Transcript Need for Logic of Argumentation

MODELING CRITICAL QUESTIONS
AS ADDITIONAL PREMISES
Douglas Walton
CRRAR
OSSA, May 19, 2011
Asking a Probing Question in Tucson
• Chris Reed, when visiting at University of Arizona
in 2001, asked a question.
• Is there any way the critical questions matching a
scheme could be represented as statements of
the kind represented on an argument diagram?
• I replied that I couldn’t figure out a way to do it,
because some critical questions defeat the
argument merely by being asked, while others
don’t, unless they are backed up by evidence.
Two Theories
What Happens When the Respondent Asks a Critical Question?
Two Theories
1. When a critical question is asked, the burden shifts to the proponent to
answer it. If no answer is given, the proponent’s argument fails.
2. To make the proponent’s argument fail, the respondent needs to
support the critical question with further argument.
Key Insight
Which theory applies depends on the argumentation scheme. A different
theory may apply to each critical question of the scheme.
The Challenge
To design a computational model of
argumentation (“argumentation framework”)
which
– Supports argumentation schemes with critical
questions.
– Allows the burden of proof (initiative) for answering
critical questions to be assigned to either the
proponent or a respondent, on a question by
question basis for each argumentation scheme.
Initiative and Burden of Proof
• We regard the concept of burden of proof as complex
(Gordon and Walton, 2009), and so we replace it here with
the simpler concept of an initiative (Hamblin, 1970, 274).
• As explained by Hamblin, a shift of initiative takes the
requirement to provide proof for some proposition from
one party in a dialogue and puts it on the other party. The
general principle is that he who asserts must prove.
• Shifts of initiative take place as the argumentation
proceeds in a case where the parties take turns making
moves. They do not represent what is called burden of
persuasion in law, but are more like tactical burden of proof
(Prakken and Sartor, 2009).
The Solution (Basic Idea)
• Arguments have three kinds of premises
Ordinary premises – for the minor and major premises of schemes
Assumptions – for critical questions to be answered by the proponent
Exceptions – for critical questions to be answered by a respondent
• Note: Critical questions are modeled as additional premises!
• Whether a premise holds depends not only on its type but also the
dialectical status of the premise’s statement in time during the
dialogue:
Stated – The initial status of a statement, when first used in an argument
Questioned – Statements which have been called into question but not yet
decided
Accepted – Statements which have been accepted
Rejected – Statements which have been rejected
Carneades (c. 213 - c. 128 B.C.)
• Leader of the Academic
Skeptics and head of (3rd)
Platonic Academy
• Developed a theory enabling
human action despite the lack
of perfect knowledge, based
on “reasonable grounds” and
“probable” inferences.
• Carneades’ notion of
probability corresponds
closely to what is now called
defeasible, plausible,
presumptive or nonmonotonic
reasoning.
The Carneades System
• Carneades is a mathematical and computational model,
meaning that all the functions of the model are computable.
• Carneades defines mathematical properties of arguments that
are used to identify, analyze and visualize real arguments.
• Carneades uses argumentation schemes, and applies them to
argument construction, analysis and evaluation
• Carneades models the structure and applicability of
arguments, the acceptability of statements, burdens of proof,
and proof standards, for example preponderance of the
evidence.
Using Carneades
• Carneades has been implemented using a functional programming
language. It has a graphical user interface that anyone can
download and use to make argument maps to analyze and evaluate
arguments.
(http://carneades.github.com).
• Statements can be questioned, stated, accepted or rejected.
• A statement that appears in a white box with no checkmark in only
stated, not accepted or rejected.
• A statement that appears in a darkened (green) box with a ✔
checkmark is accepted or acceptable.
• If a statement appears in a darkened (red) box with an ✘, its logical
complement (negation) is accepted or acceptable.
Tweety Example
The Bill Gates Example
Example Argumentation Scheme
• Scheme for Argument from Expert Opinion
– Major Premise: Source E is an expert in field F containing proposition A.
– Minor Premise: E asserts that proposition A (in field F) is true (false).
– Conclusion: A may plausibly be taken to be true (false).
• The Six Basic Critical Questions
–
–
–
–
–
–
Expertise Question: How credible 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?
Method of Evaluation
• The method of evaluating an argument like
one from expert opinion is by a shifting of
initiative in a dialogue (Walton, 1997).
• When the respondent asks one of the six
critical questions an initiative shifts back to
the proponent’s side, defeating or
undercutting the argument temporarily until
the critical question has been answered
successfully.
Burdens and Critical Questions
• Carneades distinguishes different ways the critical
questions matching an argument from expert opinion are
represented on an argument diagram.
• According to one approach, in a case where the respondent
asks any one of these critical questions, the initiative
automatically shifts back to the proponent’s side to provide
an answer, and if she fails to do so, the argument defaults
(is defeated).
• According to the other theory, asking a critical question
should not be enough by itself to make the original
argument default. On this theory, the question, if
questioned, needs to be backed up with some evidence
before it can shift any burden that would defeat the
argument.
The Shifting Initiative (SI) Theory
• Proponent puts forward argument fitting
scheme.
• Respondent asks appropriate critical question.
• Effect on Initiative: shifts to proponent to reply.
• Proponent fails to answer question
• Respondent does not have to accept argument.
• Effect on Initiative: Initiative not shifted, so
argument defaults.
• However, if proponent answers critical question,
respondent must accept argument.
The Backup Evidence (BE) Theory
• Proponent puts forward argument fitting scheme.
• Respondent asks appropriate critical question.
• Proponent: fails to answer question and asks for
backup evidence to support question.
• Respondent fails to present appropriate backup
evidence.
• Effect on Initiative: initiative shifts to respondent.
• Respondent makes no further move.
