Computational Models for Argumentation in MAS

1. Computational Models for Argumentation in MAS Leila Amgoud IRIT – CNRS France amgoud@irit.fr

2. Outline • Introduction to MAS • Fundamentals of argumentation • Argumentation in MAS • Conclusions

3. The notion of agent (Wooldridge 2000) • An agent is a computer system that is capable of autonomous (i.e. independent) action on behalf of its user or owner (figuring out what needs to be done to satisfy design objectives, rather constantly being told) • Rationality: agent will act in order to achieve its goals, and will not act in such a way as to prevent its goals being achieved — at least insofar as its beliefs permit

4. The notion of agent • An agent needs the ability to make internal reasoning: • Reasoning about beliefs, desires, … • Handling inconsistencies • Making decisions • Generating, revising, and selecting goals • ...

5. Multi-agent systems (Wooldrige 2000) • A multi-agent system is one that consists of a number of agents, which interact with one another • Generally, agents will be acting on behalf of users of different goals and motivations • To successfully interact, they will require the ability to cooperate, coordinate, and negotiatewith each other

6. Multi-agent systems • Agents need to: • exchange information and explanations • resolveconflicts of opinions • resolveconflicts of interests • make joint decisions they need to engage in dialogues

7. Dialogue types (Walton & Krabbe 1995)

8. The role of argumentation • Argumentation plays a key role for achieving the goals of the above dialogue types • Argument=Reason for some conclusion (belief, action, goal, etc.) • Argumentation= Reasoning about arguments  decide on conclusion • Dialectical argumentation= Multi-party argumentation through dialogue

9. The role of argumentation Argumentation plays a key role for reaching agreements: • Additional information can be exchanged • The opinion of the agent is explicitly explained(e.g. arguments in favor of opinions or offers, arguments in favor of a rejection or an acceptance) • Agents can modify/revise their beliefs / preferences / goals • To influence the behavior of an agent (threats, rewards)

10. A persuasion dialogue P : The newspapers have no right to publish information I. C : Why? P : Because it is about X's private life and X does not agree (P1) C : The information I is not private because X is a minister and all information concerning ministers is public (C1) P : But X is not a minister since he resigned last month (P2) P2  C1  P1

11. A negotiation dialogue Buyer: Can’t you give me this 806 a bit cheaper? Seller: Sorry that’s the best I can do. Why don’t you go for a Polo instead? Buyer: I have a big family and I need a big car(B1) Seller: Modern Polo are becoming very spacious and would easily fit in a big family. (S1) Buyer: I didn’t know that, let’s also look at Polo then.

12. Why study argumentation in agent technology? • For internal reasoning of single agents: • Reasoning about beliefs, goals, ... • Making decisions • Generating, revising, and selecting goals • For interaction between multiple agents: • Exchanging information and explanations • Resolvingconflicts of opinions • Resolvingconflicts of interests • Making joint decisions

13. Outline • Introduction to MAS • Fundamentals of argumentation • Argumentation in MAS • Conclusions

14. Defeasible reasoning • Reasoning is generallydefeasible • Assumptions, exceptions, uncertainty, ... • AI formalises such reasoning with non-monotonic logics • Default logic, etc … • New premisses can invalidate old conclusions • Argumentation logics formalise defeasible reasoning as construction and comparison of arguments

15. Constructingarguments Defining theinteractionsbetween arguments Evaluating thestrengthsof arguments Defining thestatusof arguments Drawing conclusions using a consequence relation Comparing decisions using a givenprinciple Inference problem Decision making problem Argumentation process

16. Main challenges Q1: What are the different types of arguments ? How do we construct arguments ? Q2: How can an argument interact with another argument ? Q3: How do we compute the strength of an argument ? Q4: How do we determine the status of arguments Q5: How do we conclude ? How decisions are compared on the basis of their arguments? Q6: What are the properties that an argumentation system should satisfy ?

