Commonsense Reasoning 10/11 HC 11: Structured argumentation (3) / Dialogue Systems for Argumentation (1)

1. Commonsense Reasoning 10/11HC 11: Structured argumentation (3) /Dialogue Systems for Argumentation (1) Henry Prakken 12-01-2011

2. Overview • Structured argumentation • Odd defeat loops • Floating conclusions • Which logic is the right one? • Probabilistic reasoning • Dialogue systems for argumentation • Inference vs. dialogue • Use of argumentation in MAS • General ideas

3. R: W says that p  p A: Alice says that Bob is unreliable, so Bob is unreliable Exception: W is unreliable B: Bob says that Carole is unreliable, so Carole is unreliable E D C: Carole says that Alice is unreliable, so Alice is unreliable D: Bob says that John was the killer, so John was the killer A B E: Eric says that John was not the killer, so John was not the killer C

4. R: W says that p  p A: Alice says that Bob is unreliable, so Bob is unreliable Exception: W is unreliable B: Bob says that Carole is unreliable, so Carole is unreliable E D C: Carole says that Fred is unreliable, so Fred is unreliable F: Fred says that Alice is unreliable, so Alice is unreliable A B D: Bob says that John was the killer, so John was the killer F C E: Eric says that John was not the killer, so John was not the killer

5. R: W says that p  p A: Alice says that Bob is unreliable, so Bob is unreliable Exception: W is unreliable B: Bob says that Carole is unreliable, so Carole is unreliable E D C: Carole says that Fred is unreliable, so Fred is unreliable F: Fred says that Alice is unreliable, so Alice is unreliable A B D: Bob says that John was the killer, so John was the killer F C E: Eric says that John was not the killer, so John was not the killer

6. 1. An argument is In iff all arguments defeating it are Out. 2. An argument is Out iff it is defeated by an argument that is In. E D E D A B A B C F C

7. 1. An argument is In iff all arguments defeating it are Out. 2. An argument is Out iff it is defeated by an argument that is In. E D E D A B A B C F C

8. 1. An argument is In iff all arguments defeating it are Out. 2. An argument is Out iff it is defeated by an argument that is In. 3. An argument is justified if it is In in all labellings E D E D E is justified E is not justified A B A B C F C

9. S defends A if all defeaters of A are defeated by a member of S S is admissible if it is conflict-free and defends all its members {A,C,E} is admissible … E D A B F C

10. S defends A if all defeaters of A are defeated by a member of S S is admissible if it is conflict-free and defends all its members {A,C,E} is admissible … E D {B,D,F} is admissible … A B F C

11. S defends A if all defeaters of A are defeated by a member of S S is admissible if it is conflict-free and defends all its members {E} is admissible … E D A B C

12. S defends A if all defeaters of A are defeated by a member of S S is admissible if it is conflict-free and defends all its members {E} is admissible … E D but {B,D} is not … A B C

13. S defends A if all defeaters of A are defeated by a member of S S is admissible if it is conflict-free and defends all its members {E} is admissible … E D but {B,D} is not … A B C and {A,B,D} is not

14. Validating logics with intuitions (1): the general case • The problem: check that a logic adequately formalises a reasoning practice • A method: formalise examples, and check whether the logic satisfies one’s intuitions • But whose intuitions: of logicians, of `ordinary’ language users, … • And what if intuitions conflict

15. Validating logics with intuitions (2): the defeasible case • A special problem: how to distinguish counterexamples from abnormal situations? • Hypothesis: many “counterexamples” are based on new information that invalidates a defeasible inference.

16. Floating conclusions d1: x was born in Netherlands  x is Dutch d2: x has Chinese name  x is Chinese d3: x is Dutch  x likes badminton d4: x is Chinese  x likes badminton k1: Mei-li was born in the Netherlands k2: Mei-li has a Chinese name

17. is justified iff in all p.s.a. an argument with conclusion  is In (but it does not have to be the same argument) In grounded semantics  is defensible, in preferred semantics  is justified Mei li likes badminton Mei li likes badminton Mei li is Dutch Mei li is Chinese Mei li was born in The Netherlands Mei li has a Chinese name

18. Floating conclusions: invalid? • People tend to live in the same cities as their spouses • People tend to live in the city where they work • Carole works in A, her spouse works in B, so they live in A or B. Horty’s counterexample: Carole works in A, her spouse John works in B, so they live in U (between A and B) • But isn’t this an exceptional situation?

