Commonsense Reasoning and Argumentation 13/14 HC 9 Structured argumentation (2)

1. Commonsense Reasoning and Argumentation 13/14HC 9Structured argumentation (2) Henry Prakken March 5, 2014

2. Overview • Argument schemes • Preferences • Rationality postulates

3. Domain-specific vs. inference general inference rules d1: Bird  Flies s1: Penguin  Bird Penguin K Rd = {,     } Rs = all valid inference rules of prop. l. Bird  Flies K Penguin  Bird K Penguin K Flies Bird Penguin Flies Bird Bird Flies Penguin  Bird Penguin

4. Argument(ation) schemes: general form But also critical questions Premise 1, … , Premise n Therefore (presumably), conclusion

5. Argument schemes in ASPIC • Argument schemes are defeasible inference rules • Critical questions are pointers to counterarguments • Some point to undermining attacks • Some point to rebutting attacks • Some point to undercutting attacks

6. Reasoning with generalisations Critical questions: How strong is the connection? Is there an exception? Illegal immigrant? Client of prostitute? … Involved P If P then normally Q So (presumably), Q Fleas If fleas then normally involved People who flea from a crime scene are normally involved in the crime

7. How are generalisations justified? Scientific research (induction) Experts Commonsense Individual opinions Prejudice? Very reliable Very unreliable

8. Inducing generalisations Critical questions: Is the size of the sample large enough? was the sample selection biased? Almost all observed P’s were Q’s Therefore (presumably), If P then usually Q A ballpoint shot with this type of bow will usually cause this type of eye injury In 16 of 17 tests the ballpoint shot with this bow caused this type of eye injury

9. Expert testimony(Walton 1996) • Critical questions: • 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

10. Witness testimony • Critical questions: • Is W sincere? • Does W’s memory function properly? • Did W’s senses function properly? W says P W was in the position to observe P Therefore (presumably), P

11. Temporal persistence(Forward) • Critical questions: • Was P known to be false between T1 and T2? • Is the gap between T1 and T2 too long? P is true at T1 and T2 > T1 Therefore (presumably), P is still true at T2

12. Temporal persistence(Backward) • Critical questions: • Was P known to be false between T1 and T2? • Is the gap between T1 and T2 too long? P is true at T1 and T2 < T1 Therefore (presumably), P was already true at T2

13. X murdered Y d.m.p. Y murdered in house at 4:45 V murdered in L at T & S was in L at T  S murdered V X in 4:45 accrual X in 4:45{X in 4:30} X in 4:45{X in 5:00} backw temp pers forw temp pers X left 5:00 X in 4:30 accrual X in 4:30{W1} X in 4:30{W2} testimony testimony testimony W2: “X in 4:30” W1: “X in 4:30” W3: “X left 5:00”

14. Arguments from consequences Critical questions: Does A also have bad (good) consequences? Are there other ways to bring about G? ... Action A causes G, G is good (bad) Therefore (presumably), A should (not) be done

15. Example (arguments pro and con an action) We should make spam a criminal offence We should not make spam a criminal offence Reduction of spam is good Making spam a criminal offence reduces spam Making spam a criminal offence increases workload of police and judiciary Increased workload of police and judiciary is bad

16. Example (arguments pro alternative actions) We should make spam a criminal offence We should make spam civilly unlawful Making spam a criminal offence reduces spam Making spam civilly unlawful reduces spam Reduction of spam is good Reduction of spam is good

17. Refinement: promoting or demoting legal/societal values Critical questions: Are there other ways to cause G? Does A also cause something else that promotes or demotes other values? ... Action A causes G, G promotes (demotes) legal/societal value V Therefore (presumably), A should (not) be done

18. Example (arguments pro and con an action) We should save DNA of all citizens We should not save DNA of all citizens Solving more crimes promotes security Saving DNA of all citizens leads to solving more crimes Saving DNA of all citizens makes more private data publicly accessible Making more private data publicly available demotes privacy

19. Example (arguments pro alternative actions) We should save DNA of all citizens We should have more police Solving more crimes promotes security Saving DNA of all citizens leads to solving more crimes Having more police leads to solving more crimes Solving more crimes promotes security

20. Comparing action proposals For every proposal that is based on acceptable premises: List all values that it promotes or demotes Determine the extent to which the proposal promotes or demotes the value Determine the relative importance of the values at stake Then weigh the pros and cons of all proposals But how?

