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 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 Paul’s beliefs: p pq Olga: O1: why q? O2: concede p q but why p? O3: (can I trust Paul?) Olga’s beliefs: r pq 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 We should not lower taxes Increased productivity is good Lower taxes do not increase productivity USA lowered taxes but productivity decreased Lower taxes increase inequality Increased inequality is bad We should lower taxes Lower taxes increase productivity Prof. P says that … We should not lower taxes Increased productivity is good Lower taxes do not increase productivity USA lowered taxes but productivity decreased Lower taxes increase inequality Increased inequality is bad We should lower taxes Lower taxes increase productivity Prof. P says that … People with political ambitions are not objective We should not lower taxes Increased productivity is good Prof. P is not objective Prof. P has political ambitions Lower taxes do not increase productivity USA lowered taxes but productivity decreased Lower taxes increase inequality Increased inequality is bad We should lower taxes Lower taxes increase productivity Prof. P says that … People with political ambitions are not objective We should not lower taxes Increased productivity is good Prof. P is not objective Prof. P has political ambitions Lower taxes do not increase productivity USA lowered taxes but productivity decreased Lower taxes increase inequality Increased inequality is bad We should lower taxes Lower taxes increase productivity Prof. P says that … People with political ambitions are not objective We should not lower taxes Increased productivity is good Prof. P is not objective Prof. P has political ambitions Lower taxes increase inequality Increased inequality is good Lower taxes do not increase productivity USA lowered taxes but productivity decreased Increased inequality is bad Increased inequality stimulates competition Competition is good We should lower taxes Lower taxes increase productivity Prof. P says that … People with political ambitions are not objective We should not lower taxes Increased productivity is good Prof. P is not objective Prof. P has political ambitions Lower taxes increase inequality Increased inequality is good Lower taxes do not increase productivity USA lowered taxes but productivity decreased Increased inequality is bad Increased inequality stimulates competition Competition is good 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 C B D E 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 F B C D E A winning strategy for P move A F B C D E P: A A winning strategy for P move A P: A F O: F B C D E A winning strategy for P A P: A F O: F B P: E C D move E A winning strategy for P A P: A F move O: F B P: E C D E O: B A winning strategy for P A P: A F O: F O: B P: E P: C B C D move E Interaction Argument games verify status of argument (or statement) given a single theory (knowledge base) But real argumentation dialogues have Distributed information Dynamics claim We should lower taxes claim why We should lower taxes claim why We should lower taxes since Lower taxes increase productivity Increased productivity is good 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 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 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 claim why We should lower taxes We should not lower taxes since since Lower taxes increase productivity Increased productivity is good why 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 claim why We should lower taxes We should not lower taxes since since Lower taxes increase productivity Increased productivity is good why Lower taxes increase inequality Increased inequality is bad 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 claim why We should lower taxes We should not lower taxes since since Lower taxes increase productivity why Increased productivity is good why Lower taxes increase inequality Increased inequality is bad 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 claim why We should lower taxes We should not lower taxes since since why Lower taxes increase productivity since Increased productivity is good why Lower taxes increase inequality claim Increased inequality is good Lower taxes do not increase productivity Prof. P says that … Increased inequality is bad since since USA lowered taxes but productivity decreased Increased inequality stimulates competition Competition is good claim why We should lower taxes We should not lower taxes since since why Lower taxes increase productivity since Prof. P says that … Increased productivity is good why Lower taxes increase inequality claim Increased inequality is good Lower taxes do not increase productivity Prof. P is not objective since Increased inequality is bad since since People with political ambitions are not objective Prof. P has political ambitions USA lowered taxes but productivity decreased Increased inequality stimulates competition Competition is good claim why We should lower taxes We should not lower taxes retract since why Lower taxes increase productivity since Prof. P says that … Increased productivity is good why since Lower taxes increase inequality claim Increased inequality is good Lower taxes do not increase productivity Prof. P is not objective since Increased inequality is bad since since People with political ambitions are not objective Prof. P has political ambitions USA lowered taxes but productivity decreased Increased inequality stimulates competition Competition is good 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 Rules for when an utterance is allowed Well-formed utterances 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? Fairness: does the protocol respect the participants’ goals? Agent rationality, Efficiency (relevance, termination, ...) 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) claim why We should lower taxes We should not lower taxes since since Lower taxes increase productivity Increased productivity is good why 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 Example 2 Knowledge bases Paul: r Olga: s Inference rules pq rp s r Paul Olga does not justify q but they could agree on q P1: q since p Example 2 Knowledge bases Paul: r Olga: s Inference rules pq rp s r P1: q since p O1: why p? Paul Olga does not justify q but they could agree on q Example 2 Knowledge bases Paul: r Olga: s Inference rules pq rp s r P1: q since p O1: why p? Paul Olga does not justify q but they could agree on q P2: p since r Example 2 Knowledge bases Paul: r Olga: s Inference rules pq rp s r P1: q since p O1: why p? Paul Olga does not justify q but they could agree on q P2: p since r O2: r since s Example 3 Knowledge bases Paul: p q Inference rules Modus ponens … Olga: p q p Paul Olga does not justify p but they will agree on p P1: claim p Example 3 Knowledge bases Paul: p q Inference rules Modus ponens … Olga: p q p Paul Olga does not justify q but they will agree on q P1: claim p O1: concede p Conclusion Argumentation has two sides: Inference Dialogue Both sides can be formalised But not in the same way
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