19. Which semantics is the “right” one? • Alternative semantics may each have their use in certain context • E.g. epistemic vs. practical reasoning • Dynamic aspects of reasoning makes this problem less urgent

20. Floating conclusions:still invalid? (Horty) • Witness John says: the suspect shot the victim to death • If a witness says P then usually P is the case • So, the suspect shot the victim to death • So, the suspect killed the victim • Witness Bob says: the suspect stabbed the victim to death • If a witness says P then usually P is the case • So, the suspect stabbed the victim to death • So, the suspect killed the victim One solution: add an undercutter “if two witnesses contradict each other, then they are both unreliable”

21. Floating conclusions:Don’t ignore dynamics • Any judge would ask further questions • Did you hear anything? • Where did you stand? • How dark was it? • The law’s way of dealing with dynamics: • Procedures for fair and effective dispute resolution

22. A simpler (imaginary) example • American civil law: evidence has to prove claim “on the balance of probabilities” • (Imaginary) statistic: 51% of American husbands commits adultery within 10 years. • Mary has been married to John for 10 years: can she sue John for divorce?

23. Defeasibility and probability: a paradox • The lottery paradox: • A lottery with 1 million tickets and 1 prize. • The probability that some ticket wins is 1 • The probability that a given ticket Li wins is 0.000001. • Is the conclusion that a given ticket will not win justified?

24. The lottery paradox in default logic • Problem: for no I is Li justified. • Solution HP: this is not a reasoning but a decision problem

25. Why do agents need argumentation? • For their internal reasoning • Reasoning about beliefs, goals, intentions etc often is defeasible • For their interaction with other agents • Information exchange involves explanation • Collaboration and negotiation involve conflict of opinion and persuasion

26. We should lower taxes We should not lower taxes Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad Increased inequality is good Lower taxes do not increase productivity Prof. P says that … Prof. P is not objective People with political ambitions are not objective USA lowered taxes but productivity decreased Increased inequality stimulates competition Prof. P has political ambitions Competition is good

27. claim We should lower taxes

28. claim why We should lower taxes

29. claim why We should lower taxes since Lower taxes increase productivity Increased productivity is good

30. claim why We should lower taxes We should not lower taxes since since Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad

31. claim why We should lower taxes We should not lower taxes since since Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad claim Increased inequality is good

32. claim why We should lower taxes We should not lower taxes since since Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad why claim Increased inequality is good

33. claim why We should lower taxes We should not lower taxes since since Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad why claim Increased inequality is good since Increased inequality stimulates competition Competition is good

34. claim why We should lower taxes We should not lower taxes since since Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad claim claim Increased inequality is good Lower taxes do not increase productivity since Increased inequality stimulates competition Competition is good

35. claim why We should lower taxes We should not lower taxes since since Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad why claim claim Lower taxes do not increase productivity Increased inequality is good since Increased inequality stimulates competition Competition is good

36. claim why We should lower taxes We should not lower taxes since since Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad why claim claim Increased inequality is good Lower taxes do not increase productivity since since USA lowered taxes but productivity decreased Increased inequality stimulates competition Competition is good

37. claim why We should lower taxes We should not lower taxes since since why Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad why claim claim Increased inequality is good Lower taxes do not increase productivity since since USA lowered taxes but productivity decreased Increased inequality stimulates competition Competition is good

38. claim why We should lower taxes We should not lower taxes since since why Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad since why claim claim Increased inequality is good Lower taxes do not increase productivity Prof. P says that … since since USA lowered taxes but productivity decreased Increased inequality stimulates competition Competition is good

