MODELING CRITICAL QUESTIONS AS ADDITIONAL PREMISES Douglas Walton CRRAR OSSA, May 19, 2011.

MODELING CRITICAL QUESTIONS AS ADDITIONAL PREMISES

Douglas WaltonCRRAR

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 premisesOrdinary premises – for the minor and major premises of schemesAssumptions – for critical questions to be answered by the proponentExceptions – 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 argumentQuestioned – Statements which have been called into question but not yet decidedAccepted – Statements which have been acceptedRejected – 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.