Towards a Formal Account of Reasoning about Evidence:
Argumentation Schemes and Generalisations
FLORIS BEX1, HENRY PRAKKEN12, CHRIS REED3 AND DOUGLAS WALTON4
1

Institute of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands.
{fjbex,henry}@cs.uu.nl
2Faculty of Law, University of Groningen, Groningen, The Netherlands
3
Division of Applied Computing, University of Dundee, Dundee DD1 4HN Scotland.
chris@computing.dundee.ac.uk
4
Department of Philosophy, University of Winnipeg, Winnipeg, Manitoba, R3B 3E9 Canada.
d.walton@uwinnipeg.ca

ABSTRACTThis paper studies the modelling of legal reasoning about evidence within general theories of defeasible reasoning andargumentation. In particular, Wigmore’s method for charting evidence and its use by modern legal evidence scholars is
studied in order to give a formal underpinning in terms of logics for defeasible argumentation. Two notions turn out tobe crucial, viz. argumentation schemes and empirical generalisations.

1.
INTRODUCTION
This paper addresses the formal modelling of legal reasoning about evidence within general theories
of defeasible reasoning and argumentation. In AI & Law evidential reasoning is a little studied topic.
Of the few studies that have been made, some zoom in on specific aspects, such as Lutomski (1989)
on reasoning with statistical evidence, and Bromby & Hall (2002) on the credibility of eyewitness
testimonies. Other research takes its starting point in mathematical or computational models, such asprobability theory (e.g. Jøsang & Bondi, 2000) or model-based reasoning for automated diagnosis(e.g. Keppens & Zeleznikow, 2003). We instead follow a more cognitively inspired approach, aiming
to stay close to the evidential reasoning forms used in practice. Thus we hope that our approach
might better lead to practically useful software applications, such as knowledge-based systems, andsense-making systems.
Knowledge-based systems, which are the prime focus of AI & Law research, containknowledge about a certain problem domain and reason with this knowledge in order to solve acertain concrete problem, or at least to suggest alternative solutions to it. Both Bromby & Hall (2002)
and Keppens & Zeleznikow (2003) attempt to build a knowledge-based system for evidential
reasoning. Sense-making systems (see e.g. Kirschner et al., 2003) do not themselves reason to solve a
problem. Instead, the goal of such software is to support humans in making sense of a problem. To
this end, they provide tools for structuring (usually visualising) the problem and the user’s reasoningin solving it. Often they also provide tools for manipulating these structures, e.g. by converting one
visualisation into another, by combining pieces of information, or by performing logical or
probabilistic computations on the user’s input. In addition, some sense-making systems also support
the communication between different people working on the same problem. An early example ofsense-making software for evidential reasoning is Tillers and Schum’s MarshalPlan project (Schum& Tillers, 1991), an early, pre-world-wide-web Hypertext application that supports preliminary fact
investigations. Two general sense-making systems within AI & Law are Loui et al.’s (1997) Room 5
system and Verheij’s (1999) ArguMed system. A domain independent sense-making system that
supports the use of argumentation schemes is Reed & Rowe’s (2001) Araucaria system. All systems
mentioned thus far are still experimental; a commercial sense-making system for evidential reasoning
currently being developed is Legal Apprentice, jointly developed by Vern Walker and Legal
Apprentice, Inc.1
1

1

Demos can be found at http://people.hofstra.edu/faculty/vern_r_walker/LegalReasoning.html

1The main difference between knowledge-based and sense-making systems is that the latter haveno knowledge base, i.e., no collection of permanently stored general knowledge about a certain
domain. This means that for building sense-making systems, unlike for knowledge-based systems, nolaborious and difficult knowledge-acquisition phase is necessary. This is very significant for
applications to evidential reasoning, for which knowledge acquisition seems particularly hard.
Since both knowledge-based and sense-making software are supposed to support humans inrealistic professional or educational contexts, such software arguably has a better chance of
acceptance if it is based on the reasoning forms used in practice. In the context of legal reasoning
about evidence, the use and naturalness of statistical methods has been heavily debated (e.g. Tribe,
1971, Lempert, 1986, Wagenaar et al., 1993, Schum, 1994). Although such methods certainly havetheir use (see e.g. Kadane & Schum, 1996 for an insightful probabilistic analysis of the famous Sacco& Vanzetti case), there are several reasons for taking a different approach. Firstly, statistical methods
require numbers as input, and in the majority of legal cases reliable numbers are very hard to obtain,
either because there are no reliable statistics, or because legal experts are unable or reluctant toprovide numerical estimates. Secondly, probabilistic networks have additional limitations which areespecially problematic for sense-making systems. Essentially, probabilistic networks compile allavailable knowledge into a probability distribution over certain variables of interest, and thus conceal
some important distinctions of ordinary evidential reasoning. One such distinction concerns
relationships between evidence, and the rhetorical, dialectical structure of discourse: legal disputes
often consist of an exchange of explicit arguments and counterarguments, stated by opposing sides ofthe dispute. Moreover, probabilistic networks blur the distinction between directly relevant andancillary evidence. (Ancillary evidence is evidence that has a bearing on the probative force of
directly relevant evidence. A typical example is information on the credibility of a witness.) Schum(2001, p. 1948) remarks that the need for ancillary evidence especially arises when the conditional
probabilities cannot be established by statistical relative frequencies. Moreover, even when suchstatistics are available, one may still need ancillary evidence, since lawyers often try to undermine theuse of statistics by their adversary. For all these reasons it is important to study alternative accountsof evidential reasoning, which can deal with the predominantly qualitative and adversarial nature oflegal reasoning about evidence.
We take as our starting point a specific technique developed in legal theory, studying amethod for structuring evidential reasoning that goes back to John Henry Wigmore (1931). Wigmore
developed a graphical method for charting legal evidence, a tool for making sense of a large body ofevidence. Stripped to the bones, his charts depict the arguments that can be constructed from a given
body of evidence, as well as possible sources of doubt with respect to these arguments. At the time,
Wigmore’s charting method went largely unnoticed but it was recently rediscovered by AngloAmerican “new evidence scholars”, for example, Anderson & Twining (1991), Schum & Tillers(1991) and Schum (1994). Today his method looks surprisingly modern, anticipating recent AI
models of defeasible reasoning as well as recent sense-making software for argument visualisation.
Our present aim is to explore both of these directions, capturing some of the ‘logic’ underlying
Wigmore’s charts in an outline of a formal account of evidential reasoning in terms the work of John
Pollock (1987,1995,1998) on defeasible argumentation, and illustrating this account with a casestudy using argument visualisation techniques. We have chosen Pollock’s approach since its
emphasis on epistemology makes it suitable for modelling evidential reasoning. A crucial element in
our account is the notion of argumentation schemes. When looking at evidential reasoning (or indeed
at reasoning in general), one sees that many arguments, as well as attacks on them, are instances ofrecurring patterns, such as inferences from witness or expert testimonies, causal arguments, or
temporal projections. The idea of systematising reasoning in terms of such argumentation schemes
rather than just in terms of abstract principles of inference is the subject of much current study inargumentation theory. In fact, a great deal of AI (& Law) work can also be regarded as studying
argumentation schemes (although it is usually not presented as such). For instance, we think thatJohn Pollock’s work on prima facie reasons is of this kind, as is much AI & Law research on22

modelling legal argument. However, to our knowledge, the only AI & Law work that addresses
argumentation schemes for evidential reasoning directly is Lutomski (1989), who studies ways ofusing and attacking statistical evidence.
In light of this, the aim of this paper is twofold:• Showing how recent developments in legal evidence theory can be analysed with formal
models of defeasible reasoning.
• Arguing for the relevance of the idea of argumentation schemes to models of evidential
reasoning, and indicating a possible formalisation of reasoning with such schemes.
The rest of this paper is organised as follows. In Section 2 Wigmore’s charting method is
discussed by way of a simple example chart from his original work, and in Section 3 the notion ofargumentation schemes is introduced. Then Section 4 outlines a formal account of Wigmore-styleevidential reasoning with argumentation schemes within the formal framework of Pollock andapplies it to the same example chart. In section 5 a more detailed case study is carried of a modern
use of Wigmore’s charting method by Kadane & Schum (1996) in their probabilistic analysis of the
Sacco & Vanzetti case and some conclusions are drawn from it in Section 6. We end in Section 7
with a comparison with related work and some issues for future research.
This paper is an extended and revised version of Prakken, et al. (2003) and it also reuses somematerial from Prakken (2004). The discussion in Prakken et al. (2003) of argument visualisation has
here been mostly omitted to allow space for the addition of a detailed second case study (Section 5,
adapted from Bex, 2003), and an exploration of the issues of accrual of reasons and witness
testimonies (Section 6).
2.
WIGMORE’S CHARTING METHOD
A Wigmore chart looks very much (in broad outline) like the kind of argument diagram often used inlogic textbooks to visualise the inferential structure of a given specimen of natural language
argumentation. In an argument diagram the various premises and conclusions are represented asstatements (propositions). The diagram is a set of points joined by lines. Each point represents astatement. Each statement is only represented once on the diagram. Each line represents an inference
from one or more statements to another statement. Because it represents an inference, each line isnormally drawn as an arrow, indicating a direction of the inference from premises to conclusion.
Such a diagram is fairly simple. It looks like a directed graph of the kind so familiar in AI. A
Wigmore chart looks like this too, but has all kinds of special features and notation that make ithighly distinctive. The purpose of the Wigmore chart is to represent the proof of facts in the evidence
presented on either side in a trial. Thus there are all kinds of special notations for distinguishingfeatures like circumstantial evidence as opposed to testimonial evidence. It is best to begin with an
example, to explain how the Wigmore evidence chart works.
2.1
An Example: the Umilian Case
The best source on charting is the second edition of Wigmore’s Principles (1931). In this book,
Wigmore (1931, pp. 62-66) used the case of Commonwealth v. Umilian (1901, Supreme Judicial
Court of Massachusetts, 177 Mass. 582) to illustrate how method of evidence charts can be used inan actual case. A combination of two small charts for one aspect of the case that Wigmore himself
used (1931, pp. 56,59) is displayed below in Figure 1.
Each arrow represents an inference. Wigmore describes it as “provisional force given to an
inference by affirmatory evidence, testimonial or circumstantial”. What the arrows join together (thecircles, squares, and so forth) are “kinds of evidence” representing “human assertions” offered as“testimonial facts” or “circumstantial facts” (p. 52). These could be called “facts” for short.
Circumstantial evidence is represented by a square, while testimonial evidence is represented by acircle. A triangle represents corroborative evidence that strengthens or supports an inference. For33example (p. 53), “No third person was near the parties when the knife was found” or “Witness stoodclose by, was not excited, (and) was (a) disinterested spectator”. An angle represents “explanatory
evidence” that explains away the effect of some other evidence (p. 53). A double bar at the top line of
the angle tells us that this explanatory evidence was offered by the defendant. A dot within any ofthese symbols means “we now believe it to be a fact”. The infinity symbol below a fact means thatthe fact was “observed by a tribunal, or judicially admitted or noticed” (p. 53). For example, awitness’s assertion made in court on the witness stand would fit this category, or a coat shown incourt (p. 52).

