On norms for the dynamics of argumentative interaction: argumentation as a game Henry Prakken Amsterdam January 18, 2010

Overview Lorenzen’s dialogue logic Hamblin’s formal dialecticAI’s argumentation logics MAS dialogue systems for argumentation

Lorenzen’s dialogue logic: game-theoretic semantics of connectives Paul: claims q P1: 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  q P3: that’s why Olga: O1: why q? O2: concede p  q but why p? O3: (can I trust Paul?) Paul’s beliefs: p p  q Olga’s beliefs: r p  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

AB 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: A A B C D E F move

A winning strategy for P P: A A B C D E F O: F move

A winning strategy for P P: A A 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 claimwhy

We should lower taxes Lower taxes increase productivity Increased productivity is good since claimwhy

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 claimwhy

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 claimwhy

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 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 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 USA lowered taxes but productivity decreased 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 USA lowered taxes but productivity decreased 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 Prof. P says that … Increased inequality is good Increased inequality stimulates competition Competition is good USA lowered taxes but productivity decreased 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 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 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 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 claim 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 claim why

Example 2 Paul: r Olga: s p  q r  p s   r Knowledge basesInference rules P1: q since p Paul  Olga does not justify q but they could agree on q

Example 2 Paul: r Olga: s Knowledge basesInference rules P1: q since p O1: why p? p  q r  p s   r Paul  Olga does not justify q but they could agree on q

Example 2 Paul: r Olga: s Knowledge basesInference rules P1: q since p O1: why p? P2: p since r p  q r  p s   r Paul  Olga does not justify q but they could agree on q

Example 2 Paul: r Olga: s Knowledge basesInference rules P1: q since p O1: why p? O2:  r since s P2: p since r p  q r  p s   r Paul  Olga does not justify q but they could agree on q

Example 3 Paul: p q Olga: p q   p Knowledge basesInference rules P1: claim p Modus ponens … Paul  Olga does not justify p but they will agree on p

Example 3 Paul: p q Olga: p q   p Knowledge basesInference 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