on norms for the dynamics of argumentative interaction: argumentation as a game henry prakken...

On norms for the dynamics of

argumentative interaction: argumentation as a game

Henry PrakkenAmsterdam

January 18, 2010

Overview

Lorenzen’s dialogue logic

Hamblin’s formal dialectic AI’s argumentation logics

MAS dialogue systems for argumentation

Lorenzen’s dialogue logic:game-theoretic semantics of

connectives

Paul: claims qP1: q P2: p (attacking p q) P3: you said it yourself! (against

q?)

Olga: concedes p, p q O1: q?O2: q (defending p q)

P has a winning strategy for claim given concessions S iff S entails

Hamblin’s formal dialectic:rules for substantial discussions

Paul: P1: claim q P2: q since p, p qP3: that’s why

Olga:O1: why q?

O2: concede p q but why p?

O3: (can I trust Paul?)

Paul’s beliefs:pp q

Olga’s beliefs:rp q

If Olga concedes p, she must concede q or retract p q

We should lower taxes

Lower taxes increase productivity

Increased productivity is good

We should lower taxes

Lower taxes increase productivity

Increased productivity is good

We should not lower taxes

Lower taxes increase inequality

Increased inequality is bad

We should lower taxes

Lower taxes increase productivity

Increased productivity is good

We should not lower taxes

Lower taxes increase inequality

Increased inequality is bad

Lower taxes do not increase productivity

USA lowered taxes but productivity decreased

We should lower taxes

Lower taxes increase productivity

Increased productivity is good

We should not lower taxes

Lower taxes increase inequality

Increased inequality is bad

Lower taxes do not increase productivity

Prof. P says that …

USA lowered taxes but productivity decreased

We should lower taxes

Lower taxes increase productivity

Increased productivity is good

We should not lower taxes

Lower taxes increase inequality

Increased inequality is bad

Lower taxes do not increase productivity

Prof. P says that …

Prof. P has political ambitions

People with political ambitions are not objective

Prof. P is not objective

USA lowered taxes but productivity decreased

We should lower taxes

Lower taxes increase productivity

Increased productivity is good

We should not lower taxes

Lower taxes increase inequality

Increased inequality is bad

Lower taxes do not increase productivity

Prof. P says that …

Prof. P has political ambitions

People with political ambitions are not objective

Prof. P is not objective

USA lowered taxes but productivity decreased

We should lower taxes

Lower taxes increase productivity

Increased productivity is good

We should not lower taxes

Lower taxes increase inequality

Increased inequality is bad

Lower taxes do not increase productivity

Prof. P says that …

Prof. P has political ambitions

People with political ambitions are not objective

Prof. P is not objective

Increased inequality is good

Increased inequality stimulates competition

Competition is good

USA lowered taxes but productivity decreased

We should lower taxes

Lower taxes increase productivity

Increased productivity is good

We should not lower taxes

Lower taxes increase inequality

Increased inequality is bad

Lower taxes do not increase productivity

Prof. P says that …

Prof. P has political ambitions

People with political ambitions are not objective

Prof. P is not objective

Increased inequality is good

Increased inequality stimulates competition

Competition is good

USA lowered taxes but productivity decreased

A B

C D E

1. An argument is In if all arguments defeating it are Out.2. An argument is Out if it is defeated by an argument that is In.

Dung 1995

Grounded semantics minimises node colouring Preferred semantics maximises node colouring

A sound and complete game for grounded semantics:

The rules: Each move replies to previous move Proponent does not repeat moves Proponent moves strict defeaters, opponent

moves defeaters A player wins iff the other player cannot move

Result: A is in the grounded extension iff proponent has a winning strategy in a game about A.

A defeat graph

A

B

C

D

E

F

A winning strategy for P

P: AA

B

C

D

E

F

move

A winning strategy for P

P: AA

B

C

D

E

F

O: F

move

A winning strategy for P

P: AA

B

C

D

E

F

O: F

P: E

move

A winning strategy for P

P: A

O: B

A

B

C

D

E

F

O: F

P: E

move

A winning strategy for P

P: A

O: B

P: C

A

B

C

D

E

F

O: F

P: E

move

Interaction Argument games verify status of

argument (or statement) given a single theory (knowledge base)