Figure 1: A Wigmore chart for the Umilian case
There are some bits of Wigmore’s notation that are less clearly explained. Notice that somelines have arrows while other do not, and some lines have an X on them. The X on the line signifies
that the inference represented by the line is “a strong one” (Wigmore, 1931, p. 55). Also, thepositioning of the facts, that is whether the lines are vertical or horizontal, seems to be significant.
Wigmore tells us “A supposed fact tending to prove or disprove the existence of another fact isplaced below it”, whereas an explanatory fact “tending to lessen or strengthen the force” of a fact, isplace to the right or left of it.
The case of Commonwealth v. Umilian was a murder trial in which Umilian was accused ofmurdering Jedrusik. Wigmore presented many details of the evidence in the case. It would take toolong to try to present all of this evidence. Instead we present a summary, consisting mainly of thosefacts of the case that are represented on the small chart in Figure 1.
2.2
Some Facts of the CaseU (Umilian) and J (Jedrusik) worked together as farm labourers until one day in December 1899
when J disappeared. In April, his headless body was found in the well 500 feet from the barn. In
November, U had gone to a priest to have the marriage ceremony performed between him and awoman who had been working as a maid at the farm. He found that the priest had received a lettercharging him with having a wife and children in the old country. The priest to refuse to marry him,and sent someone to investigate the letter. It turned out that J had written the letter and that its
contents were not true. U was then married by the priest, but showed that he was very angry with J,
and made threats of vengeance against him. There was much other circumstantial and testimonial
evidence listed by Wigmore, but the gist of it, in relation to the small chart, is that U and J wereisolated in the area of the barn for the period around the murder, so if anyone other than U had
committed the murder, it is highly likely that he or she would have been detected.
With every chart Wigmore presented a “key list” numbering all the facts. Below are set out
the various facts from Wigmore’s key list (pp. 64-66) that appear on the small chart. Z, he tells us (p.
4456) is “one of the ultimate probanda under the pleadings, viz. that the accused killed the deceased”.
(A probandum is something that has to be proven.) Note that, since we combine two separate charts,
the numbers 18, 19 and 20 are each used for two different nodes. The nodes referred to in the key list
as 18(2), 19(2) and 20(2) can be found in the chart’s bottom left corner.
KEY LIST
Z: The charge that U killed J.
8: Revengeful murderous emotion toward J.
9: J’s falsely charging U with bigamy, trying to prevent the marriage.
10: Letter received by priest stating that U already had a family in the old country.
11: Anonymous witnesses to 10.
12: J was author of letter (although it was in a fictitious name).
13: Anonymous witnesses to 12.
14: Letter communicated by priest to U.
15: Anonymous witnesses to 14.
16: Letter’s statements were untrue.
17: Anonymous witnesses to 16.
18: U’s marriage being finally performed, U would not have had a strong feeling of revenge.
18.1: Wigmore does not tell us what this represents. Maybe it is witness testimony.
18(2): The witness is biased.
19: U and J remaining in daily contact, wound must have rankled.
19.1: Witness to daily contact.
19(2): The witness is a discharged employee of U.
21: Anonymous witness to 19(2).
19d: Discharged employees are apt to have an emotion of hostility.
20: Wife remaining there, jealousy between U and J probably continued.
20.1: Witness to wife remaining.
20(2): The witnesses’s strong demeanor of bias while on the stand.

Putting all these components together, it is possible to get an overview of the evidence represented
on the small chart, and see how all the various items of evidence fit together in an inferential
structure leading to the ultimate probandum Z.
We now proceed to summarizing Wigmore’s explanation of argumentation represented in thesmall chart (pp. 56-57,9). Circle 8 is the revengeful murderous emotion. The arrow from 8 to Z
“signifies provisional force” that 8 gives to Z. 9 is J’s attempt to prevent U from marrying. It gives
provisional force to 8. The dot in 8 indicates that it is believed by the drawer of the chart that therevengeful emotion was excited. Angle 18, just to the left of 8, is the fact that U actually married thewoman, which tends to explain away the revengeful emotion. Square 18.1 is the testimony to the factof marriage. The infinity symbol beneath it means that the evidence was heard in court. Triangle 19means that U and J remained in daily contact after the marriage, thus keeping the emotion alive.
Triangle 20 means that the wife remained there, and thus the emotion was intensified. That covers
the top half of the chart. Looking now at the bottom half, 9 represents J’s attempts to prevent themarriage. Each of 10, 12, 14 and 16 are bits of circumstantial evidence that go towards supporting 9.
The line across these four arrows meeting the arrow that goes to 9 represents a “composite fact”
joining all four elements 10, 12, 16 and 14. Each of these is individually backed by a bit of
testimonial evidence – 11, 13, 15 and 17 respectively. The composite fact line is reminiscent of what
is called a linked argument in modern argument diagramming. Finally, the bottom left part of thechart (which Wigmore actually depicted as a separate chat on p. 59) represents an attack on thetruthfulness of one of the witnesses. Angle 18(2), placed just left of square 17, stands for the attack
that one of the witness testifying to 16 was biased, while the structure below angle 18(2) represents
support for the claim of bias.
There are good reasons to study the Wigmore chart. The diagram, when it is stripped to its
essentials, and when some newly discovered features of argument structure have been incorporated,
can reveal the logical structure of evidential reasoning in a powerful way, and this structure can be
extremely useful for automating legal argumentation of the kind especially prominent in evidence
law. Thus the theoretical implications for logic, law and AI are quite deep.

55One very important aspect of Wigmore’s method, as emphasized also by the new evidence
scholars, is that he sees charting not primarily as an attempt to express reasons for belief but toexpress reasons for doubt. Wigmore’s basic purpose is more critical than constructive. It is to laybare the possibilities of doubt by making the weak points in a chain of argumentation explicit. It
shares this purpose with recent developments in argumentation theory. Argumentation schemes
represent typical presumptive forms of reasoning that need to be analysed and evaluated in specificcases by using matching sets of critical questions. The critical questions function as a device to help
make doubts explicit.
3.
ARGUMENTATION SCHEMES
Argumentation schemes are forms of argument that represent stereotypical patterns of humanreasoning. Among other things, they have been applied to model structures of human reasoning thatare troublesome to view deductively, and that have even been classified as fallacious in the past.
Although such arguments can sometimes be fallacious, in other instances they can be reasonable. For
example, appealing to expert opinion could be reasonable if the field of the expert is appropriate, andother conditions are met. But, of course, as the logic texts have so often pointed out, such arguments
can sometimes be fallacious appeal to authority. One might try to “deductivize” the reasonableinstances, by viewing the major premise as a conditional that is true if the authority isknowledgeable. For example, a deductivist might view the major premise as the material implication:
if X says A then A is true. But this deductivist strategy fails, unless the authority is omniscient,meaning that epistemic closure of the knowledge base can be assumed. But it is rare, if it ever occurs,that an expert knows everything, and thus that her knowledge in a domain is beyond challenge. Thus
for many, or perhaps even all cases of appeal to expert opinion, the deductivist approach does notwork. Thus the motivation for much recent research into argumentation schemes has been thistension between forms of argument that are clearly reasonable in some instances, but that cannot beanalysed as deductively valid (Kienpointner, 1992; Walton, 1996a; Reed & Walton, 2001).
Perelman and Olbrechts-Tyteca (1969) cited numerous distinctive kinds of arguments thatshift a weight of evidence on a balance of considerations. Hastings (1963) worked out the firstmodern taxonomy of argumentation schemes. A comprehensive list of argumentation schemes has
been offered by Kienpointner (1992). Some schemes classified as presumptive in (Walton, 1996a)
are: argument from sign, argument from example, argument from commitment, argument fromposition to know, argument from expert opinion, argument from analogy, argument from precedent,
argument from gradualism, and the slippery slope argument.
3.1
Argument from Expert Opinion
Argument from expert opinion is not only a very common form of argumentation, it is also highly
controversial. It is represented by the following argumentation scheme in the analysis given in(Walton, 1996a, p. 65).
Source E is an expert in domain D.
E asserts that proposition A is known to be true (false).
A is within D
Therefore, A may plausibly be taken to be true (false).
As shown by experiments in social psychology, there is a tendency to defer to experts, sometimes
without questioning, resulting in fallacious appeals to authority. When confronted with such an
appeal, the best reaction is to have some critical questions ready. The following six basic criticalquestions matching the appeal to expert opinion have been recommended in (Walton, 1997, p. 223).
1. Expertise Question: How credible is E as an expert source?

