Commonsense Reasoning and Argumentation 13/14 HC 11: Structured argumentation (4)

1. Commonsense Reasoning and Argumentation 13/14HC 11: Structured argumentation (4) Henry Prakken 19 March 2014

2. Overview • Self-defeat and odd defeat loops • Can defeasible reasoning be reduced to plausible reasoning? • Applying ASPIC+ to a legislative debate • The need for dynamics

3. Parallel ‘self-defeat’ q q p p

4. r: q,r  p Serial self-defeat n(r) p A’ A

5. ¬r1 A is unreliable A: “A is unreliable” r1: W says that p  p r2: W is unreliable  ¬r1 k1: Alice says that Alice is unreliable

6. ¬r1 J is the killer A is unreliable A: “J is the killer” A: “A is unreliable”

7. ¬r1 J is the killer A is unreliable A: “J is the killer” A: “A is unreliable”

8. Grounded versus preferred semantics ¬r1 J is the not killer J is the killer A is unreliable B: “J is not the killer” A: “J is the killer” A: “A is unreliable”

9. Parallel ‘self-defeat’ q q p p

10. r: q,r  p Serial self-defeat n(r) p A’ A

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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 {B,C,D} is not

22. Can defeasible reasoning be reduced to plausible reasoning? • Is it natural to reduce all forms of attack to premise attack? • My answer: no • In classical argumentation: can the material implication represent defaults? • My answer: no

23. Default contraposition in classical argumentation Heterosexuals are normally married . John is not married Assume when possible that things are normal What can we conclude about John’s sexual orientation?

24. Default contraposition in classical argumentation Heterosexuals are normally married H &¬Ab  M John is not married (¬M) Assume when possible that things are normal ¬Ab The first default implies that non-married people are normally not heterosexual ¬M & ¬Ab  ¬H So John is not heterosexual

25. Default contraposition in classical argumentation (2) Men normally have no beard => Creatures with a beard are normally not men This type of sensor usually does not give false alarms => False alarms are usually not given by this type of sensor Witnesses interrogated by the police usually tell the truth => People interrogated by the police who do not speak the truth are usually not a witness Statisticians call these inferences “base rate fallacies”

26. The case of classical argumentation • Birds usually fly • Penguins usually don’t fly • All penguins are birds • Penguins are abnormal birds w.r.t. flying • Tweety is a penguin

27. The case of classical argumentation • Birds usually fly • Bird & ¬Ab1  Flies • Penguins usually don’t fly • Penguin & ¬Ab2  ¬Flies • All penguins are birds • Penguin  Bird • Penguins are abnormal birds w.r.t. flying • Penguin  Ab1 • Tweety is a penguin • Penguin • ¬Ab1 • ¬Ab2

28. The case of classical argumentation • Bird & ¬Ab1  Flies • Penguin & ¬Ab2  ¬Flies • Penguin  Bird • Penguin  Ab1 • Penguin • ¬Ab1 • ¬Ab2 Arguments: - for Flies using ¬Ab1 - for ¬Flies using ¬Ab2 - and for Ab1 and Ab2 But ¬Flies follows

29. The case of classical argumentation • Bird & ¬Ab1  Flies • Penguin & ¬Ab2  ¬Flies • Penguin  Bird • Penguin  Ab1 • ObservedAsPenguin & ¬Ab3  Penguin • ObservedAsPenguin • ¬Ab1 • ¬Ab2 • ¬Ab3 Arguments: - for Flies using ¬Ab1 • for ¬Flies using ¬Ab2 and ¬Ab3 • for Penguin using ¬Ab3 - and for Ab1 and Ab2 and Ab3 ¬Ab3 > ¬Ab2 > ¬Ab1 makes ¬Flies follow But is this ordering natural?

30. Contraposition of legal rules r1: Snores Misbehaves r2: Misbehaves May be removed r3: Professor  ¬May be removed K: Snores, Professor r1 < r2, r1 < r3, r3 < r2 This is the intuitive outcome May be removed May be removed R3 < R2 r2 r3 Misbehaves Professor r1 30 Snores

31. Contraposition of legal rules r1: Snores Misbehaves r2: Misbehaves May be removed r3: Professor  ¬May be removed K: Snores, Professor r1 < r2, r1 < r3, r3 < r2 But with contraposition (and any intuitive ordering) we have this outcome May be removed May be removed r2 r3 Misbehaves Professor r1 31 Snores

32. My conclusion Classical logic’s material implication is too strong for representing defeasible generalisations or legal rules => Models of legal argument (and many other kinds of argument) need defeasible inference rules Defeasible reasoning cannot be modelled as inconsistency handling in deductive logic John Pollock: Defeasible reasoning is the rule, deductive reasoning is the exception

33. An application to a legislative debate

34. Combining multiple good/bad consequences Action A results in C1 … Action A results in Cn C1 is good … Cn is good Therefore, Action A is good Action A results in C1 … Action A results in Cn C1 is bad … Cm is bad Therefore, Action A is bad

36. GC3 GC 123 BC 12 GC2 GC 23 GC1 GC 13 C1 P1 GC 12 DMP P2

37. Preferred labelling 1 GC3 1. An argument is In iff all arguments that defeat it are Out. 2. An argument is Out iff some argument that defeats it is In. GC 123 BC 12 GC2 GC 23 GC1 GC 13 C1 P1 GC 12 DMP P2

38. Preferred labelling 2 GC3 1. An argument is In iff all arguments that defeat it are Out. 2. An argument is Out iff some argument that defeats it is In. GC 123 BC 12 GC2 GC 23 GC1 GC 13 C1 P1 GC 12 DMP P2

39. Grounded labelling GC3 1. An argument is In iff all arguments that defeat it are Out. 2. An argument is Out iff some argument that defeats it is In. GC 123 BC 12 GC2 GC 23 GC1 GC 13 C1 P1 GC 12 DMP P2

41. Choosing between semantics (or not?)

42. P is justified iff all labellings make an argument with conclusion P in (but it does not have to be the same argument) In preferred semantics P is justified, in grounded semantics P is not justified The suspect killed the victim The suspect killed the victim the suspect shot the victim to death the suspect stabbed the victim to death Witness John says: the suspect shot the victim to death Witness Bob says: the suspect stabbed the victim to death 42

43. 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”

44. Undercutter formalised d(w,p): Witness w says that p  p, ud(w,w’,p,-p): Witness w says that p, Witness w’ says that -p  -d(w,p) Requires reasoning about preferences d(w,p): Witness w says that p  p, ud(w,w’,p,-p): Witness w says that p, Witness w’ says that –p, d(w,p) ≤ d(w’,-p)  -d(w,p)

45. 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

46. 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?