Legal Reasoning and Argumentation
McMaster University October 8, 2012
Douglas Walton University of
Windsor
CRRAR
Artificial intelligence, taking advantage of new
argumentation tools, has lent support to
Wigmore’s view that there is a science of proof
underlying legal reasoning different from
deductive logic (Sartor, 2005; Prakken, 2005,
2006).
In this talk it is shown how recent advances in
argumentation suggest the value of modeling
legal reasoning in this new way.
The first section and studies the kind of
reasoning that applies rules to cases in law,
including the following forms of reasoning:
argument from an established rule, argument
from a verbal classification, and argument
from precedent.
By using an example from a Supreme Court
case summary, it is shown how all three kinds
of reasoning can be combined into a chain of
reasoning that represents the structure of the
evidence used to support a conclusion to be
proved in a case.
The second section discusses argument from
analogy.
The third section extends the analysis to two
forms of reasoning that draw from conclusions
from sources, argument from witness
testimony and argument from expert opinion.
Throughout, it is hinted at how the structure of
evidential reasoning exhibited in the other
sections can be modeled in the Carneades
Argumentation system.
The fourth section briefly shows how the
notion of proof, including the notions of
standard of proof and burden of proof, need to
be defined within a procedural context of
argumentation that has three main stages.
The term ‘defeasible’ comes from medieval
English contract law. It referred to a contract
that has a clause in it that could defeat the
contract in a case the circumstances of the
case fit the clause. This meaning is now
broadened to include the notion of a
defeasible rule, a rule that is open to
exceptions. Hart, in his famous paper ‘The
Ascription of Responsibility and Rights’ (1949;
1951), extended the usage of this term even
further by writing about defeasible concepts.
His most famous example is from The Concept
of Law (1961). Consider the rule that no
vehicles are allowed in the park. This rule
could be defeated by special circumstances, for
example during a parade, but it could also be
defeated because of the open texture of the
concept of a vehicle. Even though a car is
classified as a vehicle, and would be excluded
from the park, it may be debatable whether
other objects like a bicycle or a skateboard also
fit into the same classification.
Typical argumentation schemes (a) represent
defeasible, plausible arguments that depend
on common understanding of the way things
can normally be expected to go in a kind of
case familiar to speaker and hearer, and (b)
depend on warrants that are generalizations
that hold only subject to exceptions.
ARGUMENT FROM AN ESTABLISHED RULE
(Walton, Reed and Macagno, 2008, 343).
Major Premise: If carrying out types of
actions including the state of affairs A is the
established rule for a, then (unless the case
is an exception), a must carry out A.
Minor Premise: Carrying out types of
actions including state of affairs A is the
established rule for a.
Conclusion: Therefore a must carry out A.
In this form of reasoning, a is an agent that is
capable of carrying out goal-directed actions
and recognizing the consequences of actions.
This meaning is now broadened to include the
notion of a defeasible rule, a rule that is open
to exceptions. Hart, in his famous paper ‘The
Ascription of Responsibility and Rights’ (1949;
1951), extended the usage of this term even
further by writing about defeasible concepts.
His most famous example is from The Concept
of Law (1961). Consider the rule that no
vehicles are allowed in the park. This rule
could be defeated by special circumstances, for
example during a parade, but it could also be
defeated because of the open texture of the
concept of a vehicle. Even though a car is
classified as a vehicle, and be excluded from
the park, it may be debatable whether other
objects like a bicycle or a skateboard also fit
into the same classification.
Consider the case of the drug-sniffing dog
(Brewer, 1996, Weinreb, 2005). Suppose a
trained dog sniffs luggage left in a public place
and signals to the police that it contains drugs.
Should this event be classified as a search
according to the Fourth Amendment? If so,
the evidence so obtained is not admissible as
evidence. The problem is that the concept of a
search is defeasible and law cannot define it by
means of a set of necessary and sufficient
conditions for closed to future revision
because new cases may arise.