17. Q1: Building arguments Types of arguments:(Kraus et al. 98, Amgoud & Prade 05) • Explanations (involve only beliefs) • Tweety flies because it is a bird • Threats (involve beliefs + goals) • You should do  otherwise I will do  • You should not do  otherwise I will do  • Rewards (involve beliefs + goals) • If you do , I will do  • If you don’t do , I will do  • …

18. Q1: Building arguments Forms of arguments: • An inference tree grounded in premises • A deduction sequence • A pair (Premises, Conclusion), leaving unspecified the particular proof that leads from the Premises to the Conclusion

19. S 1 p pb 2 pf 3 bf Q1: Building arguments • A: ({p, p® b, b® f}, f) • B: ({p, p®Øf}, Øf) p: pinguin b: bird f: fly

20. Q1: Building arguments Example 2. (Decision problem) • S = a propositional knowledge base • G = a goals base • D = a set of decision options • An argumentin favor of a decision d is a triple A = <S, g, d> s.t. 1. d  D 2. g  G 3. S S 4. S  {d} is consistent 5. S  {d} |- g 6. S is minimal (set ) satisfying the above conditions

21. c, u  l ¬u  ¬l u  ¬w r  ¬u  w ¬r  ¬w 1 c  r  ¬w 1 ¬l  G S Q1: Building arguments r: rain w: wet c: cloud u: umbrella l: overloaded D = {u, ¬u} • A = <{u  ¬w}, {¬w}, u> • B = <{¬u  ¬l}, {¬l}, ¬u>

22. Q2: Interactions between arguments Three conflict relations: • Rebutting attacks: twoarguments with contradictory conclusions • Assumption attacks: an argument attacks an assumption of another argument • Undercutting attacks: an argument undermines some intermediate step (inference rule) of another argument

23. ¬Tweety flies Tweety flies Rebutting attacks Tweety flies because it is a bird versus Tweety does not fly because it is a penguin

24. Tweety flies Penguin Tweety Not(Penguin Tweety) Assumption attacks Tweety flies because it is a bird, and it is not provable that Tweety is a penguin versus Tweety is a penguin

25. ¬[a, b, c /d] d a b c I ’ve seen Opus, it is a bird and it does not fly Tweety flies because all the birds I ’ve seen fly Undercutting attack An argument challenges the connection between the premisses and the conclusion

26. Q3: Strengths of arguments Why do we need to compute the strengths of arguments ? • To compare arguments • To refine the status of arguments by removing some attacks • To define decision principles

27. Preference relation between data Strength of an argument Preference relation between arguments Q3: Strengths of arguments • The strength of an argument depends on the quality of information used to build that argument • Examples: • Weakest link principle (Benferhat & al. 95, Amgoud 96) • Last link principle (Prakken & Sartor 97) • Specificity principle (Simari & Loui 92) • ...

28. 1 p pb 2 pf 3 bf Q3: Strengths of arguments Example 1. (Weakest link principle) A: ({p, pb, b f}, f) B: ({p, pf}, f) Strength(A) = 3 Strength(B) = 2 Then B is preferred to (stronger than) A

29. c, u  l ¬u  ¬l u  ¬w r  ¬u  w ¬r  ¬w 1 1  c  r  ¬w ¬l G K Q3: Strengths of arguments Example 2. • A = <{u  ¬w}, {¬w}, u> • B = <{¬u  ¬l}, {¬l}, ¬u> • Strength(A) = (1, 1) • Strength(B) = (1, ) Different preference relations between such arguments are defined (Amgoud, Prade 05)

30. A A B B < > A does not defeat B A strictly defeats B Q4: Status of arguments • Some attacks can be removed • Defeat = Attack + Preference relation between arguments • Attacking and not weaker Defeat • Attacking and stronger Strict Defeat

31. Q4: Status of arguments Given <Args, Defeat>, what is the status of a given argument A  Args? Three classes of arguments • Arguments with which a dispute can be won (justified) • Arguments with which a dispute can be lost (rejected) • Arguments that leave the dispute undecided

32. Q4: Status of arguments Two ways for computing the status of arguments: • The declarative form usually requires fixed-point definitions, and establishes certain sets of arguments as acceptable Acceptability semantics • The procedural form amounts to defining a procedure for testing whether a given argument is a member of « a set of acceptable arguments » Proof theory