• Effect on Initiative: No initiative shifted, so
proponent’s argument stays in place.
Expertise Question: How credible is E
as an expert source?
• It expresses as a quantitative question asking how
strong the expert’s mastery of the field is. The expert
presumably needs to have some mastery of the field
for the argument from expert opinion to have any
worth.
• Can it be assumed that if someone is an expert they
have at least some mastery of the field? If so, failure to
give a specific answer should not be enough to make
the argument default. But if the argument can be very
weak, depending on the context, it could default.
• Hence this question is taken to best fit the SI theory.
Field Question: Is E an expert in the
field F that A is in?
• It is part of the minor premise, even though it
is not a full premise.
• On the assumption that it is a required part of
a premise, failure to back it up adequately
means that the argument should default.
• This analysis supports classifying the field
question under the SI theory.
Opinion Question: What did E assert
that implies A?
• If the proponent fails to supply a proposition
supposedly representing what the expert claimed, her
argument should default.
• But the issue is how to judge whether the proposition
needs to match exactly what the expert said, or
whether it could be implied by logical inference from
what the expert said. It seems like there is more room
for specific criteria to apply to these kinds of cases.
• Still, if the proponent gives no answer at all to the
question, it would be a bad failure, suggesting that the
argument should default. This analysis would suggest
that the SI theory applies.
Trustworthiness Question: Is E
personally reliable as a source?
• Unless the respondent gives some evidence
indicating that the expert is untrustworthy, the
proponent could simply reply, “There is no
evidence of that at all”, shifting the burden to the
respondent’s side to back up his question with
evidence. This interpretation supports the BE
theory.
• But if the respondent offers no evidence at all to
back up the expert’s trustworthiness, his
argument seems very weak. This also supports
the BE theory.
Consistency Question: Is A consistent
with what other experts assert?
• To make this question have any force,
presumably some evidence to support it is
required.
• The proponent could reply by asking the
respondent to give some evidence that some
other expert has said something inconsistent
with A.
• Thus it fits the BE theory better.
Evidence Question: Is E’s assertion
based on evidence?
• Generally it is assumed that what a genuine
expert claims is backed up by some evidence in
the field or domain of knowledge of the expert.
This would seem to be a generally reasonable
assumption in the case of a scientific expert.
• If so, the proponent should be prepared to give
some evidence, or indication that the expert’s
pronouncement is based on evidence.
• Thus this question fits the SI theory better.
Walton and Gordon (2005)
•
•
•
•
•
•
•
•
Ordinary Premise: E is an expert.
Ordinary Premise: E asserts that A.
Ordinary Premise: A is within F.
Assumption: It is assumed to be true that E is a
knowledgeable expert.
Assumption: It is assumed to be true that what E says is
based on evidence in field F.
Exception: E is not trustworthy.
Exception: What E asserts is not consistent with what
other experts in field F say.
Conclusion: A is true.
Conclusions
• We have shown how the Carneades model applies to a
typical defeasible argumentation scheme, namely the one
for argument from expert opinion.
• We have shown how Carneades incorporates defeasible
logic and builds on it to provide a computational tool that
not only enables us to do argument mapping, but to
represent the critical questions matching defeasible
argumentation scheme on an argument map.
• Carneades can use defeasible argumentation schemes not
only to evaluate arguments but to construct them. It also
has the capability for finding arguments needed to prove a
claim in a given case.
Some Argumentation Use Cases
Argument Evaluation Structures (AES)
Arguments are evaluated in a structure consisting of:
• Stage. A set of arguments, where an argument is a
<Premises, Conclusion> pair.
• Audience. An assignment of weights to arguments and
of a procedural status (stated, issue, accepted or
rejected) to each statement of the stage.
• An assignment of a proof standard to each statement
of the stage.
Statement Acceptability and Argument
Applicability
Are defined recursively:
• A statement is acceptable if it satisfies its proof
standard
• Whether or not a proof standard is satisfied depends
on the applicability of the argument pro and con the
statement and, for some standards, the weights
assigned to the arguments by the audience.
• An argument is applicable if all of its premises hold.
• Whether a premise holds depends on its type (ordinary,
exception, assumption) and the status (stated,
questioned, accepted, rejected) and acceptability of its
statement.
•
Proof
Standards
Scintilla of Evidence (SE)
– At least one applicable pro argument
• Dialectical Validity (DV)
– SE is satisfied and no con argument is applicable.
• Preponderance of the Evidence (PE)
– SE applies and some applicable pro argument has greater weight than any
applicable con argument.
• Clear and Convincing Evidence (CCE)
– PE is satisfied
– the max weight of the applicable pro arguments exceeds some threshold α,
and
– the difference between the max weight of the applicable pro arguments and
the max weight of the applicable con arguments exceeds some threshold β
• Beyond Reasonable Doubt (BRD)
– CCE is satisfied, and
– the max weight of the applicable con arguments is less than some threshold γ
Some References
Gordon, T. F. (2010). The Carneades Argumentation Support System, Dialectics,
Dialogue and Argumentation, ed. C. Reed and C. W. Tindale, London: College
Publications.
Governatori, G. (2008). Web page on defeasible logic: http://defeasible.org/
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.
Walton, D. (1997). Appeal to Expert Opinion, University Park, Penn State Press, 1997.
Walton, D. and Godden, D. (2005). The Nature and Status of Critical Questions in
Argumentation Schemes, The Uses of Argument: Proceedings of a Conference at
McMaster University 18-21 May, 2005, ed. Hitchcock, D., Hamilton, Ontario, 2005,
476-484.
Walton D. and Gordon, T. F. (2005). Critical Questions in Computational Models of
Legal Argument, Argumentation in Artificial Intelligence and Law, IAAIL Workshop
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:
Cambridge University Press.