ARGUMENT FROM VERBAL CLASSIFICATION
(Walton, Reed and Macagno, 2008, 319). Here
the constant a represents an individual that
can be an object of any kind, including an
event, a physical object, an animal or a human
being.
Individual Premise: a has property F.
Classification Premise: For all x, if x has
property F, then x can be classified as having
property G.
Conclusion: a has property G.
ARGUMENT FROM PRECEDENT
Previous Case Premise: the source case is a
previously decided case.
Previous Ruling Premise: In the source case,
rule R was applied and produced finding F.
New Case Premise: the target case is a new
case that has not yet been decided.
Similarity Premise: the target case is similar
to the source case in relevant respects.
Conclusion: Rule R should be applied to the
target case and produce finding F.
Arguments from ordinary meaning express the
principle that if an argument can be
interpreted according to the meaning a native
speaker of a given language would ascribe to
it, the argument should be interpreted in this
way, unless there is a reason for a different
interpretation.
In this U.S. Supreme Court case (CSX
Transportation, Inc. v. Alabama Department of
Revenue et al. certiorari to the U.S. U.S. Court
of Appeals for the eleventh circuit No. 09-520,
decided February 22, 2011) CSX, claimed that
the State of Alabama had discriminated against
them
(http://www.supremecourt.gov/opinions/10pd
f/09-520.pdf).
The State taxes diesel fuel consumed by
railroads but exempts interstate motor and
water carriers. CSX claimed that this tax
scheme discriminates against railroads in
violation of the Railroad Revitalization and
Regulatory Reform Act of 1976 which bars
discriminatory taxation.
The key question thus becomes whether a tax
might be said to “discriminate” against a
railroad under subsection (b)(4) where the
State has granted exemptions from the tax to
other entities (here, the railroad's
competitors). Because the statute does not
define “discriminates,” the Court again looks to
the term's ordinary meaning, which is to fail to
treat all persons equally when no reasonable
distinction can be found between those
favored and those not favored. To charge one
group of taxpayers a 2% rate and another
group a 4% rate, if the groups are the same in
all relevant respects, is to discriminate against
the latter. That discrimination continues if the
favored group’s rate goes down to 0%, which is
all an exemption is.
To say that such a tax does not “discriminate”
is to adopt a definition at odds with the word's
natural meaning. This Court has repeatedly
recognized that tax schemes with exemptions
may be discriminatory. See, e.g., Davis v.
Michigan Department of Treasury, 489 U. S.
803. And even Department of Revenue of Ore.
v. ACF Industries, Inc., 510 U. S. 332, on which
the Eleventh Circuit heavily relied in dismissing
CSX's suit, made clear that tax exemptions
“could be a variant of tax discrimination.” Id.,
at 343. In addition, the statute's prohibition of
discrimination applies regardless whether the
favored entities are interstate or local. The
distinctions drawn in the statute are not
between interstate and local actors, as
Alabama suggests, but between railroads and
all other actors, whether interstate or local.
The version of the basic scheme for argument
from analogy from (Walton, Reed and
Macagno, 2008, 315) is presented below.
Similarity Premise: Generally, case C1 is
similar to case C2.
Base Premise: A is true (false) in case C1.
Conclusion: A is true (false) in case C2.
An argument fitting this scheme can be
evaluated by asking one or more of the
following set of critical questions.
CQ1: Are there respects in which C1 and C2
are different that would tend to undermine
the force of the similarity cited?
CQ2: Is A the right conclusion to be drawn in
C1?
CQ3: Is there some other case C3 that is also
similar to C1, but in which some conclusion
other than A should be drawn?
The basis for deciding whether one case is a
precedent for another in law is that it is based
on an underlying argument from analogy
(Walton, D., Similarity, Precedent and
Argument from Analogy Artificial Intelligence
and Law, 18 (3), 2010, 217-246) .
But how is a case where a man sued a
company because there was a decomposed
snail in his beer bottle similar to a case where
a man tried to sue because of a defective Buick
automobile?
