1 Computational Models for Argumentation in MAS Leila Amgoud IRIT – CNRS France [email protected].

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Computational Models for Argumentation in MAS

Leila Amgoud

IRIT – CNRSFrance

[email protected]

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Outline

Introduction to MAS Fundamentals of argumentation Argumentation in MAS Conclusions

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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

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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 ...

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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

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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

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Dialogue types (Walton & Krabbe

1995)

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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

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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)

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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

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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.

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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

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Outline


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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

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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

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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 ?

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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

…

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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

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A: ({p, p b, b f}, f) B: ({p, pf}, f)

p: pinguin

b: bird

f: fly

p pb

pf

bf

1

2

3

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Q1: Building argumentsExample 2. (Decision problem)

= 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 G3. S 4. S {d} is consistent5. S {d} |- g6. S is minimal (set ) satisfying the above conditions

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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 ¬lu ¬wr ¬u w¬r ¬w

c r

1

¬w

¬l

G

1

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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

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Rebutting attacks

Tweety flies because it is a bird

versus

Tweety does not fly because it is a penguin

Tweety flies ¬Tweety flies

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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)

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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]

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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

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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

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Example 1. (Weakest link principle)

A: ({p, pb, b f}, f)

B: ({p, pf}, f)

Strength(A) = 3Strength(B) = 2

Then B is preferred to (stronger than) A

p pb

pf

bf

1

2

3

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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 ¬lu ¬wr ¬u w¬r ¬w

c r

1

K

¬w

¬l

G

1

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Q4: Status of arguments

Some attacks can be removed

Defeat = Attack + Preference relation between arguments

Attacking and not weaker Defeat

Attacking and stronger Strict DefeatA B

<A B

>

A does not defeat B A strictly defeats B

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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

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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

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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

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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

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Acceptability semantics Example 1:

Only one possible labelling:

A B C

A B C

in

out

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Acceptability semantics Example 2:

Two possible labellings:

A B

A B A Band

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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

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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

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Problem with grounded semantics: floating arguments

A B

C

D

A B

C

D

We want

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Multiple labellings:

A B

C

D

A B

C

D

D is justified and C is rejected

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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 ?

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Proof theories

Let a Args. Problem: Is a in the grounded extension ?

Example: A0

A4 A5

A3A1 A2

A6

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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 j then Argi Argj

If Playeri = P (i > 1) then Argi strictly defeats Argi-1

If Playeri = C then Argi defeats Argi-1

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Proof theories (Amgoud & Cayrol

00)

A dialogue tree is a finite tree where each branch is a dialogue

P

C

C

P

A0

A4 A5

A3A1 A2

A6

A0

A4 A5

A3A1 A2

A6

Dialogue tree<Args, Defeat>

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Proof theories

A player wins a dialogue iff it ends the dialogue

P

C

C

P

A0

A4 A5

A3A1 A2

A6

won by P

won by P

won by C

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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

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Proof theories

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

C

P

A0

A4 A5

A3A1 A2

A6

A0

A4 A5

A2 A3

A6S1

A0

A4 A5

A1 A3

S2

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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

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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

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Q5: Making decisions

ArgP(d) = the arguments in E which are PRO d ArgC(d) = the arguments in E which are CON d

ArgsE = Acceptable arguments

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Decision principles:

3 categories of principles: (Amgoud, Prade 2004-2006)

Unipolar principles = only one kind of arguments (PRO or CON) is involved

Bipolar principles = both arguments PRO and CON are involved

Non-polar principles

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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

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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 ’

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Q5: Rationality postulatesIdea: 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

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Outline


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Dialogue systems

…………………

CS1 CSn …………………

Claim p

Argue (S, p)

….

An argumentation system for evaluating the outcome of the dialogue

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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

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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

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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

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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

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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

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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

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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 familyWhich argument to present and when?

Need of a formal model for practical reasoning

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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.

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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 ?

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Thank you

1 Computational Models for Argumentation in MAS Leila Amgoud IRIT – CNRS France [email protected].

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