# On the structure of arguments, and what it means for dialogue Henry Prakken COMMA-08 Toulouse, 28-05-2008.

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On the structure of arguments, and what it means for dialogue Henry Prakken COMMA-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 < 18MarriedR3 Exc(R1) Parents know Parents: “married”

LegalCapacity Person  Exc(R1) R1 Minor Person R2 < 18  Minor Person < 18MarriedR3 Exc(R1) Parents know Parents: “married” Biased ParentsParents 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 P W 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 D E says that P P 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 observed Therefore (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(?) Premises If 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 with arguments 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

LegalCapacity claim

LegalCapacity claim why

LegalCapacity Person  Exc(R1) R1 claim why since

LegalCapacity Person  Exc(R1) R1 Exc(R1) claim why since Minor R2 Exc(R1)

LegalCapacity Person  Exc(R1) R1 Exc(R1) claim why since Minor R2 Exc(R1) why

LegalCapacity Person  Exc(R1) R1 Exc(R1) claim why since Minor R2 Exc(R1) Person< 18 why since

LegalCapacity Person  Exc(R1) R1 Exc(R1) claim why since Minor R2 Exc(R1) Person< 18 why since concede

LegalCapacity Person  Exc(R1) R1 Exc(R1) claim why since Minor R2 Exc(R1) Person< 18 why since  Minor Person < 18MarriedR3 since concede

LegalCapacity Person  Exc(R1) R1 Exc(R1) claim why since Minor R2 Exc(R1) Person< 18 why since  Minor Person < 18 Married R3 since why concede

LegalCapacity Person  Exc(R1) R1 Exc(R1) claim why since Minor R2 Exc(R1) Person< 18 why since  Minor Person < 18MarriedR3 since why Parents know Parents: “married” since concede

LegalCapacity Person  Exc(R1) R1 Exc(R1) claim why since Minor R2 Exc(R1) Person< 18 why since  Minor Person < 18MarriedR3 since why Parents know Parents: “married” since concede

LegalCapacity Person  Exc(R1) R1 Exc(R1) claim why since Minor R2 Exc(R1) Person< 18 why since concede  Minor Person < 18MarriedR3 since why Parents know Parents: “married” since concede Biased ParentsParents are biased since

LegalCapacity Person  Exc(R1) R1 Exc(R1) claim why since Minor R2 Exc(R1) Person< 18 why since concede  Minor Person < 18MarriedR3 since why Parents know Parents: “married” since concede Biased Parents Parents are 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?

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

Abductive reasoning Louw has a fractured skull Louw has brain damage Louw dies

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

Abductive reasoning Louw has a fractured skull Louw has brain damage Louw dies Louw was hit on the head by an angular object Louw fell

Dialogue about abductive model Louw has a fractured skull Louw has brain damage Louw dies Louw was hit on the head by an angular object Louw fell Why the facts?

Dialogue about abductive model Louw has a fractured skull Louw has brain damage Louw dies Louw was hit on the head by an angular object Louw fell (4) Pathologist’s report (1)Police report (coroner)

Dialogue about abductive model Louw has a fractured skull Louw has brain damage Louw dies Louw was hit on the head by an angular object Louw fell (4) Pathologist’s report (1)Police report (coroner) Why the causal relations?

Dialogue about abductive model Louw has a fractured skull Louw has brain damage Louw dies Louw was hit on the head by an angular object Louw fell (4) Pathologist’s report (1)Police report (coroner)

Case study: Murder in a Frisian Boarding House (Floris Bex) 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  Murder R2: Self-defence   R1 … S hit V, V died from hammer Murder? Default logic

R1: Kill & Intent  Murder R2: Self-defence   R1 … S hit V, V died from hammer Murder? Default logic O/I transformers Causal model V’s blood on hammer Observations V died from hammer? IBE S hit V? …..……

R1: Kill & Intent  Murder R2: Self-defence   R1 … S hit V, V died from hammer Murder? Default logic Evidence Cond probs Priors P(V’s blood on hammer| E)? Bayesian PT O/I transformers Causal model V’s blood on hammer Observations V died from hammer? IBE S hit V? …..……

R1: Kill & Intent  Murder R2: Self-defence   R1 … S hit V, V died from hammer Murder? Default logic Evidence Cond probs Priors P(V’s blood on hammer| E)? Bayesian PT Priors? Testimonies Argumentation O/I transformers Ev?CPs? Causal model V’s blood on hammer Observations V died from hammer?S hit V? …..…… Obs? CM?

R1: Kill & Intent  Murder R2: Self-defence   R1 … S hit V, V died from hammer Murder? Evidence Cond probs Priors P(V’s blood| E)? Priors? Testimonies Procedural law … Proof standard? Ev?CPs? Causal model V’s blood on hammer Observations V died from hammer? S hit V? Obs? CM? …..…… Evidence Cond probs Priors’ P(V’s blood| E)? Causal model Observations V died from hammer? R1: Kill & Intent  Murder R2: 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 findings E1,..., En all explain F E1 best explains F Therefore (presumably), E1 is the case

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