6

6

2.
3.
4.
5.
6.

Field Question: Is E an expert in D?
Opinion Question: What did E assert that implies A?
Trustworthiness Question: Is E personally reliable as a source?
Consistency Question: Is A consistent with what other experts assert?
Backup Evidence Question: Is A’s assertion based on evidence?

Expert testimony has become an increasingly important type of evidence, and is the subject of muchrecent investigation (e.g. Morsek, 2001; Malsch & Nijboer, 1999). For this reason the exact
formulation of critical questions is worth further study. Suffice it to say that, in many cases, asking
one of the basic critical questions above will lead to critical subquestions at a deeper level of
examination.
3.2
Appeal to Witness Testimony
The following argumentation scheme (taken from Walton, 1996a, p. 61) represents the form ofappeal to witness opinion as an argument. The variable W refers to a witness. A witness is an agent
that has incoming information about things it can perceive as facts or data, and that can relay that
information to another agent. The variable A stands for a statement (or proposition, taken to be an
equivalent term).
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).
When evaluating an appeal to witness testimony, the evaluator has no direct access to the evidence
that the witness presumably possesses. This form of direct verification, by observation of the facts, is
not possible. Hence the best the evaluator can do is to test the consistency of the account given by thewitness, to see if the account hangs together, and is consistent with other evidence that is known
about the case independently of the testimony. Probing into the consistency of the witness’s accountis achieved by asking critical questions. Critical questions relating to consistency concern the internalconsistency of what the witness said, consistency with known external facts, and consistency withwhat other witnesses said. Wagenaar et al. (1993, p. 38) have studied such questions in evaluating theplausibility of witness testimony in accounts offered by witnesses in trials. Other critical questions
important to cite in this connection concern the bias of the witness and the plausibility of the accountoffered. There are many indicators of bias. One of the most important ones is the finding that witness
has something to gain by testifying in a certain way. Another indicator is the language used by thewitness. For example, the language may have strong emotive connotations that are accusatory.
Another indicator of bias is the selectivity of the witness's account. The account may stress details on
one side, but overlook details that should be on the other side. If a witness is biased, it doesn’tnecessarily follow that the witness is lying. The bias could be unintentional. This plausibility factor
can react on the evaluation of the appeal to witness testimony in various ways. If the statement madeby the witness is highly implausible, it can backfire on the credibility of the witness. However, insome cases, the implausibility of the statement made can actually be a basis for conjecturing thatwhat the witness claimed is really true. For example, if two independent witnesses have made thesame implausible claim, it could suggest that their observations are careful and accurate.
The role of such critical questions has been discussed extensively in the legal literature on
witness testimony. Schum (1994, p. 325) has identified three requirements of the credibility of thetestimony of a witness that can be questioned: (1) veracity, or whether the witness believes what she
said, (2) objectivity, or whether what was reported corresponds to the event believed, and (3)observational sensitivity, or observations of linkages between events. Bromby and Hall (2002)
devised a system to advise on the credibility of witness testimony by citing factors of (1) competency,

77

(2) compellability, including the connection between the witness and the accused and any immunity
the witness may have, and (3) reliability, which includes position to know factors. There remain
many fine points to be clarified. What is most important here, however, is to see how sequences of
dialogue in legal cases can involve complex argumentation in which asking critical questions canincrease or decrease the probative weight of an appeal to witness argument as evidence.
4.
A FORMAL INTERPRETATION OF WIGMORE’S CHARTSIn this section we propose a formal account of the reasoning underlying Wigmore’s charts. In doing
so we will ignore the ‘syntactic sugar’ used by Wigmore and concentrate on the following elements:
the nodes (with possibly a label), the vertical links and the horizontal links.
Which formal account is plausible? Schum (1994) and Kadane & Schum (1996) interpretthem as a predecessor of Bayesian probabilistic networks. However, as we pointed out in the
introduction, there are good reasons to explore an alternative interpretation of Wigmore’s charts, viz.
as a forerunner of theories of defeasible argumentation. In particular, we interpret the nodes asstanding for propositions, the vertical links as expressing defeasible inferences, and the horizontal
links as being relations of attack or defeat between arguments. To capture the defeasible reasoning
underlying the charts, we choose to use Pollock’s argument-based framework for defeasible
reasoning (see e.g. Pollock 1987,1995,1998), since Pollock’s emphasis on epistemological reasoning
is very relevant for evidential reasoning, and his notion of prima facie reasons is very similar to the

Figure 2: The Umilian case in Araucaria
notion of argumentation schemes. Pollock’s framework is also convenient to translate into diagrams
that summarise the relationships between argument components. For this task, the Araucaria system(Reed and Rowe, 2001) could be used, as in Figure 2 above (in which convergent and linked support
relationships are shown as vertical arrows between propositions, refutations are horizontal lines,
enthymematic arguments are greyed, strength labels can mark edges, and propositions can be labelledwith provenance). Araucaria is sufficiently flexible to be able to handle Wigmore-style notation(Prakken et al., 2003), Pollock-style inference graphs, as well as natural language argument.

88In applying the framework, we will for simplicity restrict ourselves in the following ways: we
do not discuss suppositional arguments, and we ignore issues of strength of arguments; instead, we
focus only on the representation of evidential knowledge and the construction of evidential
arguments and counterarguments with such knowledge. Moreover, since we aim to give a general
picture of how evidential reasoning fits into the formal framework, we will suppress many technicaldetails and largely abstract from underlying issues of knowledge representation.
4.1
Outline of Pollock’s Framework
Essentially, Pollock augments the inference rules of classical logic (which he calls “strict reasons”)
with a set of defeasible inference rules (which he calls “prima facie reasons”), and he defines how
defeasible inferences can be attacked. Prima facie reasons are not meant to express domain-specificgeneralisation; Pollock intends them to be general epistemic principles for obtaining beliefs fromother beliefs and perceptual inputs, such as memory, statistical reasoning and induction. Arguments
can be constructed by chaining reasons, starting from given input information. As usual in logic,
arguments can be represented in two alternative but equivalent ways. To express the order in which
the inferences are made, Pollock sometimes displays them as deductions, i.e., as sequences offormulas that are either given as input information or are derived by applying a reason to one or more
earlier members in the sequence. This is also the form in which we will display arguments below. To
represent instead the inferential dependencies between the propositions in an argument, Pollock
sometimes represents arguments as AND trees, where the links represent applications of reasons.
Finally, Pollock combines sets of such trees into an AND/OR graph and adds defeat links between
nodes, resulting in an “inference graph”. Clearly, such a graph is very similar to a Wigmore chart.
Pollock defines two ways in which a (defeasible) argument can be defeated. Such anargument can be rebut with an argument for the opposite conclusion, and it can be undercut with anargument why a prima facie reason does not apply in the given circumstances. Consider, for instance,
an argument “The suspect was at the murder scene at the time of the murder since witness John saysso” (applying a prima facie reason “if a witness says ϕ, one may infer ϕ“). This argument is rebut byanother application of the same reason: “The suspect was not at the murder scene since witness Bob
says he was with him in the pub at the time of the murder, and one cannot be in two places at thesame time”. And the argument is undercut by “It was too dark, so John could not have made areliable identification” (applying another reason “if a witness says ϕ but the circumstances makereliable observation of ϕ impossible, one may not infer ϕ“). Intuitively, undercutting attacks do notargue that the attacked conclusion is false, but only that the conclusion is not sufficiently supported
by its premises.
Finally, the dialectical status of an argument must be defined, to identify the defeasibly valid
inferences. Since Pollock’s system results in a collection of arguments and their binary defeat
relations, Dung’s (1995) general framework for argumentation is applicable. Pollock’s definition isequivalent to Dung’s preferred semantics, but nothing prevents the use of another appropriate
semantics, such as Dung’s grounded semantics (used by e.g. Prakken & Sartor, 1996).
What makes Pollock’s approach especially interesting for us is his work on the various kindsof prima facie reasons, resulting in a general theory of epistemic defeasible reasoning. For present
purposes, five reasons are especially relevant. We now paraphrase them and some of theirundercutters as defined by Pollock (1987,1995,1998). Mostly, Pollock states them with numericalprobabilities, but since, as noted above, in legal contexts reliable numbers are often not available, wegive qualitative versions. We also leave Pollock’s so-called “projectibility” conditions and sometechnical detail implicit. As for notation, if principle R says that P is a prima facie reason for Q, then
“S is an undercutting defeater of R” is shorthand for “S is a prima facie reason for “P is not a prima
facie reason for Q”” (presupposing that reasons can somehow be expressed in the object language).
The full picture can be summarised as follows. First perception is applied to sense data,
yielding specific beliefs, and memory is used to record and retrieve these data. Then induction infers

99general rules from them, after which the statistical syllogism derives new specific beliefs from theserules. Finally, beliefs thus derived persist over time.
R1: Perception: Having a percept with content ϕ is a prima facie reason to believe ϕ
In legal contexts perception applies to witness testimonies, but also to tangible evidence as presented
at trial. Pollock (1987) formulates a general undercutter for perception, which we paraphrase as
follows:“The present circumstances are such that having a percept with content ϕ is not a reliable indicatorof ϕ” undercuts R1.
Clearly, this undercutter is just the tip of the iceberg of theories on the reliability of perception.
R2: Memory: Recalling ϕ is a prima facie reason to believe ϕ.
Two undercutters defined by (Pollock, 1987) are:“ϕ was originally based on beliefs of which one is false” undercuts R2.
“ϕ was not originally believed for reasons other than R2” undercuts R2.