My answer: there is something about the
common sequence of events that makes the
one case similar to the other.
First the plaintiff bought some product that he
assumed was the normal product he expected,
and he thought therefore that the product was
reasonably safe to use. Then something in the
product turned out to be defective, and when
he used the product this defect caused some
harm that impacted badly on his health.
Script as the Basis of the Similarity
Premise in Argument from Analogy
Karen Silkwood was a chemical technician who
worked for the Kerr-McGee Corporation in
their nuclear power plant in Oklahoma. She
was active in the union. On November 5, 1974
she discovered that she had been exposed to
dangerously high levels of plutonium radiation.
High levels of radioactive contamination were
found in her apartment. She was sent to Los
Alamos Scientific Laboratory, where they
documented evidence of radioactive
contamination. After her return she arranged
to meet a reporter from the New York Times to
say that safety and quality controls at KerrMcGee on the making of the fuel rods had
been falsified. On the way to the meeting, she
died in a mysterious one-car accident.
Silkwood’s apartment was quarantined, and
her personal property from it was buried in a
nuclear waste site.
Judgment Reversed by Silkwood v. Kerr-McGee
Corp., 464 U.S. 238, 104 S.Ct. 615, 78 L.Ed.2d
443, 20 ERC 1229, 14 Envtl. L. Rep. 20,077
(U.S.Okla. Jan 11, 1984) (NO. 81-2159)
The other scheme for argument from analogy
does not use the notion if similarity. Instead it
compares specific respects in which two cases
are similar (Gurarini, 2004).
Respects Premise: Case C1 is similar to case
C2 in a certain respect.
Base Premise: A is true (false) in case C1.
Conclusion: Support is offered to the claim
that A is true (false) in case C2.
The second scheme is especially useful for
case-based reasoning.
Gerry Spence used an analogy in his famous
closing argument. The trial began in March
1979 and took 11 weeks. The jury returned a
verdict for $10,505,000, and when Kerr-McGee
appealed, punitive damages were settled at
$1.38 million (Meyer, 2002, 235). Spence
compared the Silkwood case to a familiar kind
of example from the history of English
common law often used to illustrate strict
liability. In this example someone was keeping
a lion in a cage on his property when the lion
escaped, through no fault of its owner, and
attacked some people, harming them. The
owner was held responsible for the harm.
Case-Based Reasoning
• CATO (Aleven, 1997) is based on factors representing
respects in which a case is similar to or different from
another one (critical questions).
• This can happen in case-based reasoning when some
factors support the argument while others detract from it.
• In case-based reasoning argument from analogy is a
defeasible form of argument in which further evidence can
be introduced that can go against or even defeat the
argument.
• To weigh the arguments on each side, we have to consider
the factors on each side, and determine which factors are
more “on-point”, or relevant.
Sequence of Case-Based Reasoning
Rule of law may fit
the target case.
A rule of law
applied to the
source case.
Similarity is seen
between source
and target case.
The same rule of
law is applied to
the target case.
Different facts are
emphasized as
important by a
different judge.
Difference
between two
cases may be
found.
New rule of law
can be applied to
a third case.
Rule of law may be
qualified, or a new
rule may even be
formulated.
Third case
becomes a first
case in a new
sequence.
One of the most important forms of sourcebased reasoning and law is inference from
witness testimony. The argumentation scheme
for this form of reasoning is given in (Walton,
2008, 60). It has three premises.
Position to Know Premise: Witness W is in a
position to know whether A is true or not.
Truth Telling Premise: Witness W is telling
the truth (as W knows it).
Statement Premise: Witness W states that A
is true (false).
Conclusion: Therefore (defeasibly) A is true
(false).
Six Critical Questions Matching the Argument from Witness Testimony
Internal Consistency Question: Is what the witness said internally consistent?
Factual Consistency Question: Is what the witness said consistent with the known facts of
the case (based on evidence apart from what the witness testified to)?
Consistency with Other Witnesses Question: Is what the witness said consistent with
what other witnesses have (independently) testified to?
