Argumentation in Artificial Intelligence Henry Prakken Lissabon, Portugal December 11, 2009

Why do agents need argumentation? For their internal reasoning To draw conclusions given conflicting arguments For their interaction with other agents To persuade given a conflict of opinion

Toulmin’s argument scheme ClaimData So Warrant Since Backing On account of Rebuttal Unless

Toulmin’s argument scheme João is catholic João is Portuguese So Most Portuguese are catholic Since statistics On account of João often visits a protestant church Unless

Toulmin’s argument scheme João is Portuguese João was Born In Portugal So Who is born in Portugal is Portuguese Since Portuguese law On account of João adopted another nationality Unless

From Toulmin to modern argumentation theory Toulmin’s (1958) main contributions: Arguments can be defeated Validity of arguments is procedural (and field- dependent?) This led to the idea of argument(ation) schemes. An argument is acceptable if: it instantiates an argument scheme the critical questions asked in dialogue can be answered

Argument(ation) schemes: general form But also critical questions Premise 1, …, Premise n Therefore (presumably), conclusion

Expert testimony (Walton 1996) Critical questions: Is E really expert on D? Did E really say that P? Is P really within D? Is E biased? Is P consistent with what other experts say? Is P consistent with known evidence? E is expert on D E says that P P is within D Therefore (presumably), P is the case

Witness testimony Critical questions: Is W sincere? Does W’s memory function properly? Did W’s senses function properly? W says P W was in the position to observe P Therefore (presumably), P

Arguments from consequences Critical questions: Does A also have bad consequences? Are there other ways to bring about G?... Action A brings about G, G is good Therefore (presumably), A should be done

Three layers in argumentation Logic layer Fixed theory Procedural layer Dynamic theory Strategic layer Dynamic theory My point: even logic is partly dialectic

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 iff all arguments defeating it are Out. 2. An argument is Out iff it is defeated by an argument that is In. Dung 1995 Grounded semantics minimises node colouring Preferred semantics maximises node colouring

Argument game for grounded semantics Rules of the game: Proponent starts with an argument Then each player defeats the previous move of the other player Proponent moves strict defeaters, opponent moves defeaters Proponent does not repeat his moves 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 game tree P: A A B C D E F move

A game tree P: A A B C D E F O: F move

A game tree P: A A B C D E F O: F P: E move

A game tree P: A O: B A B C D E F O: F P: E move

A game tree P: A O: B P: C A B C D E F O: F P: E move

A game tree P: A O: B P: C O: D A B C D E F O: F P: E move

A game tree P: A O: B P: CP: E O: D A B C D E F O: F P: E move

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

Structured arguments Argument structure: Trees where Nodes are formulas of a logical language L Links are applications of inference rules R s = Strict rules (  1,...,  1   ); or R d = Defeasible rules (  1,...,  1   ) Reasoning starts from a knowledge base K  L Defeat: attack on conclusion, premise or defeasible inference, + preferences Argument acceptability: Dung (1995)

Argument(ation) schemes: general form Defeasible inference rules! But also critical questions Negative answers are counterarguments Premise 1, …, Premise n Therefore (presumably), conclusion

Expert testimony (Walton 1996) Critical questions: Is E really expert on D? Did E really say that P? Is P really within D? Is E biased? Is P consistent with what other experts say? Is P consistent with known evidence? E is expert on D E says that P P is within D Therefore (presumably), P is the case

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

Three layers in argumentation Logic layer Fixed theory Procedural layer Dynamic theory Strategic layer Dynamic theory

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

A ‘real’ argumentation dialogue I claim that we should lower taxes Why? Since lower taxes increase productivity, which is good I disagree. We should not lower taxes, since that would increase inequality, which is bad. Besides, lower taxes will not increase productivity Why not? Since the USA recently lowered their taxes but productivity decreased. OK, I admit that lower taxes do not always increase productivity; I retract my claim.

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 Protocol should promote the goal of the dialogue

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

Dialogical aspects of argument schemes Some critical questions ask “why this premise?” Other critical questions ask “is there no exception?” But burden of proof is on respondent to show that there are exceptions! Dialogue systems should allow for counterarguments

Need for other speech acts (and for rhetoric) Paul: r Olga: s p  q r  p s   r Knowledge basesInference rules P1: q since p

Need for other speech acts (and for rhetoric) Paul: r Olga: s Knowledge basesInference rules P1: q since p O1: why p? p  q r  p s   r

Need for other speech acts (and for rhetoric) Paul: r Olga: s Knowledge basesInference rules P1: q since p O1: why p? P2: p since r p  q r  p s   r

Need for other speech acts (and for rhetoric) 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

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? Disregarding vs. assuming agent strategies/tactics In general it will be hard to enforce agreement …

Conclusions Argumentation theory can benefit from AI Formalisation Computer models Computer tools AI can benefit from argumentation theory Concepts Theories …