Figure 3: Temporal Persistence in the Umilian case
R3: Statistical syllogism: ‘c is an F’ and ‘F’s are usually G’s’ is a prima facie reason for ‘c is a G’
This principle drives default reasoning with empirical generalisations. The main undercutter issubproperty defeat, which we give both in a weak and a strong qualitative form:‘c is an F&H’ and ‘it is not the case that F&H’s are usually G’s’ is an undercutter of R3.
‘c is an F&H’ and ‘F&H’s are usually not G’s’ is an undercutter of R3.
R4: Induction: ‘most observed F’s were G’s’ is a prima facie reason for ‘F’s are usually G’s’

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10Pollock formulates various undercutters to induction based on bias of samples.
R5: Temporal persistence: Believing that ϕ is true at T1 is a prima facie reason for believing ϕ at alater time T2.
The general scheme for undercutters of temporal persistence arguments is“Having reason to believe ¬ϕ at T3 between T1 and T2 is an undercutter of R5”.
(Actually, Pollock restricts this to percepts of ¬ϕ). Temporal persistence is an important aspect ofevidential reasoning. For instance, in civil cases the usual way to prove that one has a legal right (e.g.
ownership) is to prove that the right was created (e.g. by sale plus delivery). The other party mustthen usually prove later events that terminated the right. Our two case studies will illustrate that
temporal-persistence arguments are also common in criminal cases.
However, the temporal persistence scheme does not apply to all kinds of facts. Clearly, many
propositions, such as a position of a moving object, do not typically persist in time, so they are not“temporally projectible”. Pollock’s projectibility condition (which we have left implicit) is meant tocapture which kinds of facts tend to persist in time. A technical example of propositions that are nottemporally projectible is disjunctive weakenings of a proposition. Suppose that P is observed to betrue at T1. Then it follows deductively that P ∨ Q is true at T1, for any Q. If next ¬P is observed at T2,then P does not persist after T2. However, if P ∨ Q is allowed to persist from T1, its persistence is notaffected by the observation of ¬P at T2, so P ∨ Q persists until T3. But then it deductively follows
that Q is true at T3. This is, of course, undesirable, so Pollock declares disjunctive weakenings ofpropositions as not temporally projectible.
This completes our very brief overview of Pollock’s theory of epistemic defeasible reasoning.
We will now discuss how evidential reasoning as captured in Wigmore’s charts can be reconstructedwithin this theory. Two notions are especially important: generalisations and argumentation schemes.
4.2
Generalisations
One point stressed by current evidence theorists (e.g. Twining 1999, Wagenaar et al., 1993) is the keyrole of empirical generalisations in evidential reasoning. According to Schum (1994), suchgeneralisations, which are usually left implicit, are the “glue” which holds evidential arguments
together. For example, in Wigmore’s chart of the Umilian case, the inference of node 8 from node 9
seems to presuppose the generalisation “If x tries to prevent y’s marriage with false claims, arevengeful murderous emotion from y towards x tends to be created”. Clearly, the probative force of
the inference depends to a large extent on the strength of this generalisation. It might be argued inthis case that the tendency expressed by this generalisation is too weak or does not exist; the point ofmaking it explicit is to reveal this source of doubt. (Interestingly, Wigmore’s chart also contains an
explicit generalisation, viz. 19d).
4.2.1

Obtaining and Applying Generalisations

In Pollock’s framework, generalisations are applied with the statistical syllogism, and part of theircritical testing can be modelled as the search for counterarguments. One subtlety not captured by ourcurrent qualitative version of the syllogism is that generalisations often come with different
modalities, such as “almost always, probably, usually, sometimes”. This is an issue that we leave for
future research.
Something also seems to be missing from Pollock’s original account. Pollock simply assumes
that all generalisations are based on the reason from induction, and that attacks on generalisations canbe expressed as undercutters of this reason. However, the generalisations used in legal evidential
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11reasoning are often not based on careful empirical testing, since in the practical context of a trial suchtesting is usually impossible. In fact, according to Twining (1999) they are often based on folk
beliefs, infected with value judgements, prejudice or ideology, and so on. Therefore, the induction
scheme must be supplemented with other sources of generalisations, and suitable undercutters forthese sources must be formulated. We now briefly sketch how this could be done.
Anderson (1999) distinguishes five kinds of generalisations according to their sources:scientific, expert-based, general knowledge, experience-based and belief-based generalisations. The
first source is captured by the induction scheme and the second source will be captured by the expert
testimony scheme (see below). Experience-based and perhaps also belief-based generalisations seemto be based on a commonsense counterpart of scientific induction (Pollock 1995, pp. 82-3).
Furthermore, the general-knowledge source could be formulated as a new prima facie reason:
R6: general knowledge: ‘It is general knowledge that ϕ’ is a prima facie reason for ϕPossible undercutters are that a piece of general knowledge is infected by prejudice or value
judgements, etcetera. Of course, simply claiming that something is general knowledge without
specific evidence (such as an inductive argument or reference to science) is in many cases rather
weak (although in the context of a legal trial, unlike in science, it is often the only available source ofgeneralisations). The point of formulating R5 and its undercutters is to make explicit how appeals togeneral knowledge can be attacked.
A typical argument is now analysed as follows (ending each line with the reason with and thepreceding lines from which the line is inferred, and suppressing classical reasoning steps):
1

It is general knowledge that “If x tries to prevent y’s marriage with false claims, then usually arevengeful murderous emotion from y towards x is created”. (Input)
2 So (presumably) If x tries to prevent y’s marriage with false claims, then usually a revengefulmurderous emotion from y towards x is created (1, R6)
3 J tried to prevent U’s marriage with false claims (Input)
4 So (presumably) a revengeful murderous emotion from U towards J was created” (2,3, Stat. Syll.)
4.2.2

Attacking Generalisations

Critically testing generalisations is just as important as obtaining and applying them. In our account,four ways to attack a generalisation can be modelled.
1 Attacking the validity of the source of the generalisation, e.g. “it is not general knowledge that If x
tries to prevent y’s marriage with false claims, then usually a revengeful murderous emotion from y
towards x is created”. This attack can be modelled as a rebutting attack on a subargument for theintermediate conclusion that something is general knowledge.
2 Attacking the defeasible derivation from the source, for instance: “it is indeed general knowledge
that if x tries to prevent y’s marriage with false claims, then usually a revengeful murderous emotion
from y towards x is created, but this particular piece of general knowledge is infected by folk belief”.
This attack can be modelled as an undercutter of R6.
3 Attacking application of the generalisation in the given circumstances. This can be modelled as theapplication of applying more specific generalisations (e.g. “If x tries to prevent y’s marriage withfalse claims but y is known to be not violent and aggressive, then usually not a revengeful murderous
emotion from y towards x is created”, or the weak form with “not usually”) Then the subproperty
defeater of the statistical syllogism undercuts the use of the general default.
4 Attacking the generalisation itself. Such an attack takes the form of an argument for the negation of
the attacked generalisation (provided that this can be expressed in the object language). An example
of such an attack is the combination of the above more specific generalisation with the claim that the1212additional condition is not unusual, or perhaps even that it is usual, as in “People are usually notaggressive and violent”.
The main difference between attacks of the third and the fourth kind is that the third kind of attack
accepts the generalisation as a general rule, but denies its application in the case at hand, while thefourth kind of attack denies the generalisation as a general rule (“it is not the case that usually ...”).
For a more detailed discussion of this difference see Prakken (2004).
4.3
Argumentation schemes
We now turn to the formulation of argumentation schemes in Pollock’s framework, focusing on theschemes from expert and witness testimony. The main question is whether these schemes must be
regarded as additional prima facie reasons or as empirical generalisations: in the latter case applying
the schemes boils down to applying the (qualitative) statistical syllogism. Technically, the maindifference is that the body of reasons is fixed while generalisations can be inferred from, and attacked
on the basis of, other knowledge. The argumentation-theoretic literature is ambiguous about whether
argumentation schemes can best be analysed as inference rules or as generalised content (seeHitchcock, 2003 for a similar discussion about Toulmin's notion of warrants). In this paper we havechosen to regard them as defeasible inference rules, so (within Pollock's framework) as prima faciereasons. This is mainly since thus the representation of arguments is more concise. However,formulating them instead as generalisations is straightforward. For instance, R6 can be formulated as
the generalisation
If it is general knowledge that ϕ then usually ϕThen in the above argument an extra line 1’ between 1 and 2 must be added containing thisgeneralisation and 2 is then derived from 1 and 1’ by the statistical syllogism. Undercutters of R6
should now be represented as conflicting conditionals with a more specific antecedent. For example:
If it is general knowledge that ϕ but ϕ is infected with prejudice then it is not the case that usually ϕ

In cases where ϕ is indeed infected with prejudice, this gives rise to an instance of the subproperty
defeater of the statistical syllogism.
We first discuss the scheme from expert testimony. Its precise formulation depends on what
may be presumed. Suppose that the trustworthiness of the expert and the availability of backup
evidence may be presumed. This yields:
R7: Expert testimonies: ‘E says ϕ and ϕ is within domain S and E is expert in domain S’ is a prima
facie reason to believe ϕ.
Of the critical questions listed above in Section 3.1, we believe that the first is a matter of adding
strength of reasons to our account, the fifth searches for rebutting applications of the same scheme,
while the second and third question seem to be challenges of the premises of R7. This leaves thetrustworthiness and backup evidence question as possible pointers to undercutters. Alternatively, if
the expert’s trustworthiness and the availability of backup evidence cannot be presumed, thesestatements must be added as conditions of R7.
Next we discuss the scheme from witness testimony. Several formulations of this scheme arepossible. Our version follows the terminology of Schum (1994). Recall from Section 3.2 that Schumdecomposes the quality of a witness testimony into three issues: the witness' veracity, objectivity andobservational sensitivity. Objectivity and observational sensitivity are summarised in the firstpremise of the scheme as presented in Section 3.2 while veracity corresponds to the main critical13

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question of the scheme as proposed by Walton (1996a). As with the expert testimony scheme, theprecise formulation of the witness testimony scheme also depends on what may be presumed. On our
account, the witness' veracity, objectivity and observational sensitivity are presumed (alternatively,
they can be regarded as additional premises of the relevant schemes).
R8: Witness testimonies:‘Witness W says ϕ’ is a prima facie reason for believing ϕ.

