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Introduction May all beings be happy. May they live in safety and - PowerPoint PPT Presentation

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Trumpet Reincarnations: Abstract Argumentation 1 Christof Spanring Department of Computer Science, University of Liverpool, UK Institute of Information Systems, TU Wien, Austria Porgy & Bess: Lost & Found April 24, 2017 1 This research

  1. Trumpet Reincarnations: Abstract Argumentation 1 Christof Spanring Department of Computer Science, University of Liverpool, UK Institute of Information Systems, TU Wien, Austria Porgy & Bess: Lost & Found April 24, 2017 1 This research has been supported by FWF (project I1102).

  2. Introduction May all beings be happy. May they live in safety and joy. All living beings, Whether weak or strong, Tall, stout, average or short, Seen or unseen, near or distant, Born or to be born, May they all be happy. Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 1 / 21

  3. Introduction safe May all beings be happy. May they live in safety and joy. joy All living beings, Whether weak or strong, happy Tall, stout, average or short, Seen or unseen, near or distant, weak Born or to be born, May they all be happy. strong Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 1 / 21

  4. Introduction safe May all beings be happy. May they live in safety and joy. joy All living beings, Whether weak or strong, happy Tall, stout, average or short, Seen or unseen, near or distant, weak Born or to be born, May they all be happy. strong Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 1 / 21

  5. Introduction safe May all beings be happy. May they live in safety and joy. joy All living beings, Whether weak or strong, happy Tall, stout, average or short, Seen or unseen, near or distant, weak Born or to be born, May they all be happy. strong Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 1 / 21

  6. Introduction safe May all beings be happy. May they live in safety and joy. joy All living beings, Whether weak or strong, happy Tall, stout, average or short, Seen or unseen, near or distant, weak Born or to be born, May they all be happy. strong Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 1 / 21

  7. Introduction safe May all beings be happy. May they live in safety and joy. joy All living beings, Whether weak or strong, happy Tall, stout, average or short, Seen or unseen, near or distant, weak Born or to be born, May they all be happy. strong Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 1 / 21

  8. Introduction safe joy happy weak strong Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 1 / 21

  9. Introduction safe joy happy weak strong Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 1 / 21

  10. Introduction safe joy happy weak strong Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 1 / 21

  11. Introduction safe joy happy weak strong Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 1 / 21

  12. Introduction s j h w r in: s,r out: w,j undec: h Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 1 / 21

  13. Introduction s s j j h h w w r r in: s,r in: j,r out: w,j out: s,w undec: h undec: h Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 1 / 21

  14. Introduction s s s j j j h h h w w w r r r in: s,r in: j,r in: w,j out: w,j out: s,w out: s,h,r undec: h undec: h undec: Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 1 / 21

  15. Outline Introduction 1 Stable Extensions and Conflict 2 Variations of Stable Semantics 3 Collapse 4 Perfection 5 References 6 Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 2 / 21

  16. What are the stable extensions? p d c · · · t 3 t 2 t 1 u r a b Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 3 / 21

  17. What are the stable extensions? p d c · · · t 3 t 2 t 1 u r a b Stable Extensions: { c , r , b , t 1 , t 2 , t 3 , . . . } Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 3 / 21

  18. What are the stable extensions? p d c · · · t 3 t 2 t 1 u r a b Stable Extensions: { c , r , b , t 1 , t 2 , t 3 , . . . } { d , b , t 1 , t 2 , t 3 , . . . } Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 3 / 21

  19. Relation between arguments c and u ? p d c · · · t 3 t 2 t 1 u r a b Stable Extensions: { c , r , b , t 1 , t 2 , t 3 , . . . } { d , b , t 1 , t 2 , t 3 , . . . } Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 4 / 21

  20. Relation between arguments c and u ? p d c · · · t 3 t 2 t 1 u r a b Stable Extensions: { c , r , b , t 1 , t 2 , t 3 , . . . } { d , b , t 1 , t 2 , t 3 , . . . } Arguments c and u are implicitly in conflict. Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 4 / 21

  21. Relation between arguments c and u ? p d c · · · t 3 t 2 t 1 u r a b Stable Extensions: { c , r , b , t 1 , t 2 , t 3 , . . . } { d , b , t 1 , t 2 , t 3 , . . . } Arguments c and u are implicitly in conflict. An attack ( c , u ) does not change the extension sets. Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 4 / 21

  22. Implicit Conflicts made Explicit in a Simpler Case 3 2 1 4 Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 5 / 21

  23. Implicit Conflicts made Explicit in a Simpler Case 2 3 1 4 Stable Extensions: { 3 , 1 } { 4 , 2 } Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 5 / 21

  24. Implicit Conflicts made Explicit in a Simpler Case 2 3 1 4 Stable Extensions: { 3 , 1 } { 4 , 2 } Only Implicit Conflict: 1 vs. 4 Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 5 / 21

  25. Implicit Conflicts made Explicit in a Simpler Case 2 3 1 4 Stable Extensions: { 3 , 1 } { 4 , 2 } Only Implicit Conflict: 1 vs. 4 Resultion: ( 1 , 4 ) Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 5 / 21

  26. Implicit Conflicts made Explicit in a Simpler Case 2 3 1 4 Stable Extensions: { 3 , 1 } { 4 , 2 } Only Implicit Conflict: 1 vs. 4 Resultion: ( 1 , 4 ) ( 4 , 1 ) or Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 5 / 21

  27. Implicit Conflicts made Explicit in a Simpler Case 2 3 1 4 Stable Extensions: { 3 , 1 } { 4 , 2 } Only Implicit Conflict: 1 vs. 4 Resultion: ( 1 , 4 ) ( 4 , 1 ) or or both Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 5 / 21

  28. Implicit Conflicts vs. Explicit Conflicts III b 2 u 0 u 1 y 0 a 0 x 2 a 1 y 1 x 1 y 2 x 0 b 1 b 0 v 1 v 0 a 2 Argument set of interest: { a 0 , a 1 , y 2 , u 0 , u 1 , v 0 , v 1 } Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 6 / 21

  29. Implicit Conflicts vs. Explicit Conflicts III b 2 u 0 u 1 y 0 a 0 x 2 a 1 y 1 x 1 y 2 x 0 b 1 b 0 v 1 v 0 a 2 Theorem Some implicit conflicts can not be made explicit for stable semantics. Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 6 / 21

  30. Outline Introduction 1 Stable Extensions and Conflict 2 Variations of Stable Semantics 3 Collapse 4 Perfection 5 References 6 Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 7 / 21

  31. What are the stable extensions? 2 1 3 6 4 5 Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 8 / 21

  32. What are the stable extensions? 2 1 3 6 4 5 Stable Extensions: { 1 , 3 , 5 } and { 2 , 4 , 6 } Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 8 / 21

  33. What are the stable extensions? 1 2 5 3 4 Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 8 / 21

  34. What are the stable extensions? 1 2 5 3 4 Stable Extensions: There are none!!! Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 8 / 21

  35. What are the stable extensions? 1 2 1 2 5 3 6 3 4 5 4 Why is collapse a problem? Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 8 / 21

  36. Collapse Solutions 3 1 2 4 Example Collapse of Stable Semantics. Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 9 / 21

  37. Collapse Solutions 3 1 2 4 Definition (Stage) Consider argument sets where undecided arguments are minimized. Stage Extensions: { 2 } Christof Spanring, Porgy & Bess: Lost & Found Trumpet Reincarnations: Abstract Argumentation 9 / 21

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