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Argumentation

Argumentation. Henry Prakken SIKS Basic Course Learning and Reasoning May 26 th , 2009. Why do agents need argumentation?. For their internal reasoning Reasoning about beliefs, goals, intentions etc often is defeasible For their interaction with other agents

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Argumentation

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  1. Argumentation Henry Prakken SIKS Basic Course Learning and Reasoning May 26th, 2009

  2. Why do agents need argumentation? • For their internal reasoning • Reasoning about beliefs, goals, intentions etc often is defeasible • For their interaction with other agents • Information exchange, negotiation, collaboration, …

  3. Overview • Inference (logic) • Abstract argumentation • Rule-based argumentation • Dialogue

  4. Part 1:Inference

  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. Sources of conflict • Default generalisations • Conflicting information sources • Alternative explanations • Conflicting goals, interests • Conflicting normative, moral opinions • …

  13. Application areas • Medical diagnosis and treatment • Legal reasoning • Interpretation • Evidence / crime investigation • Intelligence • Decision making • Policy design • …

  14. 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

  15. A B E D C

  16. Status of arguments: abstract semantics (Dung 1995) • INPUT: a pair Args,Defeat • OUTPUT: An assignment of the status ‘in’ or ‘out’ to all members of Args • So: semantics specifies conditions for labeling the ‘argument graph’. • Should capture reinstatement: A B C

  17. Possible labeling conditions • Every argument is either ‘in’ or ‘out’. 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’. • Works fine with: • But not with: A B C A B

  18. Two solutions • Change conditions so that always a unique status assignment results • Use multiple status assignments: • and A B C A B A B C A B A B

  19. Unique status assignments • Grounded semantics (Dung 1995): • S0: the empty set • Si+1: Si + all arguments defended by Si • ... • (S defends A if all defeaters of A are defeated by a member of S)

  20. A B E D C Is B or E defended by S2? Is B, D or E defended by S1?

  21. A problem(?) with grounded semantics We have: We want(?): A B A B C C D D

  22. A problem(?) with grounded semantics A B C A = Frederic Michaud is French since he has a French name B = Frederic Michaud is Dutch since he is a marathon skater C = F.M. likes the EU since he is European (assuming he is not Dutch or French) D = F.M. does not like the EU since he looks like a person who does not like the EU D

  23. A problem(?) with grounded semantics E A B C A = Frederic Michaud is French since Alice says so B = Frederic Michaud is Dutch since Bob says so C = F.M. likes the EU since he is European (assuming he is not Dutch or French) D = F.M. does not like the EU since he looks like a person who does not like the EU D E = Alice and Bob are unreliable since they contradict each other

  24. Multiple labellings A B A B C C D D

  25. A B C Status assignments (1) • Given Args,Defeat: • A status assignmentis a partition of Args into sets In and Out such that: 1. An argument is in In if all arguments defeating it are in Out. 2. An argument is in Out if it is defeated by an argument that is in In.

  26. Status assignments (1) • Given Args,Defeat: • A status assignmentis a partition of Args into sets In and Out such that: 1. An argument is in In if all arguments defeating it are in Out. 2. An argument is in Out if it is defeated by an argument that is in In. A B C

  27. Status assignments (1) • Given Args,Defeat: • A status assignmentis a partition of Args into sets In and Out such that: 1. An argument is in In if all arguments defeating it are in Out. 2. An argument is in Out if it is defeated by an argument that is in In. A B C

  28. Status assignments (1) • Given Args,Defeat: • A status assignmentis a partition of Args into sets In and Out such that: 1. An argument is in In if all arguments defeating it are in Out. 2. An argument is in Out if it is defeated by an argument that is in In. A B C

  29. Status assignments (1) • Given Args,Defeat: • A status assignmentis a partition of Args into sets In and Out such that: 1. An argument is in In if all arguments defeating it are in Out. 2. An argument is in Out if it is defeated by an argument that is in In. A B C

  30. Status assignments (2) • Given Args,Defeat: • A status assignment is a partition of Args into sets In, Out and Undecided such that: 1. An argument is in In if all arguments defeating it are in Out. 2. An argument is in Out if it is defeated by an argument that is in In. • A status assignment is stable if Undecided = . • In is a stable extension • A status assignment is preferred if Undecided is -minimal. • In is a preferred extension • A status assignment is grounded if Undecided is -maximal. • In is the grounded extension

  31. Dung’s original definitions • Given Args,Defeat, S  Args, A  Args: • S is conflict-free if no member of S defeats a member of S • S defends A if all defeaters of A are defeated by a member of S • S is admissible if it is conflict-free and defends all its members • S is a preferred extension if it is -maximally admissible • S is a stable extension if it is conflict-free and defeats all arguments outside it • S is the grounded extension if S is the -smallest set such that A  S iff S defends A.

  32. S defends A if all defeaters of A are defeated by a member of S S is admissible if it is conflict-free and defends all its members A B E D C Admissible?

  33. S defends A if all defeaters of A are defeated by a member of S S is admissible if it is conflict-free and defends all its members A B E D C Admissible?

  34. S defends A if all defeaters of A are defeated by a member of S S is admissible if it is conflict-free and defends all its members A B E D C Admissible?

  35. S defends A if all defeaters of A are defeated by a member of S S is admissible if it is conflict-free and defends all its members A B E D C Admissible?

  36. S defends A if all defeaters of A are defeated by a member of S S is admissible if it is conflict-free and defends all its members A B E D C S is preferred if it is maximally admissible Preferred?

  37. S defends A if all defeaters of A are defeated by a member of S S is admissible if it is conflict-free and defends all its members A B E D C S is preferred if it is maximally admissible Preferred?

  38. S defends A if all defeaters of A are defeated by a member of S S is admissible if it is conflict-free and defends all its members A B E D C S is preferred if it is maximally admissible Preferred?

  39. S defends A if all defeaters of A are defeated by a member of S S is admissible if it is conflict-free and defends all its members A B E D C S is groundeded if it is the smallest set s.t. A  S iff S defends A Grounded?

  40. S defends A if all defeaters of A are defeated by a member of S S is admissible if it is conflict-free and defends all its members A B E D C S is groundeded if it is the smallest set s.t. A  S iff S defends A Grounded?

  41. Properties • The grounded extension is unique • Every stable extension is preferred (but not v.v.) • There exists at least one preferred extension • The grounded extension is a subset of all preferred and stable extensions • …

  42. The ‘ultimate’ status of arguments (and conclusions) • With grounded semantics: • A is justified if A  g.e. • A is overruled if A  g.e. and A is defeated by g.e. • A is defensible otherwise • With preferred semantics: • A is justified if A  p.e for all p.e. • A is defensible if A  p.e. for some but not all p.e. • A is overruled otherwise (?) • In all semantics: •  is justified if  is the conclusion of some justified argument •  is defensible if  is not justified and  is the conclusion of some defensible argument

  43. The status of arguments: proof theory • Argument games between proponent and opponent: • Proponent starts with an argument • Then each party replies with a suitable counterargument • Possibly backtracking • A winning criterion • E.g. the other player cannot move • An argument is (dialectically) provable iff proponent has a winning strategy in a game for it.

  44. The G-game for grounded semantics: • A sound and complete game: • 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.

  45. A game tree A F B C E D

  46. A game tree P: A A F B C E D

  47. A game tree P: A A F O: F B C E D

  48. A game tree P: A A F O: F B P: E C E D

  49. A game tree P: A A F O: B O: F B P: E C E D

  50. A game tree P: A A F O: B O: F B P: E P: C C E D

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