We define the following undercutter: “Witness W is not truthful” is an undercutter of R8.
Must we also formulate lack of a witness’ objectivity and observational sensitivity as
undercutters of this scheme? We think that this is not necessary, since a witness will usually talkabout his or her past observations, so usually it will be possible to interpret ϕ as “I recall that I
observed ψ”. On this account, arguments using witness testimonies apply a chain of three prima faciereasons: first the witness scheme is used to infer “I recall I observed ψ”, then the memory scheme
provides “I observed ψ” and finally the perception scheme yields ψ. Thus lack of objectivity can behandled by undercutters of both memory and perception, and defects in observational sensitivity byundercutters of perception. Summarising, on our account the first premise of the scheme as presented
in Section 3.2 is decomposed into undercutters of the perception and memory reasons R1 and R2,
while the second premise is captured as the sole premise of R8.
However, a refinement of this analysis is necessary. If we have a closer look at Pollock’s
perception and memory reasons, we see that they provide reasons for a single agent to form beliefs
on the basis of the agent’s own memory or observations. By contrast, memories and observations of
witnesses are used by other agents to form beliefs, such as triers of fact. Accordingly, the memory
and perception reasons must be generalised. Perception becomes:
R1’: Perception: Agent Ai having a percept with content ϕ is a prima facie reason for agent Aj tobelieve ϕ(where Ai and Aj may or may not be identical). Likewise for the memory reason.
4.4
Outline of a Formal Analysis of the Umilian Case
We now briefly outline a formal analysis of the Umilian case (for a more detailed analysis see
Prakken, 2004). The case contains several uses of the witness testimony scheme. Wigmore discusses
one attack on such a use, viz. on the inference of 16 from 17 on the ground that the witness was adischarged employee of the suspect (angle 18(2) and its supporting nodes). This is an undercutter,concluding to “the witness is not truthful”. Arguably the case also contains two applications of thetemporal persistence scheme (although the chart leaves them implicit). Firstly, the revengefulemotion created when the priest refuses to marry U is assumed to persist till the time of the murder(shown in Figure 3 as a possible extension of Figure 2). This persistence argument is undercut by theargument that the emotion disappeared when the priest still agreed to marry U. This conclusion inturn persists till the time of the murder. Arguably, this application of temporal persistence is undercutby the argument that the emotion was recreated since U and J remained in daily contact and U’s wife
also remained there. The other inferences in the chart all seem based on implicit generalisations,which all seem to be of the general-knowledge, experience-based or belief-based type.
Determining the dialectical status of node 8 in our Pollock-style analysis, two sources of
doubt prevent it from being a defeasible consequence of the theory. The first is the rebuttingargument for node 18. This attack should be neutralised by looking at the relative strength of theconflicting arguments, or by undercutting the appeals to witness testimony on which node 18 isbased. The second source of doubt is that one of the supporting child nodes, node 16, is undercut.
This attack can be neutralised by providing alternative evidence of 16, or by attacking the argumentthat witness 17 is biased. An obvious target for such an attack seems the generalisation 19d.
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5.
A SECOND CASE STUDY: SACCO & VANZETTI
We now turn to an analysis of a modern use of Wigmore’s charting method, as used by Kadane &Schum (1996) in their probabilistic analysis of the Sacco & Vanzetti case. Unlike our brief informal
account of the Umilian case, we will now give our Pollock-style reconstruction in full detail, in orderto fully illustrate our approach and to learn more about it.
5.1
The Sacco & Vanzetti Case
We start with a brief description of the case (following Kadane & Schum’s (1996) own description).
Nicola Sacco and Bartolomeo Vanzetti were convicted and executed for shooting and killing a
payroll guard, Alessandro Berardelli, during a robbery that took place in South Braintree,
Massachusetts on April 15, 1920. Berardelli and another payroll guard, Frederick Parmenter, were
supposed to take a total of over $15 000 in two iron boxes from one factory of the Slater and Morril
shoe factory to the second Slater and Morril factory in South Braintree. During their route, theypassed two men leaning against a piperail fence and, as they passed, were attacked from behind bythese two men. Berardelli was shot four times and Parmenter two times. After this, the two men
picked up the iron boxes containing the money and fled, along with three other men, in a black
touring car which had approached the scene of the crime. Berardelli died about an hour later,
Parmenter succumbed to his wounds the following morning.
Sacco and Vanzetti were known members of an anarchist movement in the US. The
investigators knew that members of an anarchist group were involved in the robbery, and following aseries of events, Sacco and Vanzetti were arrested on May 5. After a long trial with many witnesses,
they were found guilty of the shooting of Berardelli while performing a criminal act, the robbery. An
appeals process was launched and the Governor of Massachusetts launched his own investigation of
the case. The committee entitled with this investigation also found Sacco and Vanzetti guilty as
charged. Final appeals to the Supreme Court did not have any effect, and on August 23, 1927, Sacco
and Vanzetti were executed.
Numerous books and articles have been written on this case by experts from fields including
law, history and social sciences, since many felt that the case was probably one of the worst
miscarriages of justice in American legal history. Recent studies of, for example, Young and Kaiser(1985) have introduced new evidence and evidence never introduced at the trial. Kadane & Schumcarried a thorough probabilistic analysis of the case based on their modernised, more user-friendly
version of Wigmore’s charting method. Their analysis consisted of two parts. First they represented
all the available evidence in 28 connected Wigmore charts, and then they used several of these charts
to carry out probabilistic sensitivity analyses. Such an analysis intends to investigate the sensitivity ofa probabilistic variable of interest (for instance, whether it was Sacco who shot Berardelli) tovariations in the probability of other variables (for instance, whether Sacco was one of the men
leaning against the piperail fence just before the murder). To carry out this analysis, Kadane &Schum reinterpreted their Wigmore charts of the case as Bayesian probabilistic networks, added
various estimates of probability distributions on the networks and investigated their consequenceswith standard software tools for Bayesian networks.
5.2
The Wigmore chart
Our case study concerns one of Kadane & Schum’s Wigmore charts, viz. Chart 4 (p.290) whichdisplays evidence concerning the identification of Sacco as present at the scene of the crime while it
was being committed. This chart was chosen since it is of realistic yet manageable size and since it
illustrates the use of most of the prima facie reasons discussed above. We have copied the chart in
Figure 4. Our analysis concerns only part of the chart. We take the proposition labelled ‘18’ in thechart, that Sacco was at the scene of the robbery when it occurred, as the main probandum andtherefore ignore the part of the chart above node 18. Also, we ignore the post-trial Young & Kaiser
evidence (labelled YK in the chart).
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The directly relevant evidence given by the prosecution’s witnesses and its interim probanda
are represented as circles, and the ancillary evidence given by the prosecution’s witnesses and its
interim probanda are represented as squares. The prosecution had two witnesses. Lewis Pelser
testified (26) that he saw Sacco at the scene of the robbery and the shootings from the window of the
Rice and Hutchins factory. The prosecution inferred from this that Sacco was at the scene of thecrime (18). Lewis Wade testified (25) that he saw someone who looked like Sacco at the scene of thecrime (18a), which, according to the prosecution, implied that Sacco was at the scene of the crime.
The directly relevant evidence given by the defense witnesses and its interim probanda arerepresented as diamonds, and the ancillary evidence given by the defense witnesses and its interim
probanda are represented as triangles. A defense witness called Albert Frantello testified (324) that
Sacco was not one of the men leaning against the fence when he passed it five minutes before therobbery occurred (323). The defense argued from this that Sacco could thus not have been at thescene of the crime when the robbery took place. The reasoning from Frantello's testimony wasstrengthened by the fact that, according to Frantello (326), the man on the fence spoke “American”(325) while, as observable during trial (328) Sacco spoke broken English (327). The prosecution
argued that Frantello's powers of observation were weak (329) since at cross-examination (330) he
incorrectly identified characteristics of jurors he had been asked to view, and thus his testimony
carried less weight towards 323. Further defense witnesses were brought forth to cast doubt upon
whether Pelser could have actually seen the robbery. McCullum testified (318c) that Pelser could nothave seen the shooting for reasons not further specified (318b). Constantino testified (317) that
Pelser was under a bench when the shootings took place (316), and thus Pelser could not have seen
the shooting, weakening the link between 26 and 18. On cross-examination (318a), however,Constantino had doubts about his observation (318), weakening his own argument that Pelser wasunder the bench. Pelser nevertheless admitted (319) that he was under the bench on crossexamination, strengthening 316. Brenner testified (321) that Pelser was not near the window (320) sothat he could not have seen the robbery. At his cross-examination, Brenner also expressed (322a)
doubts about where Pelser was (322), weakening the defense's argument from 321 to 320.

