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On norms for the dynamics of argumentative interaction: argumentation as a game

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 dialectic. AI’s argumentation logics. MAS dialogue systems for argumentation.

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On norms for the dynamics of argumentative interaction: argumentation as a game

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

  2. Overview Lorenzen’s dialogue logic Hamblin’s formal dialectic AI’s argumentation logics MAS dialogue systems for argumentation

  3. 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 

  4. 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  qbut 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

  5. We should lower taxes Lower taxes increase productivity Increased productivity is good

  6. We should lower taxes We should not lower taxes Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad

  7. We should lower taxes We should not lower taxes Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad Lower taxes do not increase productivity USA lowered taxes but productivity decreased

  8. We should lower taxes We should not lower taxes Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad Lower taxes do not increase productivity Prof. P says that … USA lowered taxes but productivity decreased

  9. We should lower taxes We should not lower taxes Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad Lower taxes do not increase productivity Prof. P says that … Prof. P is not objective People with political ambitions are not objective USA lowered taxes but productivity decreased Prof. P has political ambitions

  10. We should lower taxes We should not lower taxes Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad Lower taxes do not increase productivity Prof. P says that … Prof. P is not objective People with political ambitions are not objective USA lowered taxes but productivity decreased Prof. P has political ambitions

  11. We should lower taxes We should not lower taxes Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad Increased inequality is good Lower taxes do not increase productivity Prof. P says that … Prof. P is not objective People with political ambitions are not objective USA lowered taxes but productivity decreased Increased inequality stimulates competition Prof. P has political ambitions Competition is good

  12. We should lower taxes We should not lower taxes Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad Increased inequality is good Lower taxes do not increase productivity Prof. P says that … Prof. P is not objective People with political ambitions are not objective USA lowered taxes but productivity decreased Increased inequality stimulates competition Prof. P has political ambitions Competition is good

  13. 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. Grounded semantics minimises node colouring Preferred semantics maximises node colouring Dung 1995 A B E D C

  14. 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.

  15. A defeat graph A F B C E D

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

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

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

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

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

  21. Interaction • Argument games verify status of argument (or statement) given a single theory (knowledge base) • But real argumentation dialogues have • Distributed information • Dynamics

  22. claim We should lower taxes

  23. claim why We should lower taxes

  24. claim why We should lower taxes since Lower taxes increase productivity Increased productivity is good

  25. claim why We should lower taxes We should not lower taxes since since Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad

  26. claim why We should lower taxes We should not lower taxes since since Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad Increased inequality is good since Increased inequality stimulates competition Competition is good

  27. claim why We should lower taxes We should not lower taxes since since Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad claim Increased inequality is good Lower taxes do not increase productivity since Increased inequality stimulates competition Competition is good

  28. claim why We should lower taxes We should not lower taxes since since Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad why claim Lower taxes do not increase productivity Increased inequality is good since Increased inequality stimulates competition Competition is good

  29. claim why We should lower taxes We should not lower taxes since since Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad why claim Increased inequality is good Lower taxes do not increase productivity since since USA lowered taxes but productivity decreased Increased inequality stimulates competition Competition is good

  30. claim why We should lower taxes We should not lower taxes since since why Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad why claim Increased inequality is good Lower taxes do not increase productivity since since USA lowered taxes but productivity decreased Increased inequality stimulates competition Competition is good

  31. claim why We should lower taxes We should not lower taxes since since why Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad since why claim Increased inequality is good Lower taxes do not increase productivity Prof. P says that … since since USA lowered taxes but productivity decreased Increased inequality stimulates competition Competition is good

  32. claim why We should lower taxes We should not lower taxes since since why Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad since why claim Increased inequality is good Lower taxes do not increase productivity Prof. P says that … Prof. P is not objective since since since People with political ambitions are not objective USA lowered taxes but productivity decreased Increased inequality stimulates competition Prof. P has political ambitions Competition is good

  33. claim why We should lower taxes We should not lower taxes retract since since why Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad since why claim Increased inequality is good Lower taxes do not increase productivity Prof. P says that … Prof. P is not objective since since since People with political ambitions are not objective USA lowered taxes but productivity decreased Increased inequality stimulates competition Prof. P has political ambitions Competition is good

  34. 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

  35. Dialogue game systems • A communication language • Well-formed utterances • Rules for when an utterance is allowed • Protocol • Turntaking rules • Termination rules

  36. 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

  37. 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!

  38. 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)

  39. claim why We should lower taxes We should not lower taxes since since Lower taxes increase productivity Increased productivity is good Lower taxes increase inequality Increased inequality is bad why claim Lower taxes do not increase productivity Increased inequality is good since Increased inequality stimulates competition Competition is good

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

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

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

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

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

  45. Example 3 Knowledge bases Inference rules Modus ponens … Paul: p q P1: claim p O1: concede p Olga: p q  p Paul  Olga does not justify q but they will agree on q

  46. Conclusion • Argumentation has two sides: • Inference • Dialogue • Both sides can be formalised • But not in the same way

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