On the structure of arguments, and what it means for dialogue

1
On the structure of arguments, and what it means
for dialogue

• Henry Prakken
• COMMA-08
• Toulouse, 28-05-2008

2
Overview

• The structure of arguments overview of
  state-of-the art
• Argument schemes
• A legal example
• Abstraction in dialogue
• Combining modes of reasoning
• Conclusions

3
The structure of arguments current accounts

• Assumption-based approaches
• T theory
• A assumptions, - is conflict relation on A
• R inference rules
• A1 ? A yields an argument for p if A1 ? T -R p
• A2 for q attacks A1 if q - a for some a ? A1
• Inference-rule approaches
• T theory
• R inference rules, ? is conflict relation on R
• T1 ? T yields an argument for p if T1-R p
• T2 attacks T1 if T1 applies r1 and T2 applies r2
  and r2 ? r1

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The structure of argumentsAn integrated view

• Arguments have
• Premises
• Of various types
• A conclusion
• Ways to get from premises to conclusion
• Of various types
• So arguments can be attacked on
• Their premises
• Some types excluded
• Their conclusion
• The connection between premises and conclusion
• Some types excluded

5
LegalCapacity
Person
?Exc(R1)
R1
6
LegalCapacity
Person
?Exc(R1)
R1
Exc(R1)
Minor
R2
Person
lt 18
7
LegalCapacity
Person
?Exc(R1)
R1
Exc(R1)
Minor
R2
?Minor
Person
lt 18
Person
lt 18
Married
R3
Parents know
Parents married
8
LegalCapacity
Person
?Exc(R1)
R1
Exc(R1)
Minor
R2
?Minor
Person
lt 18
Person
lt 18
Married
R3
Biased
Parents know
Parents married
Parents
Parents are biased
9
Argument schemes

• Many arguments (and attacks) follow patterns
• Much work in argumentation theory (Perelman,
  Toulmin, Walton, ...)
• Argument schemes
• Critical questions

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Witness testimony(Walton 1996)

• Critical questions
• Is W really in the position to know about P?
• Did W really say that P?
• Is W biased?

Witness W is in the position to now about P W
says that P Therefore (presumably), P
is the case
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Expert testimony(Walton 1996)
E is expert on D E says that P P is within D
Therefore (presumably),
P is the case

• Critical questions
• Is E a genuine expert on D?
• Did E really say that P?
• Is P really within D?
• Is E biased?
• Is P consistent with what other experts say?
• Is P consistent with known evidence?

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From evidence to hypothesis(Walton 1996)

• Critical questions
• Is it the case that if P is true then Q is true?
• Has Q been observed?
• Could there be another reason why Q has been
  observed?

If P is the case, then Q will be observed Q has
been observed Therefore (presumably), P is the
case
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What is the logic of argument schemes? (1)

• Generalised conditional premise
• e.g. Katzav Reed
• Defeasible inference rule
• e.g. me, Gordon(?), Verheij(?)

Premises If Premises then typically Conclusion
Therefore (presumably), Conclusion
Premises Therefore (presumably),
Conclusion
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Argumentation schemes in AI

• Pollocks reasons
• Perception
• Memory
• Induction
• Statistical syllogism
• Temporal persistence
• ...

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What can be done witharguments in dialogue?

• State them (step-by-step or at once)
• Speech acts for claiming, arguing
• Attack them (stating a counterargument)
• React to the premises
• Speech acts for challenging, conceding,
  retracting, denying statements
• React to the inference(?)

16
Theory building in dialogue

• In my approach to (persuasion) dialogue
• Agents build a joint theory during the dialogue
• An argument graph
• Result (ideally) determined by arguments with no
  challenged or retracted premises

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claim
LegalCapacity
18
claim
why
LegalCapacity
19
claim
why
LegalCapacity
since
Person
?Exc(R1)
R1
20
claim
why
LegalCapacity
since
Person
?Exc(R1)
R1
Exc(R1)
Exc(R1)
since
Minor
R2
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claim
why
LegalCapacity
since
Person
?Exc(R1)
R1
Exc(R1)
Exc(R1)
since
Minor
R2
why
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claim
why
LegalCapacity
since
Person
?Exc(R1)
R1
Exc(R1)
Exc(R1)
since
Minor
R2
since
why
Person
lt 18
23
claim
why
LegalCapacity
since
Person
?Exc(R1)
R1
Exc(R1)
Exc(R1)
since
Minor
R2
since
why
Person
lt 18
concede
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claim
why
LegalCapacity
since
Person
?Exc(R1)
R1
Exc(R1)
Exc(R1)
since
Minor
R2
?Minor
since
since
why
Person
lt 18
Person
lt 18
Married
R3
concede
25
claim
why
LegalCapacity
since
Person
?Exc(R1)
R1
Exc(R1)
Exc(R1)
since
Minor
R2
?Minor
since
since
why
Person
lt 18
Person
lt 18
Married
R3
why
concede
26
claim
why
LegalCapacity
since
Person
?Exc(R1)
R1
Exc(R1)
Exc(R1)
since
Minor
R2
?Minor
since
since
why
Person
lt 18
Person
lt 18
Married
R3
why
concede
since
Parents know
Parents married
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claim
why
LegalCapacity
since
Person
?Exc(R1)
R1
Exc(R1)
Exc(R1)
since
Minor
R2
?Minor
since
since
why
Person
lt 18
Person
lt 18
Married
R3
why
concede
since
Parents know
Parents married
concede
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claim
why
LegalCapacity
since
Person
?Exc(R1)
R1
Exc(R1)
Exc(R1)
since
Minor
R2
?Minor
since
since
why
Person
lt 18
Person
lt 18
Married
R3
concede
why
Biased
since
since
Parents know
Parents married
Parents
Parents are biased
concede
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claim
why
LegalCapacity
since
Person
?Exc(R1)
R1
Exc(R1)
Exc(R1)
since
Minor
R2
?Minor
since
since
why
Person
lt 18
Person
lt 18
Married
R3
concede
why
Biased
since
since
Parents know
Parents married
Parents
Parents are biased
concede
why
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Reacting to inferences in dialogue