Figure 4: Chart 4 of Kadane & Schum (1996)

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5.3
A formal reconstruction
We now transform our selection from Kadane & Schum’s Chart 4 into a formalisation in Pollock's
system as explained in Section 4. This formalisation is a shorter and revised version of the one given
in Bex (2003). We have tried to be faithful to the original chart except in one or two places where aslightly different interpretation is necessary. Moreover, we have added generalisations wherever they
are left implicit in the original chart. Of course our choices can be debated but, as remarked above in
Section 4.2, the point of making generalisations explicit is precisely to make them the subject of
debate.
The chart contains two main witnesses for the prosecution, Wade and Pelser. We start with
Wade's testimony that he saw someone who looked like Sacco at the scene of the crime when therobbery and shooting occurred. From this an argument can be built for the claim that Sacco was at
the crime scene.
Argument P1 (Kadane and Schum: 25 18a)
1. Wade says: "I recall I saw someone who looked like Sacco at the crime scene when the crime
occurred" (Input)
2. Wade recalls having seen someone who looked like Sacco at the crime scene when the crime
occurred (1, Witness Testimony)
3. Wade saw someone who looks like Sacco at the crime scene when the crime occurred (2,Memory)4. If a person X saw someone who looks like person Y, then usually X saw Y (Input)
5. Wade saw Sacco at the crime scene when the crime occurred (3,4, Stat. Syll.)
6. Sacco was at the crime scene when the crime occurred (5, Perception)
Wade's argument was weakened by the fact that he would not admit that it was Sacco who shot
Berrardelli. Wade never denied that the man he saw "looked like Sacco", but he did express his
doubts about the fact that the man he saw actually was Sacco. This gives rise to the following
undercutting argument, which begins in the same way as the first argument.
Argument D1 (Kadane and Schum: 334d 334c)
1. Wade says: “I recall I saw someone who looked like Sacco at the scene of the crime when it
occurred” (Input)
2. Wade recalls having seen someone who looked like Sacco at the scene of the crime when it
occurred (1, Witness Testimony)
3. Wade saw someone who looks like Sacco at the scene of the crime when it occurred (2,Memory)4. Wade would not say “Sacco is the man I saw shooting Berrardelli at the crime” (Input)
5. If a person X saw someone who looked like person Y, but X will not testify he saw Y, thenusually X has doubts about Y's look-alike being Y (Input)
6. Wade had doubts about the fact that the man who looked like Sacco actually was Sacco(3,4,5, Stat. Syll.)
7. If a person X saw someone who looks like person Y, but X has doubts about Y's look-alike
being Y, then it is not usually the case that if a person X saw someone who looks like Person
Y, then person X saw person Y (Input)
8. Wade saw someone who looks like Sacco at the scene of the crime when it occurred & Wade
had doubts about the fact that the man who looked like Sacco actually was Sacco & If aperson X saw someone who looks like person Y, but X has doubts about Y's look-alike being
Y, then it is not usually the case that if a person X saw someone who looks like Person Y, thenperson X saw person Y (3,6,7, strict reason)

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This argument undercuts argument P1 at line 5. It is an instance of the subproperty defeater of thestatistical syllogism: the antecedent of the generalisation 7 in D1 is more specific than the antecedentof the generalisation 4 in P1 and it has a contradictory consequent.
The second main prosecution witness, Pelser, testified that he saw Sacco from the window of
the Rice and Hutchins factory. This gives rise to a second argument for the claim that Sacco was at
the crime. (To make the observational-sensitivity undercutters apply to Pelser’s testimony, weinterpret it as an example of self-observation.)Argument P2 (Kadane and Schum: 26 18)
1. Pelser says “I recall that I experienced I was at the window and that I saw Sacco at the sceneof the crime when it occurred” (Input)
2. Pelser recalls that he experienced he was at the window and that saw Sacco at the scene of thecrime when it occurred (1, Witness Testimony)
3. Pelser experienced he was at the window and Pelser saw Sacco at the scene of the crime when
it occurred (2, Memory)
4. Pelser saw Sacco at the scene of the crime when it occurred (3, strict reason)
5. Sacco was at the scene of the crime when it occurred (4, Perception)
The defense witnesses McCullum, Constantino, Brenner and Frantello all cast doubt on Pelser’s
testimony. McCullum gave an equivocal testimony from which the defense argued that Pelser could
not have seen Sacco (318c318b), but McCullum was not clear on why Pelser could not have seen
Sacco, so his testimony is ambiguous between an undercutter of the Witness, Memory or Perception
reason. We formalise it as an undercutter of the Perception reason.
Argument D2 (Kadane and Schum: 318c 318b)
1. McCullum says: “I recall that Pelser could not have seen Sacco” (Input)
2. McCullum recalls that Pelser could not have seen Sacco (1, Witness Testimony)
3. Pelser could not have seen Sacco (2, Memory)
4. X could not have seen P → X’s perception of P is not a reliable indicator of P (Input)
5. Pelser’s perception of Sacco at the scene of the crime when it occurred is not a reliable indicator ofthis fact (3,4, strict reason)
Argument D2 undercuts the application of the Perception reason at line 5 of argument P2.

The second defense witness, Constantino, testified that Pelser was not at the window so thathe could not have seen Sacco (from the window). Like McCullum’s testimony, Constantino’s
testimony is also ambiguous in how exactly it attacks Pelser’s testimony. For purposes of illustration
we formalise it as an undercutter of the Witness Testimony reason.
Argument D3 (Kadane and Schum: 317 316)
1. Constantino says “I recall I have seen Pelser under a bench” (Input)
2. Constantino recalls having seen Pelser under a bench (1, Witness Testimony)
3. Constantino saw Pelser under a bench (2, Memory)
4. Pelser was under a bench (3, Perception)
5. Pelser was under a bench → Pelser was not at the window (Input)
6. Pelser was not at the window (4,5, strict reason)
7. It is not the case that Pelser was at the window and that he saw Sacco at the scene of thecrime when it occurred (6, strict reason)
8. If X says he recalls he was in circumstances Y but X was not in circumstances Y, then usually
X is not truthful. (Input)
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9. Pelser says “I recall that I was at the window and that I saw Sacco at the scene of the crime
when it occurred” (Input)
10. Pelser is not truthful (7,8,9, Stat. Syll.)
Argument D3 undercuts the application of the Witness testimony reason at line 2 of argument P2.
Constantino admitted during cross-examination that he had doubts about where Pelser was. It
is not exactly clear from Kadane & Schum (1996) why Constantino had these doubts. This is a third
example of a testimony that is ambiguous in its nature. We interpret Constantino’s doubts as about
his memory of Pelser's whereabouts:
Argument P3 (Kadane and Schum: 318a 318)
1. Constantino says “I have doubts about my memory of Pelser's whereabouts” (Input)
2. Constantino has doubts about his memory of Pelser's whereabouts (1, Witness testimony)
3. If a witness has doubts about his memory of P, then usually P was originally based on false
beliefs (Input)
4. Constantino’s recollection of having seen Pelser under a bench was originally based on false
beliefs (2,3, Stat. Syll.)
Argument P3 undercuts the application of the memory reason at line 3 of argument D3, using the firstundercutter of this scheme.
Witness Brenner did not say where Pelser was, but he did testify that Pelser was not near thewindow. This gives rise to an attack on P2 similar to D3.
Argument D4 (Kadane and Schum: 321 320)
1. Brenner says: “I recall I saw that Pelser was not near the window” (Input)
2. Brenners recalls having seen that Pelser was not near the window (1, Witness Testimony)
3. Brenner saw that Pelser was not near the window (2, Memory)
4. Pelser was not near the window (3, Perception)
5. Pelser was not near the window → Pelser was not at the window (Input)
6. Pelser was not at the window (4,5, strict reason)
And further as argument D3.
On cross-examination, Brenner also expressed doubts about his memory.
Argument P4 (Kadane and Schum: 322a 322)
1. Brenner says “I have doubts about my memory of Pelser’s whereabouts” (Input)
2. Brenner has doubts about his memory of Pelser’s whereabouts (1, Witness testimony)
3. If a witness has doubts about his memory of P, then usually P was originally based on false
beliefs (Input)
4. Brenner’s recollection of having seen that Pelser was not near the window was originallybased on false beliefs (2,3, Stat. Syll.)
Argument P4 undercuts the application of the memory reason at line 3 of argument D4, using the firstundercutter of this reason.
The final defense witness, Frantello, testified that Sacco was not at the scene of the crime 5
minutes before it happened. Frantello also testified that he heard the man leaning on the pipe-rail
fence who might resemble Sacco speak American. This contradicts the fact observable in court that
Sacco speaks broken English. Kadane & Schum regard the latter two facts as two pieces of ancillaryevidence strengthening Frantello’s that Sacco was not at the scene of the crime 5 minutes before it
happened. We think that it is more natural to formalise Frantelli’s statements as two independent

