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

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.

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

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

  4. 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

  5. “Persons have the capacity to perform legal acts, unless the law provides otherwise” LegalCapacity Person Exc(R1) R1

  6. LegalCapacity Person Exc(R1) R1 Exc(R1) R2 Minor Person < 18

  7. LegalCapacity Person Exc(R1) R1 Exc(R1) R2 Minor Minor Person < 18 Person < 18 Married R3 Parents know Parents: “married”

  8. “Undercutters” Undercutter! LegalCapacity Person Exc(R1) R1 Exc(R1) R2 Minor Minor Person < 18 Person < 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. Argumentation schemes in AI • Pollock’s reasons • Perception • Memory • Induction • Statistical syllogism • Temporal persistence • ...

  15. 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

  17. 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 R2 Minor

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

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

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

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

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

  26. claim why LegalCapacity since Person Exc(R1) R1 Exc(R1) Exc(R1) since R2 Minor Minor since since why Person < 18 Person < 18 Married R3 concede why since Parents know Parents: “married”

  27. claim why LegalCapacity since Person Exc(R1) R1 Exc(R1) Exc(R1) since R2 Minor Minor since since why Person < 18 Person < 18 Married R3 concede why since Parents know Parents: “married” concede

  28. claim why LegalCapacity since Person Exc(R1) R1 Exc(R1) Exc(R1) since R2 Minor Minor since since why Person < 18 Person < 18 Married R3 concede why Biased since since Parents know Parents: “married” Parents Parents are biased concede

  29. claim why LegalCapacity since Person Exc(R1) R1 Exc(R1) Exc(R1) since R2 Minor Minor since since why Person < 18 Person < 18 Married R3 concede why Biased since since Parents know Parents: “married” Parents are biased Parents concede why

  30. 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 …

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

  32. Why?

  33. Why?

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

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

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

  37. 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

  38. 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

  39. Dialogue about abductive model (4) Pathologist’s 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

  40. Dialogue about abductive model (4) Pathologist’s 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

  41. Dialogue about abductive model (4) Pathologist’s 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

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

  43. Conclusions from the case study • Steps in an argument sometimes compresscomplex 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

  44. Default logic Murder? R1: Kill & Intent  Murder R2: Self-defence  R1 … S hit V, V died from hammer

  45. Default logic O/I transformers IBE 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 V’s blood on hammer Observations …..……

  46. Bayesian PT 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 V’s blood on hammer Observations …..…… IBE P(V’s blood on hammer| E)? Evidence Cond probs Priors

  47. Obs? CM? 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 V’s blood on hammer Observations …..…… P(V’s blood on hammer| E)? Evidence Cond probs Priors Bayesian PT Ev? CPs? Argumentation Priors? Testimonies

  48. 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 V’s blood on hammer Observations Causal model Observations Proof standard? P(V’s blood| E)? P(V’s blood| E)? Procedural law … Evidence Cond probs Priors Evidence Cond probs Priors’ Obs? Ev? CPs? Priors? CM? Testimonies

  49. 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

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