• Critical questions of argument schemes
• either ask about a premise
• covered above
• or ask about defeaters. Since schemes are
  defeasibly valid
• Dont ask the question but state a
  counterargument
• But there is another way of asking about an
  inference

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Case study Murder in a Frisian Boarding House
(Floris Bex)
Why?
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Why?
33
Why?
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Case study Murder in a Frisian Boarding House
(Floris Bex)
Why?
Why?
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Abductive reasoning
Louw has a fractured skull
Louw dies
Louw has brain damage
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Case study Murder in a Frisian Boarding House
(Floris Bex)
Why?
Why?
Why?
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Abductive reasoning
Louw has a fractured skull
Louw was hit on the head by an angular object
Louw dies
Louw has brain damage
Louw fell
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Dialogue about abductive model
Why the facts?
Louw has a fractured skull
Louw was hit on the head by an angular object
Louw dies
Louw has brain damage
Louw fell
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Dialogue about abductive model
(4) Pathologists report

• Police report
• (coroner)

Louw has a fractured skull
Louw was hit on the head by an angular object
Louw dies
Louw has brain damage
Louw fell
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Dialogue about abductive model
(4) Pathologists report

• Police report
• (coroner)

Why the causal relations?
Louw has a fractured skull
Louw was hit on the head by an angular object
Louw dies
Louw has brain damage
Louw fell
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Dialogue about abductive model
(4) Pathologists report

• Police report
• (coroner)

Louw has a fractured skull
Louw was hit on the head by an angular object
Louw dies
Louw has brain damage
Louw fell
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Case study Murder in a Frisian Boarding House
(Floris Bex)
Why?
Why?
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(No Transcript)
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Conclusions from the case study

• Steps in an argument sometimes compress complex
  lines of reasoning
• Dialogue systems should allow for unpacking
• Sometimes dialogues build theories that are not
  argument graphs
• Sometimes these theories combine several forms of
  reasoning
• A logic for such combinations is needed

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Murder?
R1 Kill Intent ? Murder R2 Self-defence ?
?R1 S hit V, V died from hammer
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Murder?
R1 Kill Intent ? Murder R2 Self-defence ?
?R1 S hit V, V died from hammer
V died from hammer?
S hit V?
Causal model Vs blood on hammer Observations
..
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Murder?
R1 Kill Intent ? Murder R2 Self-defence ?
?R1 S hit V, V died from hammer
Default logic
O/I transformers
V died from hammer?
S hit V?
Causal model Vs blood on hammer Observations
..
IBE
P(Vs blood on hammer E)?
Evidence Cond probs Priors
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Murder?
R1 Kill Intent ? Murder R2 Self-defence ?
?R1 S hit V, V died from hammer
Default logic
O/I transformers
V died from hammer?
S hit V?
Causal model Vs blood on hammer Observations
..
P(Vs blood on hammer E)?
Evidence Cond probs Priors
Bayesian PT
Ev?
CPs?
Argumentation
Priors?
Testimonies
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Murder?
Murder?
R1 Kill Intent ? Murder R2 Self-defence ?
?R1 S hit V, V died from hammer
R1 Kill Intent ? Murder R2 Self-defence ?
?R1 S hit V
S hit V?
V died from hammer?
V died from hammer?
..
Causal model Vs blood on hammer Observations
Causal model Observations
P(Vs blood E)?
Proof standard?
P(Vs blood E)?
Evidence Cond probs Priors
Procedural law
Evidence Cond probs Priors
Ev?
CPs?
Obs?
Priors?
Testimonies
CM?
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Final conclusions

• Inference
• Study the combination of reasoning forms
• Be open-minded dont force everything into the
  format of arguments
• Dialogue
• Allow that argument can be about something else
  than arguments
• Allow for switching between levels of abstraction

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Abduction(Walton 2001)

• Critical questions
• How good is E in itself as an explanation of F?
• How much better is E1 than E2,..., En?
• Are there further findings that change the
  assessment of E1?
• Are there further explanations that change the
  assessment of E?

F is a set of findings E1, ..., En all explain
F E1 best explains F Therefore
(presumably), E1 is the case