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The Toulmin Argument Model in Artificial Intelligence Or: how semi-formal, defeasible argumentation schemes creep into logic. Bart Verheij Artificial Intelligence, University of Groningen, The Netherlands. The Uses of Argument. Original aim:

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slide1

The Toulmin Argument Model in Artificial IntelligenceOr: how semi-formal, defeasible argumentation schemes creep into logic

Bart Verheij

Artificial Intelligence, University of Groningen, The Netherlands

the uses of argument
The Uses of Argument

Original aim:

‘to criticize the assumption, made by most Anglo-American academic philosophers, that any significant argument can be put in formal terms: not just as a syllogism, since for Aristotle himself any inference can be called a ‘syllogism’ or ‘linking of statements’, but a rigidly demonstrative deduction of the kind to be found in Euclidean geometry.’

the uses of argument4
The Uses of Argument

‘In no way had I set out to expound a theory of rhetoric or argumentation: my concern was with twentieth-century epistemology, not informal logic.’

toulmin s model
Toulmin’s model

Hitchcock, D., & B. Verheij (eds.) (2006). Arguing on the Toulmin Model. New Essays in Argument Analysis and Evaluation.Argumentation Library, Vol. 10. Springer, Dordrecht.

Hitchcock, D. & B. Verheij (2005). The Toulmin model today: Introduction to special issue of Argumentation on contemporary work using Stephen Edelston Toulmin's layout of arguments. Argumentation, Vol. 19, No. 3, pp. 255-258.

main themes of toulmin 1958
Main themes of Toulmin (1958)
  • Argument analysis involves half a dozen distinct elements, not just two.
slide8
(1) Anne is one of Jack’s sisters;

All Jack’s sisters have red hair;

So, Anne has red hair.

(2) P(t)

(x) (P(x) → Q(x))

-----------------------

Q(t)

slide9
(1, backing version)

Anne is one of Jack’s sisters;

Each one of Jack’s sisters has (been checked individually to have) red hair;

So, Anne has red hair.

(1, warrant version)

Anne is one of Jack’s sisters;

Any sister of Jack’s will (i.e. may be taken to) have red hair;

So, Anne has red hair.

slide10
Toulmin's adaptation of (1):

Datum: Anne is one of Jack’s sisters.

Claim: Anne has red hair.

Warrant: Any sister of Jack’s will (i.e. may be taken to) have red hair.

Backing: All his sisters have previously been observed to have red hair.

Qualifier: Presumably

Rebuttal: Anne has dyed/gone white/lost her hair ...

main themes of toulmin 195811
Main themes of Toulmin (1958)
  • Argument analysis involves half a dozen distinct elements, not just two.
  • Many, if not most, arguments are substantial, hence defeasible.
slide12
Three warrants:

A whale will be a mammal

A Bermudan will be a Briton

A Saudi Arabian will be a Muslim

Point to similar inferential connections:

Infer that a particular whale is a mammal

Infer that a particular Bermudan is a Briton

Infer that a particular Saudi Arabian is a Muslim

slide13
But are based on different kinds of standards:

A whale will be (i.e. is classifiable as) a mammal

A Bermudan will be (in the eyes of the law) a Briton

A Saudi Arabian will be (found to be) a Muslim

Backings use:

A system of taxonomical classification

Statutes governing the nationality of people born in the British colonies

Statistics on the distribution of religious beliefs among nationalities

main themes of toulmin 195814
Main themes of Toulmin (1958)
  • Argument analysis involves half a dozen distinct elements, not just two.
  • Many, if not most, arguments are substantial, hence defeasible.
  • Standards of good reasoning and argument assessment are non-universal.
slide15
Logic as psychology

Describe an individual thinker’s thinking

Logic as sociology

Describe general habits and practices

Logic as technology

Provide recipes for rationality

Logic as mathematics

Find truths about logical relations

Logic as jurisprudence

Emphasize the cases we make for our claims

main themes of toulmin 195816
Main themes of Toulmin (1958)
  • Argument analysis involves half a dozen distinct elements, not just two.
  • Many, if not most, arguments are substantial, hence defeasible.
  • Standards of good reasoning and argument assessment are non-universal.
  • Logic is to be regarded as generalised jurisprudence.
the reception and refinement of toulmin s ideas in artificial intelligence
The reception and refinement of Toulmin’s ideas in Artificial Intelligence