39. claim why We should lower taxes We should not lower taxes since since why Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad since why claim claim Increased inequality is good Lower taxes do not increase productivity Prof. P says that … Prof. P is not objective since since since People with political ambitions are not objective USA lowered taxes but productivity decreased Increased inequality stimulates competition Prof. P has political ambitions Competition is good

40. claim why We should lower taxes We should not lower taxes retract since since why Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad since why claim claim Increased inequality is good Lower taxes do not increase productivity Prof. P says that … Prof. P is not objective since since since People with political ambitions are not objective USA lowered taxes but productivity decreased Increased inequality stimulates competition Prof. P has political ambitions Competition is good

41. Dialogue Type Dialogue Goal Initial situation Persuasion resolution of conflict conflict of opinion Negotiation making a deal conflict of interest Deliberation reaching a decision need for action Information seeking exchange of information personal ignorance Inquiry growth of knowledge general ignorance Types of dialogues (Walton & Krabbe)

42. P: I offer you this Peugeot for $10000. P: why do you reject my offer? P: why are French cars no good? P: why are French cars unsafe? P: Meinwagen is biased since German car magazines usually are biased against French cars P: why does Meinwagen have a very high reputation?. P: OK, I accept your offer. O: I reject your offer O: since French cars are no good O: since French cars are unsafe O: since magazine Meinwagen says so O: I concede that German car magazines usually are biased against French cars, butMeinwagen is not since it has a very high reputation. O: OK, I retract that French cars are no good. Still I cannot pay $10.000; I offer $8.000. Example

43. P: I offer you this Peugeot for $10000. P: why do you reject my offer? P: why are French cars no good? P: why are French cars unsafe? P: Meinwagen is biased since German car magazines usually are biased against French cars P: why does Meinwagen have a very high reputation?. P: OK, I accept your offer. O: I reject your offer O: since French cars are no good O: since French cars are unsafe O: since magazine Meinwagen says so O: I concede that German car magazines usually are biased against French cars, but Meinwagen is not since it has a very high reputation. O: OK, I retract that French cars are no good. Still I cannot pay $10.000; I offer $8.000. Example (2)

44. P: I offer you this Peugeot for $10000. P: why do you reject my offer? P: why are French cars no good? P: why are French cars unsafe? P: Meinwagen is biased since German car magazines usually are biased against French cars P: why does Meinwagen have a very high reputation?. P: OK, I accept your offer. O: I reject your offer O: since French cars are no good O: since French cars are unsafe O: since magazine Meinwagen says so O: I concede that German car magazines usually are biased against French cars, but Meinwagen is not since it has a very high reputation. O: OK, I retract that French cars are no good. Still I cannot pay $10.000; I offer $8.000. Example (3)

45. Inference vs dialogue • Dialogue systems for argumentation have: • A communication language (well-formed utterances) • A protocol (which utterances are allowed at which point?) • Termination and outcome rules • Argument games are a proof theory for a logic • But real argumentation dialogues have real players! • Distributed information • Richer communication languages • Dynamics

46. Standards for argumentation formalisms • Logical argument games: soundness and completeness wrt some semantics of an argumentation logic • Dialogue systems: effectiveness wrt dialogue goal and fairness wrt participants’ goals • Argumentation: • Dialogue goal = rational resolution of conflicts of opinion • Participants’ goal = to persuade

47. Some properties of dialogue systems that can be studied • Correspondence of outcome with players’ beliefs • If the union of participants’ beliefs justifies p, can/will agreement on p result? • If participants’ agree on p, does the union of their beliefs justify p? • Disregarding vs. assuming participants’ personalities

48. Game for grounded semantics unsound in distributed settings Knowledge bases Inference rules p  q s q r s r p Paul: p, r P1: q since p Olga: s

49. Game for grounded semantics unsound in distributed settings Knowledge bases Inference rules p  q s q r s r p Paul: p, r P1: q since p Olga: s O1: q since s

50. Game for grounded semantics unsound in distributed settings Knowledge bases Inference rules p  q s q r s r p Paul: p, r P1: q since p Olga: s, r O1: q since s P2: s since r