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testimonies and the observable fact as a component in one of them. See further Section 5.4 below.
Argument D5 (Kadane and Schum: 324 323)
1. Frantello says “I recall I saw that Sacco was not one of the men leaning on the pipe-rail fence
5 minutes before the crime” (Input)
2. Frantello recalls that he saw that Sacco was not one of the men leaning on the pipe-rail fence
5 minutes before the crime (1, Witness testimony)
3. Frantello saw that Sacco was not one of the men leaning on the pipe-rail fence 5 minutes
before the crime (2, Memory)
4. Sacco was not one of the men leaning on the pipe-rail fence 5 minutes before the crime (3,Perception)
5. If Sacco was not one of the men leaning on the pipe-rail fence 5 minutes before the crimethen presumably Sacco was not at scene of the crime 5 minutes before it occurred (Input)
6. Sacco was not at scene of the crime 5 minutes before it occurred (5, Stat. Syll.)
7. Sacco was not at the scene of the crime when it occurred (6, Temporal persistence)
Argument D5 rebuts and is rebut by line 6 of P1 and line 5 of P2. Note, by the way, that line (5) is acase-specific generalisation; this is why we have expressed it with “presumably” instead of with“usually”.
Argument D6 (Kadane and Schum: 326 325 and 328 327)
1. Frantello: “I recall I heard the man leaning on the fence 5 minutes before the crime speak
American” (Input)
2. Frantello recalls having heard the man leaning on the fence 5 minutes before the crime speak
American (1, Witness testimony)
3. Frantello heard the man leaning on the fence 5 minutes before the crime speak American (2,Memory)4. The man leaning on the fence 5 minutes before the crime spoke American (3, Perception)
5. Sacco speaks broken English (Input)
6. If the man leaning on the fence 5 minutes before the crime spoke American & Sacco speaks
broken English then presumably Sacco was not the man leaning on the fence 5 minutes before
the crime (Input)
7. Sacco was not one of the men leaning on the pipe-rail fence 5 minutes before the crime(4,5,6, Stat. Syll.)
8. If Sacco was not one of the men leaning on the pipe-rail fence 5 minutes before the crimethen presumably Sacco was not at scene of the crime 5 minutes before it occurred (Input)
9. Sacco was not at scene of the crime 5 minutes before it occurred (7,8, Stat. Syll.)
10. Sacco was not at the scene of the crime when it occurred (9, Temporal persistence)
Argument D6 also rebuts and is rebut by line 6 of P1 and line 5 of P2. (Note that line 6 of D6 contains
another case-specific generalisation.)Frantello's cross-examination in the courtroom gives rise to a counterargument against D5 andD6, since Frantello performed poorly in recalling characteristics of some of the jurors he had beenasked to view.
Argument P5 (Kadane and Schum: 330 329)
1. Frantello incorrectly identified characteristic of jurors he had been asked to view (Input)
2. If person X cannot identify characteristics of people he has been asked to view, then usually
X's observational powers are weak (Input)
3. Frantello's observational powers are weak (1, 2, Stat. Syll.)

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4. If a person's observational powers are weak, then that person having a percept of P usually is
not a reliable indicator of P (Input)
5. Frantello having seen that the man on the fence was not Sacco is not a reliable indicator for
the fact that the man on the fence was not Sacco (3, 4, Stat. Syll.)
Argument P5 undercuts the application of the Perception reason at line 4 of arguments D5 and D6.
Although thus all four defense witnesses who cast doubt on Pelser’s testimony can be
attacked, Pelser himself admitted during cross-examination that was under a bench. Like
Constantino’s testimony, Pelser’s is also ambiguous in the precise way it undermines his original
testimony. We interpret it in the same way as Constantino’s testimony.
Argument D7 (Kadane and Schum: 319 316)
1 Pelser says “I recall I experienced I was under a bench” (Input)
2 Pelser recalls he experienced he was under a bench (1, Witness testimony)
3 Pelser experienced he was under a bench (2, Memory)
4 Pelser was under a bench (3, Perception)
And further as argument D3.
Argument D7 undercuts the application of the Witness Testimony reason at line 2 of argument P2.
What remains is to determine the dialectical status of all arguments. Figure 5 shows all

Figure 5: The argument grapharguments, their defeat relations and their status: the grey arguments are justified and the blankarguments are overruled (in this case grounded and preferred semantics yield the same result).
Because of space limitations this figure does not represent the structure of the arguments or the exact
ways in which arguments defeat each other. Thin lines stand for rebutting defeat relations and thicklines for undercutting defeat relations. Since we have not specified strengths of arguments, allmutually rebutting arguments defeat each other, while all undercutting arguments strictly defeat their

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target. A decision maker or analyst could use such information to determine the consequences of hisor her relative assessments of conflicting arguments. If one argument of a rebutting pair is regarded
as significantly stronger than another, than their mutual defeat relation will turn into a one-sided
relation. If an undercutting argument is regarded as stronger than or equally strong as its target, thestrict defeat relation remains unchanged. However, if it is regarded as weaker, the result depends onwhether Pollock’s treatment of weak undercutters is followed or not. According to Pollock (1995) an
undercutter that is weaker than its target does not defeat it. This has the somewhat strange
consequence that an undercutting argument and its target can both be dialectically justified. An
alternative solution is to let undercutting result in defeat whatever the strength is of the undercutter.
We adopt he latter solution, resulting in the dialectical assessment of the arguments as shown in
Figure 5. It turns out that both of the prosecution’s arguments that Sacco was at the scene of thecrime when it occurred are overruled. To turn, say, P1 into a justified argument, the trier of fact
should find a convincing counterattack on both of Frantello’s testimonies (D5 and D6) and on
Wade’s doubts at cross-examination (D1).
6.

DISCUSSION

We now draw some conclusions from the case study and discuss some issues that arise from it.
6.1
Revealing sources of doubt
Both Wigmore and Kadane & Schum stress that one benefit of the charting method is that it reveals
sources of doubt in evidential arguments. One way in which our analysis achieves this is that it forces
us to make implicit generalisations explicit. In many cases these generalisations will become thesubject of debate and testing (see e.g. Twining, 1999 and Wagenaar et al., 1993 for instructive
examples). Another way in which our analysis reveals sources of doubt is by indicating the precise
argumentation schemes used in an argument. Thus we are, for instance, able to represent the fact that
Wade’s testimony is (ceteris paribus) inherently weaker than Pelser’s: in our analysis Wade’s
testimony has an additional attacking point, viz. the generalisation “If a person X saw someone wholooks like person Y, then usually X saw Y”. This generalisation was the target of the counterargument
D1. A similar counterargument cannot be launched against Pelser’s testimony as used in argument P2.
6.2
Different levels of abstraction
A few times a counterargument was stated at a higher level of abstraction than its target. For
instance, while Pelser’s testimony was decomposed into applications of the Memory, Witness
Testimony and Perception schemes, the testimonies of the counterwitnesses McCullum, Constantino
and Brenner did not specifically attack any of these three inferences but instead seem to be an attackon the more abstract version of the witness testimony scheme that witnesses usually speak the truth.
We think that this is not a weakness of our approach or the underlying formalism; any analysis of areasoning problem will have to choose an appropriate level of abstraction. However, this problem
may offer a justification for representing argumentation schemes as generalisations (i.e., aspropositions) instead of as reasons (i.e., as inference rules): if depending on the dialogical context
argumentation schemes can be expressed at different levels of abstraction, then it may not be wise to
fix their formulation in a set of inference rules. Finally, in dialogical models of evidential reasoning it
may be interesting to investigate principles that enforce dialogues to be coherent in their level ofabstraction, or to investigate moves in a dialogue that are suitable for changing the dialogue’s level ofabstraction. For instance, Loui & Norman (1995) model moves for ‘unpacking’ an opponent’s
argument “P therefore Q” into “P therefore R, therefore Q” and then attacking the new argument on
its intermediate conclusion R.

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6.3
Ancillary evidence.
Ancillary evidence is evidence that has a bearing on the probative force of other evidence. In theircharts, Kadane & Schum depict ancillary evidence as links from a node to an evidence link. In ourformal reconstruction ancillary evidence can be represented in various ways, depending on its exact
nature. Ancillary evidence weakening the probative force of a piece of evidence is easily modelled asa counterargument, usually an undercutter. See for instance, argument P5 on Frantello’s weakobservational powers, attacking the arguments D5 and D6 based on his testimony. However, themodelling of ancillary supporting evidence is less obvious. Kadane & Schum depict Frantello’s
testimony as ancillary evidence, drawing links from his testimony 326 and the observable fact 328 to
the link between 324 and 323. However, it seems hard to see how the testimony 326 supports the link
between Frantello’s other testimony and the claim 323. It seems more natural to regard these
testimonies as two separate reasons for the same claim, which may be stronger when combined thanwhen considered in isolation. We formalised this interpretation in arguments D5 and D6.This brings
us to the issue of accrual of reasons. First, however, we note that genuine supporting ancillaryevidence will often be stated in the form of counterattacks on undercutting arguments. For instance,
an attack on a witness’s truthfulness may be countered with reasons why he is truthful.
6.4
Accrual of reasons.
Something which has not been modelled in the arguments above is the accrual of reasons for aconclusion. For example, both Wade’s and Pelser’s testimonies are used to conclude that Sacco wasat the scene of the crime when it occurred, and Constantino’s and Brenner’s testimonies can be
combined with Pelser’s testimony at cross-examination to conclude that Pelser was not truthful.
Most, if not all, triers of fact operate under the assumption that, other things being equal, a higher
number of witnesses testifying to the same proposition increases the evidential support of that
proposition. How can this assumption be modelled in our account? It has been suggested that anargument based on accrual of reasons is neither an argument with disjunctive premises nor one withconjunctive premises but a special type of argument (e.g. Walton, 1996b). Verheij (1996) argues thatan argument-based logic should somehow let the force of these two arguments accrue to reflect thefact that having two arguments for a conclusion is stronger than having one argument. Against this,Pollock (1995, pp. 101/2) argues that accrual of arguments (or reasons) is not a matter of logic.
Discussing the example of witness testimonies (which he expresses as a generalisation “Witnesses
usually speak the truth” and applies with the statistical syllogism), he argues that whether witness
testimonies accrue, depends on the linguistic community which the speakers are part of. We could
have, for example, one community in which speakers make assertions completely independently ofeach other, and then the strength of the combined reason would be greater than the strength of eitherof the separate reasons. But we could also be dealing with a community where the second speakertends to assert every proposition of which the first speaker said it was false. Then the strength of the
combined reason would be less than the strength of the first separate reason. Thus, Pollock argues,
the degree of justification for a proposition in such cases depends on a separate instance of thestatistical syllogism, applied to a separate generalisation “If two witnesses say that P, then usually P”.
Let us see how this account can be formalised in our present use of Pollock’s framework. One
way is to apply the Witness Testimony and Memory Reasons to the individual testimonies and tocombine the resulting observation statements in a many-agent version of the Perception reason. In
fact, a new version of this reason is needed for each natural number n. These reasons are combined in
the following template:
R1n: Multiple-agent observations: ‘Agent A1 observed ϕ and ... and agent An observed ϕ’ is a
prima facie reason for agent A to believe ϕ.
(where A may or may not be among Ai, ... An). The undercutters of the original Perception reason