3.1 Reiter’s default rules

3.2 Pollock’s undercutting and rebutting defeaters

3.3 Prakken, Sartor & Hage on reasoning with legal rules

3.4 Dung’s admissible sets

3.5 Walton’s argumentation schemes

3.6 Reed & Rowe’s argument analysis software

3.7 Verheij’s formal reconstruction of Toulmin’s scheme

admissible sets

Admissible sets

Admissible, e.g.: {, }, {, , , , }

Not admissible, e.g.: {, }, {}

dung s types of extensions 1995
Dung’s types of extensions (1995)

A conflict-free set of arguments is a stable extension if all arguments that are not in the set are attacked by an argument in the set.

An admissible set of arguments is a preferred extension if it is an admissible set that is maximal with respect to set inclusion.

A set of arguments is a complete extension if it is an admissible set that contains all arguments of which all attackers are attacked by the set.

A set of arguments is a (the) grounded extension if it is a minimal complete extension.

from sets to labelings 1996
From sets to labelings (1996)

A stage extension is a is a conflict free set of arguments, for which the union of the set with the set of arguments attacked by it is maximal.

A set of arguments is a admissible stage extension if it is an admissible set, for which the union of the set with the set of arguments attacked by it is maximal.

from sets to labelings 199623
From sets to labelings (1996)

A stage extension is a is a conflict free set of arguments, for which the union of the set with the set of arguments attacked by it is maximal.

A set of arguments is a admissible stage extension if it is an admissible set, for which the union of the set with the set of arguments attacked by it is maximal.

semi-stable extension (2006)

slide24
Compatibility types

Dialectical justification types

a forest of extension types
A forest of extension types

Compatibility types

Dialectical justification types

a forest of extension types26
A forest of extension types … :-(

Compatibility types

Dialectical justification types

slide27
From sets to labelings
  • A forest of extension types
  • Don't forget about support
pros cons
Pros & cons

Peter has assaulted Jack

Peter has assaulted Jack

Police officer Jim testifies that he saw Peter assaulting Jack

Police officer Anne testifies that she saw Peter not assaulting Jack

toulmin s 1958 warrants
Toulmin’s 1958 warrants

Peter has assaulted Jack

The warrant

Police officers normally are right

Police officer Jim testifies that he saw Peter assaulting Jack

pollock s 1987 undercutting defeaters
Pollock’s 1987 undercutting defeaters

Peter has assaulted Jack

The undercutter

Jim is lying

Police officer Jim testifies that he saw Peter assaulting Jack

preferred and stable extensions
Preferred and stable extensions

The notions of admissibility and preferred and stable extensions can be generalized to this setting.

E.g., direct translation of admissibility:

Require defense against all attacking subsets of Δ

Subtle difference (admissible*):

Require defense against all incompatible subsets of Δ

For attack graphs: admissible = admissible*.

the gluing theorem
The ‘gluing’ theorem

Theorem. There is a stable extension of Δ if and only if there is a conflict-free set of sentences DA  Δ (the disambiguation) such that there is a DA-compatible admissible proof or an admissible refutation (and not both) for each element of Δ.

Without *:

holds for attack graphs, but not for attack-support graphs with nesting (entangled dialectical arguments)

With*:

holds for both.

*

*

example
Example

All 3-element subsets are admissible. All sentences are admissibly provable, and none is admissibly refutable1. Still there is no stable extension.

But no sentence is admissible*.

p2

p1 ~> q

p2 ~> (q ~> q)}

p1, p2

p1

q

1 Admissible refutation is here defined as attack by an admissible,

and not as non-membership of the union of admissibles.

slide34
From sets to labelings
  • A forest of extension types
  • Don't forget about support
  • Finding warrants is a knowledge engineering task
walton on argumentation schemes
Walton on argumentation schemes

Generic AH

a is a bad person.

Therefore, a’s argument A should not be accepted.

-> a semi-formal rule of inference

walton on argumentation schemes36
Walton on argumentation schemes

Argumentation schemes come with critical questions, e.g., for Generic AH:

CQ1 Is the premise true (or well supported) that a is a bad person?