33. A C B A reinstates C Acceptability semantics • Semantics = specifies conditions for labelling the argument graph • The labelling should: • accept undefeated arguments • capture the notion of reinstatement

34. Acceptability semantics Example of labelling: L: Args  {in, out, und} • An argument is in if all its defeaters are out • An argument is out if it has a defeater that is in • An argument is und otherwise

35. in A C A C B B out Acceptability semantics • Example 1: • Only one possible labelling:

36. A A A B B B and Acceptability semantics • Example 2: • Two possible labellings:

37. Acceptability semantics Two approaches: • A unique status approach • An argument is justified iff it is in • An argument is rejected if it is out • An argument is undecided it is und • A multiple status approach • An argument is justified iff it is in in any labelling • An argument is rejected if it is out in any labelling • An argument is undecided it is in in some labelling and out in others

38. Acceptability semantics • Unique status: Grounded semantics (Dung 95) • E1 = all undefeated arguments • E2 = E1 + all arguments reinstated by E1 • … • It exists only if there are undefeated arguments

39. A C D A C D B B We want Acceptability semantics • Problem with grounded semantics: floating arguments

40. A C D A C D B B D is justified and C is rejected Acceptability semantics • Multiple labellings:

41. Proof theories • Let <Args, Defeat> be an AS • S1, …, Sn its extensions under a given semantics. Problem: Let a  Args • Is a in one extension ? • Is a in every extension ?

42. A0 A3 A6 A4 A1 A5 A2 Proof theories • Let a  Args. • Problem: Is a in the grounded extension ? • Example:

43. Proof theories (Amgoud & Cayrol 00) • A dialogue is a non-empty sequence of moves s.t: Movei = (Playeri, Argi) (i  0) where: • Playeri = P iff i is even, Playeri = C iff i is odd • Player0 = P and Arg0 = a • If Playeri = Playerj = P and i ¹ j then Argi¹ Argj • If Playeri = P (i > 1) then Argistrictly defeats Argi-1 • If Playeri = C then Argidefeats Argi-1

44. A0 P C A0 P A3 C A3 A6 A6 <Args, Defeat> Dialogue tree A1 A4 A1 A4 A5 A5 A2 A2 Proof theories (Amgoud & Cayrol 00) • A dialogue tree is a finite tree where each branch is a dialogue

45. A0 P won by P C won by P won by C P A3 C A6 A4 A1 A5 A2 Proof theories • A playerwins a dialogueiffit ends the dialogue

46. Proof theories • A candidate sub-treeisa sub-tree of thedialogue tree containing all the edges of an even move (P) and exactly one edge of an odd move (C) • A solution sub-treeis a candidate subtree whose branches are all won by P • P wins a dialogue tree iff the dialogue tree has a solution sub-tree • Complete construction: ‘ a ’ the grounded extension iff  a dialogue tree whose root is ‘ a ’ and won by P

47. A0 A0 A0 P C A2 A3 A1 A3 P A3 C A6 A6 S1 S2 Each branch of S2 is won by P  S2 is a solution sub-tree A0 is in the grounded extension A1 A4 A4 A4 A5 A2 A5 A5 Proof theories • Two candidate sub-trees:

48. Q5: Consequence relations • : a knowledge base built from a logical language L, • x: a formula of L • <Args, Defeat>: an argumentation system • S1, …, Sn: the extensions under a given semantics. •  |~ x iff  an argument A for x s.t. A  Si,  Si, i = 1, …, n •  |~ x iff  Si,  an argument A for x, and A  Si •  |~ x iff  Si st  an argument A for x and A  Si, and  Sj st  an argument A for x and A  Si •  |~ x iff  Si st  an argument A for x and A  Si

49. Q5: Making decisions • D = a set of decision options • Problem = to define a preordering on D • <Args, Defeat> = an argumentation system • Let d  D <P1, …, Pn, C1, …, Cm> Arg. PRO d Arg. CON d

50. Args E = Acceptable arguments Q5: Making decisions • ArgP(d) = the arguments in E which are PRO d • ArgC(d) = the arguments in E which are CON d