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also apply to each multiple-agent version of perception. Note that attacks on the witness’s veracityand objectivity can still be modelled as undercutters of the reasons applied to the individual
testimonies. Does R1n also have new undercutters? An often-used way to discredit appeals tomultiple witnesses is to argue that the witnesses conferred before their testimonies and knowingly or
unknowingly influenced each other’s testimonies. We think that this can still be represented asattacks on the individual testimonies. For instance, if witnesses conferred to fabricate a story, thenthe following generalisation gives rise to an instance of the truthfulness undercutter:
If Witness Wi conferred with agent Aj before his testimony to fabricate a story then usually Wi is nottruthful.
The situation that witnesses are truthful but are influenced in unconscious ways so that they are notobjective, can be expressed as an additional undercutter of the Memory reason:‘Agent Ai recalls ϕ but was influenced concerning ϕ before recalling it’ is an undercutter of R2’.
Note that this undercutter also covers cases where a witness was influenced by, for instance, news
reports.
Let us illustrate our proposal with the testimonies of Constantino, Brenner and Pelser-atcross-examination that Pelser was not at the window of the Rice and Hutchins factory when thecrime occurred. An instance of R1n must be used with n = 3. (We leave implicit the parts of theargument that conclude to 1,4 and 7. Note that premises 2,5 and 8 capture that, although thewitnesses made different statements, these statements all imply the same thing.)
Argument D8
1 Constantino saw Pelser was under a bench (line 3 of D3)
2 Constantino saw that Pelser was under a bench → Constantino saw that Pelser was not at thewindow (Input)
3 Constantino saw that Pelser was not at the window (1,2, strict reason)
4 Brenner saw that Pelser was not near the window” (line 3 of D4)
5 Brenner saw that Pelser was not near the window → Brenner saw that Pelser was not at thewindow (Input)
6 Brenner saw that Pelser was not at the window (5,6, strict reason)
7 Pelser experienced he was under a bench” (line 3 of D7)
8 Pelser experienced he was under a bench → Pelser experienced he was not at the window(Input)9 Pelser experienced he was not at the window (3,4, strict reason)
10 Pelser was not at the window (3,6,9, R13).
Note that P3 undercuts D3 and thereby D8 while P4 undercuts D4 and thereby D8. Interestingly, thetestimonies might be combined again to save D8, viz. in a generalisation
If a witness has doubts about his memory of P but other witnesses also recall P, then it is not usually
the case that P was originally based on false beliefs
This generalisation gives rise to a subproperty defeater of P3 and P4 at their lines 4 so that D8 isreinstated. However, suppose that for whatever reason the defeater of P4 is in turn defeated. Then thisattempt to reinstate D8 does not work. If the trier-of-fact still wants to conclude that Pelser was not at
the window on the basis of Constantino’s and Pelser’s testimonies, then s/he has to formulate aweaker version of D8 with an instance of R1n with n = 2.

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One consequence of this analysis is that the set of relevant arguments in our case study islarger than as depicted in Figure 5: since we now have R1n as a reason, we must add four newarguments in Figure 5: Wade + Pelser, Constantino + Brenner, Constantino + Pelser, Brenner +Pelser and Constantino + Pelser + Brenner. By contrast, in formalisms that somehow aggregate
multiple reasons, such as Bayesian Networks, Reason-based logic (Hage, 1996) or Krause et al.’s(1995) LA system it suffices to represent a link from each individual observation statement to the
supported claim; the aggregation mechanism ensures that only the applicable statements exert theirinfluence on the claim (note, however, that in such formalism the strength of the combined reasons isstill independent of the strengths of the individual reasons; this agrees with Pollock’s analysis of
accrual). It remains to be seen whether this difference is an advantage or a disadvantage of thepresent approach. For instance, our approach induces the following kind of dialogue, which seems
quite natural:
D: Constantino, Brenner and Pelser observed that Pelser was not at the window, so, Pelser
was not at the window.
P: But Brenner was not sure about his memory where Pelser was.
D: OK, but still Constantino’s and Pelser’s observations together suffice to prove that Pelser
was not at the window.
The problem of accrual of reasons is not confined to witness testimonies. Firstly, sometimes
generalisations have to be combined. For instance, the arguments D5 and D6 based on Frantello’s
testimonies both use a generalisation with the consequent ‘Sacco was not the man leaning on thefence 5 minutes before the crime’, viz. at line 5 of D5 and line 6 of D6. To combine Frantello’s two
testimonies, a third generalisation must be formulated with the same consequent but conjoining theantecedents of these two generalisations. Applying the statistical syllogism to the new generalisation
results in a fifth addition to the argument graph of Figure 5.
The most complicated case of accrual is when reasons of a different nature have to be
combined. For instance, the prosecution presented another piece of evidence against Sacco, viz. a capthat was found at the crime scene that allegedly belonged to Sacco. This gives rise to anotherargument for the conclusion that Sacco was at the scene of the crime when it occurred, based on a
generalisation, say ‘If a cap found at the scene of the crime belongs to Sacco, then presumably Sacco
was at the scene of the crime’, to which the statistical syllogism can be applied. To combine thisargument with Wade’s and Pelser’s testimonies, reason R1n cannot be used. Instead thegeneralisation used in the new argument must be combined with Wade’s and Pelser’s testimonies
into a new generalisation:
If witnesses W1 and W2 observed that Sacco was at the scene of the crime when it occurred and acap found at the scene of the crime belongs to Sacco, then presumably Sacco was at the scene of thecrime.
In fact, the need for this generalisation yields a second reason why it might be better to formulate theargumentation schemes introduced in this paper as generalisations (the first reason we identified wasthat witness testimonies are often expressed at different levels of abstraction).
7.
CONCLUSION
In this paper we have studied how some common reasoning forms used in evidential legal reasoning
can be analysed within general theories of defeasible reasoning and argumentation. We have seenthat within Pollock’s logic for defeasible argumentation a natural account can be given of two key
concepts of evidential reasoning, viz. argumentation schemes and generalisations, in a way that
captures the spirit of both Wigmore’s charts and recent research of evidence theory scholars. Our

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account made it possible to formally distinguish four ways in which generalisations can be attacked.
We have also discussed a method for combining different pieces of evidence supporting the sameconclusion, especially witness statements. Our discussion suggests that combining evidence in anargument-based framework leads to less compact representations of a problem than in, for instance,
Bayesian networks or reason-based logic, but that an argument-based approach may induce morenatural dialogues.
As for related research, we know of only one earlier formal proposal to model evidential legal
reasoning as defeasible argumentation, viz. Verheij (2000). He develops his proposal as analternative to Wagenaar et al.’s (1993) anchored-narratives theory. According to this theory legal
proof should have the form of persuasive stories about what happened. The stories should not only be
persuasive but also be anchored in the available evidence with empirical generalisations. An
important aspect of the anchored-narratives theory is that these anchors should be progressively
refined in a critical testing procedure until they are sufficiently plausible to be accepted. Verheij
argues like us that anchors can be modelled as default rules, which can be used to build arguments
and, being defeasible, give rise to counterarguments. (Twining, 1999 also claims that arguments are agood alternative to stories, stressing some dangers of using stories in legal proof, such as that they
can deceptively appeal to the emotions of the triers of fact.) Verheij also stresses the need for a
formal theory of the dynamics of fact-finding investigations, to account for the testing ofgeneralisations as proposed in the anchored narratives theory. Finally, Verheij (2002) suggests like usthat argumentation schemes can be regarded as defeasible inference rules and negative answers tosome critical questions as undercutters. Probably the main contributions of the present paper toVerheij’s work are our detailed formal analysis of some of the main argumentation schemes
operative in evidential reasoning, our systematic account of various ways to attack generalisations
and our detailed discussion of accrual of evidential arguments.
As for future research, our Pollock-style approach should be further developed by adding
qualitative means to express strength of evidential arguments and by investigating more evidential
argumentation schemes, such as schemes for causal reasoning. Also, our suggested approach toaccrual of reasons should be compared in more detail to approaches using other formalisms, As forsense-making systems, it remains to be tested how our argument-based account can be used toprovide the formal foundations of implemented sense-making systems and whether the possibility of
expressing argumentation schemes (as in Araucaria) is indeed a useful feature of such systems.
Another research issue concerns the treatment of different levels of abstraction in evidential
reasoning. It has been stressed by e.g. Wagenaar et al. (1993) and Verheij (2000) that evidential
reasoning does not only consist of the construction of arguments and counterarguments, but also inthe progressive refinement of these arguments and the statements from which they are composed.
This was clearly illustrated by our second case study. This issue should be addressed in models of the
dynamics of fact-finding investigation.
Finally, in this paper we have employed a high level of abstraction, focussing mainly on theplace of evidential reasoning forms in a general theory of reasoning. When applying our account in aknowledge-based system, it must be supplemented with detailed knowledge-engineering research on
the relevant knowledge and argumentation schemes used in evidential arguments. Nevertheless, our
account provides a framework in which such detailed research can be put to use.
8.

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