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On norms for the dynamics of
argumentative interaction: argumentation as a game
Henry PrakkenAmsterdam
January 18, 2010
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Overview
Lorenzen’s dialogue logic
Hamblin’s formal dialectic AI’s argumentation logics
MAS dialogue systems for argumentation
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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
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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
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We should lower taxes
Lower taxes increase productivity
Increased productivity is good
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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A defeat graph
A
B
C
D
E
F
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A winning strategy for P
P: AA
B
C
D
E
F
move
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A winning strategy for P
P: AA
B
C
D
E
F
O: F
move
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A winning strategy for P
P: AA
B
C
D
E
F
O: F
P: E
move
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A winning strategy for P
P: A
O: B
A
B
C
D
E
F
O: F
P: E
move
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A winning strategy for P
P: A
O: B
P: C
A
B
C
D
E
F
O: F
P: E
move
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Interaction Argument games verify status of
argument (or statement) given a single theory (knowledge base)
But real argumentation dialogues have Distributed information Dynamics
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We should lower taxes
claim
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We should lower taxes
claim why
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We should lower taxes
Lower taxes increase productivity
Increased productivity is good
since
claim why
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Dialogue game systems A communication language
Well-formed utterances Rules for when an utterance is
allowed Protocol
Turntaking rules Termination rules
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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
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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!
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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)
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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
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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
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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
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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
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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
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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
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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
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Conclusion Argumentation has two sides:
Inference Dialogue
Both sides can be formalised But not in the same way