. This also resembles the way in which alternative explanations in scenarios are linked to attacking arguments as we discussed in Section 3.
A natural definition of negation follows from the fact that assignments for a node are mutually exclusive; all mutually exclusive assignments to a variable negate each other. We extract defeasible rules from the Bayesian network by looking at a probabilistic measure of inferential strength. We enumerate candidate rules and assign strengths to them according to the so-called normalized likelihood. A number of different measures of strength have been introduced in the literature, and, while they often vary in exact numerical valuations of inferences, for many of these measures the resulting strength ordering on rules is proven to be the same see Crupi et al.
Since we are going to use the measure of strength only to compare inference rules any of these will do. We construct a set of accepted rules R d of all rules with a strength greater than one. This is not an arbitrary threshold but a fundamental one. Since even rules with a strength slightly greater than one have a positive effect on the conclusion. This choice means that we accept every rule, however weak it may be. If the strength equals one, then the premises are independent of the conclusion and if the strength is below one the premises actually have a negative effect on the conclusion.
In the latter case, another rule with the opposite conclusion will automatically have a positive strength. This is necessary because the rules have a counterfactual character. When some evidence is present, we have to speculate on what would have happened if it had not been the case, to be able to say something about the correlation of the evidence with other variables.