CQ2 Is the allegation that a is a bad person relevant to judging a’s argument A?

CQ3 Is the conclusion of the argument that A should be (absolutely) rejected even if other evidence to support A has been presented, or is the conclusion merely (the relative claim) that a should be assigned a reduced weight of credibility, relative to the total body of evidence available?

finding warrants is a knowledge engineering task
Finding warrants is a knowledge engineering task

1. Determine the relevant types of sentences

2. Determine the conditional relations, i.e., the antecedents and consequents of the argumentation schemes

  • Determine the exceptions, i.e, the arguments against the use of the argumentation schemes
  • Determine the conditions of use for the argumentation schemes

(Not necessarily in this order and perhaps sometimes going back to earlier steps)

slide38
From sets to labelings
  • A forest of extension types
  • Don't forget about support
  • Finding warrants is a knowledge engineering task
  • How much logic helps?
argumentation software
Argument assistants are computer programs that support argumentative tasks

Analogy:

Text writing assistants (aka word processing software) are computer programs that support text writing tasks

Argumentation software
slide40

Underlying defeasible logic

  • Automatic evaluation
  • Argument construction
  • Natural moves
  • Arguing about rules and exceptions

1999 ICAIL conference, 2003 Artificial Intelligence journal, 2005 Virtual Arguments book

slide45
From sets to labelings
  • A forest of extension types
  • Don't forget about support
  • Finding warrants is a knowledge engineering task
  • How much logic helps?
  • Stories and/or arguments?
a 1931 wigmore chart
A 1931 Wigmore chart

Umilian was accused of murdering Jedrusik.

ten universal rules of evidence
Ten universal rules of evidence

1. The prosecution must present at least one well-shaped narrative.

2. The prosecution must present a limited set of well-shaped narratives.

3. Essential components of the narrative must be anchored.

4. Anchors for different components of the charge should be independent of each other.

5. The trier of fact should give reasons for the decision by specifying the narrative and the accompanying anchoring.

6. A fact-finder's decision as to the level of analysis of the evidence should be explained through an articulation of the general beliefs used as anchors.

7. There should be no competing story with equally good or better anchoring.

8. There should be no falsifications of the indictment's narrative and nested sub-narratives.

9. There should be no anchoring onto obviously false beliefs.

10. The indictment and the verdict should contain the same narrative.

Wagenaar, W.A., van Koppen, P.J., and Crombag, H.F.M. (1993), Anchored Narratives. The Psychology of Criminal Evidence (London: Harvester Wheatsheaf).

ten universal rules of evidence48
Ten universal rules of evidence

1. The prosecution must present at least one well-shaped narrative.

2. The prosecution must present a limited set of well-shaped narratives.

3. Essential components of the narrative must be anchored.

4. Anchors for different components of the charge should be independent of each other.

5. The trier of fact should give reasons for the decision by specifying the narrative and the accompanying anchoring.

6. A fact-finder's decision as to the level of analysis of the evidence should be explained through an articulation of the general beliefs used as anchors.

7. There should be no competing storywith equally good or better anchoring.

8. There should be no falsifications of the indictment's narrative and nested sub-narratives.

9. There should be no anchoring onto obviously false beliefs.

10. The indictment and the verdict should contain the same narrative.

Wagenaar, W.A., van Koppen, P.J., and Crombag, H.F.M. (1993), Anchored Narratives. The Psychology of Criminal Evidence (London: Harvester Wheatsheaf).

a mixed argumentative narrative perspective

Events

Chronology

Evidence

A mixed argumentative-narrative perspective

Floris Bex (2009). Evidence for a Good Story. A Hybrid Theory of Arguments, Stories and Criminal Evidence. Dissertation, University of Groningen.

slide50
From sets to labelings
  • A forest of extension types
  • Don't forget about support
  • Finding warrants is a knowledge engineering task
  • How much logic helps?
  • Stories and/or arguments?
main themes of toulmin 195851
Main themes of Toulmin (1958)
  • Argument analysis involves half a dozen distinct elements, not just two.
  • Many, if not most, arguments are substantial, hence defeasible.
  • Standards of good reasoning and argument assessment are non-universal.
  • Logic is to be regarded as generalised jurisprudence.