21. Argument preference • In general its origin is undefined • Could be defined in terms of  (on Rd) and ’ (on Kp) • Origins of  and ’: domain-specific!

22. Argument preference: two alternatives (Informal: ordering on K ignored, no argument strict and firm) Weakest link comparison: A <aB iff theweakest defeasible rule of B is strictly preferred over the weakest defeasible rule of A Last-link comparison: A <aB iffthe last defeasible rules of B are strictly preferred over the last defeasible rules of A

23. Example Rd: r1: p  q r2: p  r r3: s  t Rs: q, r  ¬t K: p,s

24. Comparing ordered sets (elitist ordering) • Ordering <s onsets in terms of an ordering  (or ’) on their elements: • If S1 =  then not S1 <s S2 • If S1 ≠  and S2 =  then S1 <s S2 • Else S1 <s S2 if there exists an s1  S1 such that for all s2  S2: s1 < s2

25. Last link vs. weakest link (1) r1: Born in Scotland Scottish r2: Scottish Likes Whisky r3: Fitness Lover  ¬Likes Whisky K: Born in Scotland, Fitness Lover r1 < r2, r1 < r3, r2 ≈r3 Likes Whisky Likes Whisky r2 r3 Scottish Fitness lover r1 Born in Scotland

26. Weakest link r1: Born in Scotland Scottish r2: Scottish Likes Whisky r3: Fitness Lover  ¬Likes Whisky K: Born in Scotland, Fitness Lover r1 < r2, r1 < r3, r2 ≈r3 Likes Whisky Likes Whisky r2 r3 Scottish Fitness lover r1 Born in Scotland

27. Last link r1: Born in Scotland Scottish r2: Scottish Likes Whisky r3: Fitness Lover  ¬Likes Whisky K: Born in Scotland, Fitness Lover r1 < r2, r1 < r3, r2 ≈r3 Likes Whisky Likes Whisky r2 r3 Scottish Fitness lover r1 Born in Scotland

28. Last link vs. weakest link (2) r1: Snores Misbehaves r2: Misbehaves May be removed r3: Professor  ¬May be removed K: Snores, Professor r1 < r2, r1 < r3, r2 ≈r3 May be removed May be removed r2 r3 Misbehaves Professor r1 Snores

29. Consistency in ASPIC+(with symmetric negation) For any SL S is directly consistent iff S does not contain two formulas  and– The strict closure Cl(S) of S is S + everything derivable from S with only Rs. S is indirectly consistent iffCl(S) is directly consistent. Parametrised by choice of strict rules 29

30. Rationality postulates(Caminada & Amgoud 2007) Let E be any Dung-extension and Conc(E) = {| = Conc(A) for some A E } An AT satisfies subargument closure iff BE whenever AE and B Sub(A) direct consistency iff Conc(E) is directly consistent strict closure iff Cl(Conc(E)) = Conc(E) indirect consistency iff Conc(E) is indirectly consistent

31. Trans- and contraposition • Transposition: • If S  p Rs then S/{s} U {–p}  –s Rs • Contraposition: • If S |- p and s  S then S/{s} U {– p} |- –s

32. Rationality postulatesfor ASPIC+ (whether consistent premises or not) Closure under subarguments always satisfied Direct and indirect consistency: without preferences satisfied if Rs closed under transposition or AS closed under contraposition; and Kn is indirectly consistent with preferences satisfied if in addition is ‘reasonable’ Weakest- and last link ordering are reasonable