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Argumentation Logics Lecture 5: Argumentation with structured arguments (1) argument structure

Argumentation Logics Lecture 5: Argumentation with structured arguments (1) argument structure. Henry Prakken Chongqing June 2, 2010. Contents. Structured argumentation: Arguments Argument schemes. Merits of Dung (1995). Framework for nonmonotonic logics Comparison and properties

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Argumentation Logics Lecture 5: Argumentation with structured arguments (1) argument structure

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  1. Argumentation LogicsLecture 5:Argumentation with structured arguments (1) argument structure Henry Prakken Chongqing June 2, 2010

  2. Contents • Structured argumentation: • Arguments • Argument schemes

  3. Merits of Dung (1995) • Framework for nonmonotonic logics • Comparison and properties • Guidance for development • From intuitions to theoretical notions • But should not be used for KR

  4. The structure of arguments: two approaches • Both approaches: arguments are inference trees • Assumption-basedapproaches (Dung-Kowalski-Toni, Besnard & Hunter, …) • Sound reasoning from uncertain premises • Arguments attack each other on their assumptions (premises) • Rule-based approaches (Pollock, Vreeswijk, …) • Risky (‘defeasible’) reasoning from certain premises • Arguments attack each other on applications of defeasible inference rules

  5. Aspic framework: overview Argument structure: • Trees where • Nodes are wff of a logical language L • Links are applications of inference rules • Rs = Strict rules (1, ..., 1  ); or • Rd= Defeasible rules (1, ..., 1  ) • Reasoning starts from a knowledge base K L • Defeat: attack on conclusion, premise or inference, + preferences • Argument acceptability based on Dung (1995)

  6. Argumentation systems An argumentation system is a tuple AS = (L, -,R,) where: L is a logical language - is a contrariness function from L to 2L R = Rs Rd is a set of strict and defeasible inference rules  is a partial preorder on Rd If   -() then: if   -() then  is a contrary of ; if   -() then  and  are contradictories  = _,  = _ 

  7. Knowledge bases A knowledge base in AS = (L, -,R,= ’) is a pair (K, =<’) where K L and ’ is a partial preorder on K/Kn. Here: Kn = (necessary) axioms Kp = ordinary premises Ka = assumptions

  8. Structure of arguments • An argumentA on the basis of (K, ’) in (L, -,R, ) is: •  if K with • Conc(A) = {} • Sub(A) =  • DefRules(A) = • A1, ..., An if there is a strict inference rule Conc(A1), ..., Conc(An)   • Conc(A) = {} • Sub(A) = Sub(A1)  ...  Sub(An)  {A} • DefRules(A) = DefRules(A1)  ...  DefRules(An) • A1, ..., An if there is a defeasible inference rule Conc(A1), ..., Conc(An)  • Conc(A) = {} • Sub(A) = Sub(A1)  ...  Sub(An)  {A} • DefRules(A) = DefRules(A1)  ...  DefRules(An)  {A1, ..., An}

  9. P Q1 Q2 R1 R2 Q1, Q2  P Q1,R1,R2 K R1, R2  Q2

  10. Example R: • r1: p  q • r2: p,q  r • r3: s  t • r4: t  ¬r1 • r5: u  v • r6: v,q  ¬t • r7: p,v  ¬s • r8: s  ¬p Kn = {p}, Kp = {s,u}

  11. Types of arguments An argument A is: Strict if DefRules(A) =  Defeasible if not Firm if Prem(A)  Kn Plausible if not firm S |-  means there is a strict argument A s.t. Conc(A) =  Prem(A)  S

  12. Domain-specific vs. inference general inference rules R1: Bird  Flies R2: Penguin  Bird Penguin K Rd = {,     } Rs = all deductively valid inference rules Bird  Flies K Penguin  Bird K Penguin K Flies Bird Penguin Flies Bird Bird Flies Penguin  Bird Penguin

  13. Argument(ation) schemes: general form Defeasible inference rules! But also critical questions Negative answers are counterarguments Premise 1, … , Premise n Therefore (presumably), conclusion

  14. 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

  15. 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

  16. Arguments from consequences • Critical questions: • Does A also have bad consequences? • Are there other ways to bring about G? • ... Action A brings about G, G is good Therefore (presumably), A should be done

  17. 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

  18. 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

  19. X murdered Y dmp Y murdered in house at 4:45 X in 4:45 V murdered in L at T & S was in L at T  S murdered V 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”

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