But real argumentation dialogues have Distributed information Dynamics

We should lower taxes

claim

We should lower taxes

claim why

We should lower taxes

Lower taxes increase productivity

Increased productivity is good

since

claim why

We should lower taxes

Lower taxes increase productivity

Increased productivity is good

We should not lower taxes

Lower taxes increase inequality

Increased inequality is bad

since since

claim why

We should lower taxes

Lower taxes increase productivity

Increased productivity is good

We should not lower taxes

Lower taxes increase inequality

Increased inequality is bad

Increased inequality is good

Increased inequality stimulates competition

Competition is good

since since

since

claim why

We should lower taxes

Lower taxes increase productivity

Increased productivity is good

We should not lower taxes

Lower taxes increase inequality

Increased inequality is bad

Lower taxes do not increase productivity

Increased inequality is good

Increased inequality stimulates competition

Competition is good

since since

since

claim

claim

why

We should lower taxes

Lower taxes increase productivity

Increased productivity is good

We should not lower taxes

Lower taxes increase inequality

Increased inequality is bad

Lower taxes do not increase productivity

Increased inequality is good

Increased inequality stimulates competition

Competition is good

since since

since

claim

claim

why

why

We should lower taxes

Lower taxes increase productivity

Increased productivity is good

We should not lower taxes

Lower taxes increase inequality

Increased inequality is bad

Lower taxes do not increase productivity

Increased inequality is good

Increased inequality stimulates competition

Competition is good

USA lowered taxes but productivity decreased

since

since since

since

claim

claim

why

why

We should lower taxes

Lower taxes increase productivity

Increased productivity is good

We should not lower taxes

Lower taxes increase inequality

Increased inequality is bad

Lower taxes do not increase productivity

Increased inequality is good

Increased inequality stimulates competition

Competition is good

USA lowered taxes but productivity decreased

since

since since

since

claim

claim

why

why

why

We should lower taxes

Lower taxes increase productivity

Increased productivity is good

We should not lower taxes

Lower taxes increase inequality

Increased inequality is bad

Lower taxes do not increase productivity

Prof. P says that …

Increased inequality is good

Increased inequality stimulates competition

Competition is good

USA lowered taxes but productivity decreased

since

since since

since

since

claim

claim

why

why

why

We should lower taxes

Lower taxes increase productivity

Increased productivity is good

We should not lower taxes

Lower taxes increase inequality

Increased inequality is bad

Lower taxes do not increase productivity

Prof. P says that …

Prof. P has political ambitions

People with political ambitions are not objective

Prof. P is not objective

Increased inequality is good

Increased inequality stimulates competition

Competition is good

USA lowered taxes but productivity decreased

since

since since

since since

since

claim

claim

why

why

why

We should lower taxes

Lower taxes increase productivity

Increased productivity is good

We should not lower taxes

Lower taxes increase inequality

Increased inequality is bad

Lower taxes do not increase productivity

Prof. P says that …

Prof. P has political ambitions

People with political ambitions are not objective

Prof. P is not objective

Increased inequality is good

Increased inequality stimulates competition

Competition is good

USA lowered taxes but productivity decreased

since

since since

since since

since

claim

claim

why

why

why

retract

Dialogue systems (according to Carlson 1983)

Dialogue systems define the conditions under which an utterance is appropriate

An utterance is appropriate if it furthers the goal of the dialogue in which it is made

Appropriateness defined not at speech act level but at dialogue level

Dialogue game approach

Dialogue game systems A communication language

Well-formed utterances Rules for when an utterance is

allowed Protocol

Turntaking rules Termination rules

Standards for game rules Logical argument games: soundness

and completeness wrt some logical semantics

Dialogical argument games: effectiveness wrt dialogue goal and fairness wrt participants’ goals Argumentation:

Dialogue goal = rational conflict resolution Participants’ goal = to win

Some quality aspects of dialogue protocols

Effectiveness: does the protocol further the dialogue goal? Agent rationality, Efficiency (relevance,

termination, ...) Fairness: does the protocol respect the

participants’ goals? Flexibility, opportunity, …

Trade-off between effectiveness and fairness!

Some properties that can be studied

Correspondence with participants’ beliefs If union of beliefs implies p, can/will agreement

on p result? If participants agree on p, does union of beliefs

imply p? Correspondence with participants’

commitments and arguments If P wins, is his main claim justified by the

exchanged arguments ? (except those with retracted or challenged premises)

We should lower taxes

Lower taxes increase productivity

Increased productivity is good

We should not lower taxes

Lower taxes increase inequality

Increased inequality is bad

Lower taxes do not increase productivity

Increased inequality is good

Increased inequality stimulates competition

Competition is good

since since

since

claim

claim

why

why

Example 2

Paul: r

Olga: s

p qr ps r

Knowledge bases Inference rules

P1: q since p

Paul Olga does not justify q but they could

agree on q

Example 2

Paul: r

Olga: s

Knowledge bases Inference rules

P1: q since p

O1: why p?

p qr ps r

Paul Olga does not justify q but they could

agree on q

Example 2

Paul: r

Olga: s

Knowledge bases Inference rules

P1: q since p

O1: why p?

P2: p since r

p qr ps r

Paul Olga does not justify q but they could

agree on q

Example 2

Paul: r

Olga: s

Knowledge bases Inference rules

P1: q since p

O1: why p?

O2: r since s

P2: p since r

p qr ps r

Paul Olga does not justify q but they could

agree on q

Example 3

Paul: pq

Olga: pq p

Knowledge bases Inference rules

P1: claim pModus ponens

…

Paul Olga does not justify p but they will

agree on p

Example 3

Paul: pq

Olga: pq p

Knowledge bases Inference rules

P1: claim p

O1: concede p

Modus ponens

…

Paul Olga does not justify q but they will

agree on q

Conclusion Argumentation has two sides:

Inference Dialogue

Both sides can be formalised But not in the same way