Trustworthiness Question: Is the witness personally reliable as a source?
Plausibility Question: How plausible is the statement A asserted by the witness?
Exception if what the witness says is implausible.
Bias Question: Is there some kind of bias that can be attributed to the account given by
the witness?
The most basic version of the form of
argument from expert opinion is modified
from the one in (Walton, Reed and Macagno,
2008, 310) as follows.
Major Premise: Source E is an expert in field
F.
Minor Premise: E asserts that proposition A
is true (false).
Second Minor Premise: A is within F.
Conclusion: A is true (false).
Legal Expert Opinion Scheme
• Competence Premise (Ordinary Premise): E is an expert in knowledge
domain D.
• Statement Premise (Ordinary Premise): E said the sentence S*.
• Interpretation Premise (Ordinary Premise): S is a reasonable interpretation
of S*.
• Domain Premise (Assumption): S is in D.
• Depth of Knowledge Premise (Assumption): The knowledge of E about D is
deep enough to know about S.
• Careful Analysis Premise (Assumption 3): E’s testimony S* is based on his
own careful analysis of evidence in this case.
• Other Experts Premise (Exception): S is inconsistent with what other
experts in D say.
• Trustworthiness Premise (Exception): E is not trustworthy.
• Conclusion: S may plausibly be taken to be true.
Expertise Question: How knowledgeable is E as
an expert source?
Field Question: Is E an expert in the field F that
A is in?
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 E’s assertion
based on evidence?
Salmon’s Case (Wigmore)
Salmon sold medicines in London. M’Kensie bought from
him some pills for rheumatism; after numerous doses he died.
The medical men, on a postmortem examination, affirmed that
certain ingredients of these pills had caused his death; and
Salmon was indicted for manslaughter. But on the trial he
produced many witnesses, who had taken the same kind of
pills with much benefit; one witness affirmed that he had
taken twenty thousand of them within the past two years, to
his great benefit! If these circumstances were true, the
inference was inevitable that the pills were not lethal. But was
the testimony to this circumstance true?
Araucaria Diagram of
Salmon Case
Carneades takes the approach that the way
critical questions are modeled depends on the
individual argumentation scheme, by
distinguishing three kinds of premises.
Ordinary premises are just the regular
premises of an argumentation scheme that are
explicitly given in the scheme itself. But there
are two additional kinds of premises not stated
in the scheme. Assumptions are to be
acceptable unless called into question.
Exceptions are modeled as premises that are
not assumed to be acceptable and that can
defeat an argument as it proceeds. Ordinary
premises of an argument, like assumptions, are
assumed to be acceptable, but they must be
supported by further arguments in order to be
judged acceptable.
Proof Standards in Law
•
•
•
•
•
There are four main proof standards for factual issues in common law (B.A. Garner,
Black’s Law Dictionary (9th ed.), Thomson Reuters, St Paul, Minn., 1990, 241).
The scintilla of evidence proof standard is met if “even the slightest amount of
relevant evidence exists on an issue” (1464).
The preponderance of evidence standard is met by “evidence that has the most
convincing force, superior evidentiary weight that […] is still sufficient to incline a
fair and impartial mind to one side of the issue rather than the other” (1301).
Clear and convincing evidence is “evidence indicating that the thing to be proved is
highly probable or reasonably certain” (636). This standard is supposed to be
higher than that of preponderance of the evidence, but not as high as the highest
standard in law, that of evidence beyond a reasonable doubt.
The beyond reasonable doubt standard is used to determine guilt in criminal
cases, and is often equated with the presumption that the defendant is innocent.
Standards of Proof (Carneades)
 Scintilla of Evidence (SE) is met if there is at least one applicable
argument for a claim.
 Preponderance of the Evidence (PE) is met if SE is satisfied and the
maximum weight assigned to an applicable pro argument (for the
claim) is greater than the maximum weight of an applicable con
argument (against the claim).
