1. Computational Models for Argumentation in MAS
Leila Amgoud
IRIT – CNRS
France
Utrecht University

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 negotiate with each other

6. they need to engage in dialogues
Multi-agent systems
Agents need to:
exchange information and explanations
resolve conflicts of opinions
resolve conflicts 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
Resolving conflicts of opinions
Resolving conflicts of interests
Making joint decisions

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

14. Defeasible reasoning Reasoning is generally defeasible
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. Argumentation process
Defining the interactions between arguments
Evaluating the strengths of arguments
Defining the status of arguments
Drawing conclusions using a
consequence relation
Comparing decisions using
a given principle
Inference problem
Decision making problem
Constructing arguments

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. Q1: Building arguments Example 1. (Inference problem)
Let S be a propositional knowledge base
An argument A is a paire A = (H, h) such that:
1. H Í S
2. H is consistent
3. H |- h
4. H is minimal (for set inclusion) satisfying 1, 2 and 3

20. Q1: Building arguments A: ({p, p® b, b® f}, f) B: ({p, p®Øf}, Øf)2 3 S
p: pinguin
b: bird
f: fly

21. Q1: Building arguments Example 2. (Decision problem)
S = a propositional knowledge base
G = a goals base
D = a set of decision options
An argument in 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

22. 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> c,
u  l
¬u  ¬l
u  ¬w
r  ¬u  w
¬r  ¬w
c  r 1  S ¬w ¬l G 

23. Q2: Interactions between arguments
Three conflict relations:
Rebutting attacks: two arguments 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

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

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

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

27. 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

28. 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)
...
Preference relation between data
Strength of an argument
Preference relation between arguments

29. 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 p
pb
pf
bf 1 2 3

30. 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) c,
u  l
¬u  ¬l
u  ¬w
r  ¬u  w
¬r  ¬w
c  r 1  K ¬w ¬l G  1

31. 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 A B
<
>
A does not defeat B
A strictly defeats B

32. 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

33. 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

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

35. 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

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

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

38. 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

39. 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

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

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

42. 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 ?

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

44. 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 Argi ¹ Argj
If Playeri = P (i > 1) then Argi strictly defeats Argi-1
If Playeri = C then Argi defeats Argi-1

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

46. Proof theories A player wins a dialogue iff it ends the dialogue P C
won by P
won by C

47. Proof theories
A candidate sub-tree is a sub-tree of the dialogue tree containing all the edges of an even move (P) and exactly one edge of an odd move (C)
A solution sub-tree is 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

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

49. 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

50. Q5: Making decisions Problem = to define a preordering on D
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

51. 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
Args
E = Acceptable arguments

52. Q5: Making decisions Decision principles:
3 categories of principles: (Amgoud, Prade )
Unipolar principles = only one kind of arguments (PRO or CON) is involved
Bipolar principles = both arguments PRO and CON are involved
Non-polar principles

53. Q5: Making decisions Unipolar principles: Let d, d’  D.
Counting arguments PRO: d d’ iff |ArgP(d)| > |ArgP(d’)|
Counting arguments CON: d d’ iff |ArgC(d)| < |ArgC(d’)|
Promotion focus: d  d’ iff  P  ArgP(d) st.  P’  ArgP(d’),
P is stronger than P’.
Prevention focus: d d’ iff  C’  ArgC(d’) st.  C  ArgC(d),
C’ is stronger than C.

54. Q5: Making decisions Bipolar principles: Let d, d’  D. d  d’ iff
 P  ArgP(d) s.t.  P’  ArgP(d’), P is stronger than P’, and
 C’  ArgC(d’) s.t.  C  ArgC(d), C’ is stronger than C

55. Q5: Making decisions Non-polar principles: Let d, d’  D
<P1, …, Pn, C1, …, Cm> <P’1, …, P’k, C’1, …, C’l>
 ’
d  d’ iff  is stronger than ’

56. Q5: Rationality postulates
Idea: What are the properties/rationality postulates that any AS should satisfy ? (Amgoud, Caminada 05)
Consistency = AS should ensure safe conclusions
the set {x |  |~ x } should be consistent
the set of conclusions of each extension should be consistent
Closedness = AS should not forget safe conclusions
the set {x |  |~ x } should be closed
the set of conclusions of each extension should be closed

57. Outline Introduction to MAS Fundamentals of argumentation
Argumentation in MAS
Conclusions

58. Dialogue systems CS1 CSn Claim p Argue (S, p) ….
…………………
CS1
CSn
Claim p
Argue (S, p) ….
An argumentation system for evaluating the outcome of the dialogue

59. Components of a dialogue system
Communication language + Domain language
Protocol = the set of rules for generating coherent dialogues
Agent Strategies = the set of tactics used by the agents to choose a move to play
Outcome
One of a set of possible deals, or
Conflict
Protocol + Strategies Outcome

60. Communication language
A syntax = a set of locutions, utterances or speech acts (Propose, Argue, Accept, Reject, etc.)
A semantics = a unique meaning for each utterance
Mentalistic approaches
Social approaches
Protocol-based approaches

61. Dialogue Protocol
Protocol is public and independent from the mental states of the agents
Main parameters:
the set of allowed moves (e.g. Claim, Argue, ...)
the possible replies for each move
the number of moves per turn
the turntaking
the notion of Backtracking
the computation of the outcome
Identifies more or less rich dialogues

62. <Args(CS1  …  CSn), Defeat>, or
Dialogue Protocol
Computing the outcome: two approaches
The protocol is equipped with an argumentation system that evaluates the content of CS1  …  CSn:
<Args(CS1  …  CSn), Defeat>, or
<Args, Defeat>
The rules of the proof theory are encoded in the protocol

63. Dialogue Protocol
For persuasion dialogues, the two approaches return the same result if:
the other parameters are fixed in the same way
the acceptability semantics used is the same

64. Dialogue Strategies BDI agent Protocol CS1 … CSn
Set of allowed replies
Argumentation-based decision model
Next move to play
Move = Locution + Content
locution
argument type
argument
offer

65. Dialogue Strategies Different arguments are exchanged: about beliefs
about goals
Eg. I have a big family and I need a big car
referring to plans (instrumental arguments)
Eg. Modern Polo are becoming very spacious and
would easily fit in a big family
Which argument to present and when?
Need of a formal model for practical reasoning

66. Dialogue Strategies Dialogue strategies are at early stages
Thus, not possible yet to characterize the outcome of the dialogue, i.e. when the outcome is optimal, etc.

67. Open issues How goals are generated ? How / when are they revised ?
Do we always privilege new goals ?
The answer = NO
Threats ---> the goal can be adopted
Rewards ---> the goal can be ignored
AGM postulates for revising goals ?

68. Thank you