on the structure of arguments, and what it means for dialogue henry prakken comma-08 toulouse,...

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

Henry PrakkenCOMMA-08

Toulouse, 28-05-2008

Overview The structure of arguments: overview of

state-of-the art Argument schemes A legal example

Abstraction in dialogue Combining modes of reasoning

Conclusions

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 T’2 attacks T1 if T1 applies r1 and T2 applies r2 and

r2 r1

The structure of arguments:An 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

LegalCapacity

Person Exc(R1) R1

“Persons have the capacity to perform legal acts,

unless the law provides otherwise”

LegalCapacity

Person Exc(R1) R1

Minor

Person

R2

< 18

Exc(R1)

LegalCapacity

Person Exc(R1) R1

Minor

Person

R2

< 18

Minor

Person < 18 Married R3

Exc(R1)

Parents know

Parents: “married”

LegalCapacity

Person Exc(R1) R1

Minor

Person

R2

< 18

Minor


Exc(R1)

Parents know


Biased

Parents Parents are biased

“Undercutters”

Undercutter!

Argument schemes

Many arguments (and attacks) follow patterns Much work in argumentation theory

(Perelman, Toulmin, Walton, ...) Argument schemes Critical questions

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 PW says that P Therefore (presumably), P is the case

Expert testimony(Walton 1996)

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?

E is expert on DE says that PP is within D Therefore (presumably), P is the case

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 observedTherefore (presumably), P is the case

What is the logic of argument schemes? (1)

Generalised conditional premise e.g. Katzav & Reed

Defeasible inference rule e.g. me, Gordon(?), Verheij(?)

PremisesIf Premises then typically Conclusion Therefore (presumably), Conclusion

Premises Therefore (presumably), Conclusion

Argumentation schemes in AI

Pollock’s reasons Perception Memory Induction Statistical syllogism Temporal persistence ...

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(?)

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

LegalCapacityclaim

LegalCapacityclaim why

LegalCapacity

Person Exc(R1) R1

claim whysince

LegalCapacity

Person Exc(R1) R1

Exc(R1)

claim whysince

since

Minor R2

Exc(R1)

LegalCapacity

Person Exc(R1) R1

Exc(R1)

claim whysince

since

Minor R2

Exc(R1)

why

LegalCapacity

Person Exc(R1) R1

Exc(R1)

claim whysince

since

Minor R2

Exc(R1)

Person < 18

why

since

LegalCapacity

Person Exc(R1) R1

Exc(R1)

claim whysince

since

Minor R2

Exc(R1)

Person < 18

why

since

concede

LegalCapacity

Person Exc(R1) R1

Exc(R1)

claim whysince

since

Minor R2

Exc(R1)

Person < 18

why

since Minor


since

concede

LegalCapacity

Person Exc(R1) R1

Exc(R1)

claim whysince

since

Minor R2

Exc(R1)

Person < 18

why

since Minor


since

whyconcede

LegalCapacity

Person Exc(R1) R1

Exc(R1)

claim whysince

since

Minor R2

Exc(R1)

Person < 18

why

since Minor


since

why

Parents know


since

concede

LegalCapacity

Person Exc(R1) R1

Exc(R1)

claim whysince

since

Minor R2

Exc(R1)

Person < 18

why

since Minor


since

why

Parents know


since

concede

concede

LegalCapacity

Person Exc(R1) R1

Exc(R1)

claim whysince

since

Minor R2

Exc(R1)

Person < 18

why

since

concede

Minor


since

why

Parents know


since

concede

Biased


since

LegalCapacity

Person Exc(R1) R1

Exc(R1)

claim whysince

since

Minor R2

Exc(R1)

Person < 18

why

since

concede

Minor


since

why

Parents know


since

concede

Biased


since

why

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: Don’t ask the question but state a

counterargument But there is another way of asking

about an inference …

Case study: Murder in a Frisian Boarding House (Floris Bex)

Why?


Why?Why?

Abductive reasoning

Louw has a fractured skull

Louw has brain damage

Louw dies


Why?Why?

Why?

Abductive reasoning



Louw dies

Louw was hit onthe head by anangular object

Louw fell

Dialogue about abductive model



Louw dies


Louw fell

Why the

facts?




Louw dies


Louw fell

(4) Pathologist’sreport

(1) Police report(coroner)




Louw dies


Louw fell



Why the causal

relations?




Louw dies


Louw fell




Why?

Why?

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

R1: Kill & Intent MurderR2: Self-defence R1…S hit V, V died from hammer

Murder?

Default logic


Murder?

Default logic

O/I transformers

Causal modelV’s blood on hammerObservations

V died from hammer?

IBE

S hit V?

…..……


Murder?

Default logic

EvidenceCond probsPriors

P(V’s blood on hammer| E)?

Bayesian PT

O/I transformers


V died from hammer?

IBE

S hit V?

…..……


Murder?

Default logic


P(V’s blood on hammer| E)?

Bayesian PT

Priors?Testimonies

Argumentation

O/I transformers

Ev? CPs?


V died from hammer? S hit V?

…..……

Obs?

CM?


Murder?


P(V’s blood| E)?

Priors?Testimonies

Procedural law…

Proof standard?

Ev? CPs?


V died from hammer? S hit V?

Obs?

CM?

…..……

EvidenceCond probsPriors’

P(V’s blood| E)?

Causal modelObservations

V died from hammer?

R1: Kill & Intent MurderR2: Self-defence R1…S hit V

Murder?

Final conclusions Inference:

Study the combination of reasoning forms

Be open-minded: don’t 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

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 findingsE1, ..., En all explain FE1 best explains F Therefore (presumably), E1 is the case

on the structure of arguments, and what it means for dialogue henry prakken comma-08 toulouse,...

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