 Clear and Convincing Evidence (CCE), is met if PE is satisfied, the
maximum weight of applicable pro arguments exceeds some
threshold α, and the difference between the maximum weight of the
applicable pro arguments and the maximum weight of the applicable
con arguments exceeds some threshold β.
 Beyond Reasonable Doubt (BRD)is met if CCE is satisfied and the
maximum weight of the applicable con arguments is less than some
threshold γ.
In law, there is a fundamental distinction
between two main types of burden of proof
(Prakken and Sartor, 2009). One is the setting
of the global burden of proof at the opening
stage, called the burden of persuasion. It does
not change during the argumentation stage,
and is the device used to determine which side
has won at the closing stage. The other is the
local setting of burden of proof at the
argumentation stage, often called the burden
of production in law. This burden can shift back
and forth as the argumentation proceeds. For
example, if one side puts forward a strong
argument, the other side must meet the local
burden to respond to that argument by
criticizing in or presenting a counter-argument,
or otherwise the strong argument will hold.
BRD and IBE
• It is regarded as very dangerous for a judge to try to define ‘beyond
reasonable doubt’ in a criminal trial, as there is judicial hostility to
attempting any precise definition, and there is a very real danger of
appeal, because such a precization is not established in precedent.
• There is a vocal acceptance in law of the view that the beyond reasonable
doubt standard cannot be quantified by using numbers. That does not
mean it cannot be modeled using computational tools.
• Pardo and Allen (2007, 238) argue that it can modeled using IBE: “In
criminal cases, rather than inferring the best explanation from the
potential ones, fact-finders infer (and should infer) the defendant’s
innocence whenever there is a sufficiently plausible explanation of the
evidence consistent with innocence (and ought to convict when there is
no plausible explanation consistent with innocence, assuming there is a
plausible explanation consistent with guilt).
A dialogue is formally defined as an ordered 3tuple (O, A, C) where O is the opening stage, A
is the argumentation stage, and C is the closing
stage (Gordon & Walton, 2009, p. 5). Dialogue
rules (protocols) define what types of moves
are allowed by the parties during the
argumentation stage (Walton & Krabbe, 1995).
At the opening stage, the participants agree to
take part in some type of dialogue that has a
collective goal. Each party has an individual
goal and the dialogue itself has a collective
goal. The initial situation is framed at the
opening stage, and the dialogue moves
through the opening stage toward the closing
stage.
References
Gordon, T. F. (2010). The Carneades Argumentation Support System, Dialectics,
Dialogue and Argumentation, ed. C. Reed and C. W. Tindale, London: College
Publications.
Gordon, T. F. and Walton, D. (2009). Proof Burdens and Standards. Argumentation and
Artificial Intelligence, ed. I. Rahwan and G. Simari. Berlin: Springer, 239-260.
Prakken, H. (2010).On the Nature of Argument Schemes. Dialectics, Dialogue and
Argumentation, ed. Chris Reed and Christopher W. Tindale, London: College
Publications, 167-185.
Reed, C. and Walton, D. (2003). Diagramming, Argumentation Schemes and Critical
Questions, Anyone Who Has a View: Theoretical Contributions to the Study of
Argumentation, ed. F. H. van Eemeren, J. A. Blair, C. A. Willard and A. Snoek
Henkemans. Dordrecht: Kluwer, 195-211.
Verheij, B. (2001). Legal Decision Making as Dialectical Theory Construction with
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and Law: Proceedings of the Conference, New York Association for Computing
Machinery, 225-236. Available at http://www.ai.rug.nl/~verheij/publications.htm.
Walton, D. Appeal to Expert Opinion. University Park: Penn State Press, 1997.
Walton D. and Gordon, T. F. (2005). Critical Questions in Computational Models of
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Series, ed. Dunne, P. E. and T. J. M. Bench-Capon. Nijmegen: Wolf Legal Publishers,
103-111.
Walton, D., Reed, C. and Macagno, F. (2008). Argumentation Schemes, Cambridge:
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