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YALLA Yet Another Logic Language for Argumentation Pierre Bisquert, - PowerPoint PPT Presentation

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YALLA Yet Another Logic Language for Argumentation Pierre Bisquert, Claudette Cayrol, Florence Dupin de Saint-Cyr, Marie-Christine Lagasquie-Schiex INRA & IRIT, France 2nd Madeira Workshop on Belief Revision and Argumentation February

  1. YALLA Yet Another Logic Language for Argumentation Pierre Bisquert, Claudette Cayrol, Florence Dupin de Saint-Cyr, Marie-Christine Lagasquie-Schiex INRA & IRIT, France 2nd Madeira Workshop on Belief Revision and Argumentation February 9th-13th 2015 P. Bisquert YALLA BRA 2015 1 / 38

  2. A Lawyer During a Trial a c b blabla . . . my client d innocent . . . . . . blabla . . . guilty Audience Lawyer Prosecutor A lawyer (the agent) is going to make her final address to an audience (the target). She knows (approximatively) the argumentation system (AS) of the target. P. Bisquert YALLA BRA 2015 2 / 38

  3. A lawyer during a trial a c b d e attacks c Audience Lawyer Prosecutor She wants to force the audience to accept specific arguments. She has to make a change to the target AS: P. Bisquert YALLA BRA 2015 3 / 38

  4. A lawyer during a trial e a c b d e attacks c Audience Lawyer Prosecutor She wants to force the audience to accept specific arguments. She has to make a change to the target AS: ◮ by adding an argument P. Bisquert YALLA BRA 2015 3 / 38

  5. A lawyer during a trial a c b d Objection against c Audience Lawyer Prosecutor She wants to force the audience to accept specific arguments. She has to make a change to the target AS: ◮ by adding an argument ◮ or by doing an objection about an argument (to remove it). P. Bisquert YALLA BRA 2015 3 / 38

  6. A lawyer during a trial a b d Objection against c Audience Lawyer Prosecutor She wants to force the audience to accept specific arguments. She has to make a change to the target AS: ◮ by adding an argument ◮ or by doing an objection about an argument (to remove it). P. Bisquert YALLA BRA 2015 3 / 38

  7. acc ( d ) a e c a c b d b d Objection against c Target Agent Agent: ◮ has a private argumentation system (her knowledge) ◮ has a goal w.r.t. the target ◮ should respect some constraints ⇒ notion of executable operation P. Bisquert YALLA BRA 2015 4 / 38

  8. Outline YALLA and Abstract Argumentation 1 Dung Framework Semantics YALLA and Argumentation Dynamics 2 Concluding Remarks 3 P. Bisquert YALLA BRA 2015 5 / 38

  9. Dung framework According to Dung, an abstract argumentation system is a pair ( A , R ), where : ◮ A is a finite nonempty set of arguments and ◮ R is a binary relation on A , called attack relation This system can be represented by a graph denoted G 1 2 3 P. Bisquert YALLA BRA 2015 6 / 38

  10. Dung framework According to Dung, an abstract argumentation system is a pair ( A , R ), where : ◮ A is a finite nonempty set of arguments and ◮ R is a binary relation on A , called attack relation This system can be represented by a graph denoted G 1 2 3 YALLA: a term is a set of arguments ◮ singl ( { 1 } ) ∧ singl ( { 2 } ) ∧ singl ( { 3 } ) ∧ ( { 1 } ⊲ { 2 } ) ∧ ( { 2 } ⊲ { 3 } ) P. Bisquert YALLA BRA 2015 6 / 38

  11. Universe A universe ( A U , R U ) = all arguments and their interactions. Mr. X is not guilty of the murder of Mrs. X 0 Universe 0 P. Bisquert YALLA BRA 2015 7 / 38

  12. Universe A universe ( A U , R U ) = all arguments and their interactions. Mr. X is not guilty of the murder of Mrs. X 0 Mr. X is guilty of the murder of Mrs. X 1 Universe 1 0 P. Bisquert YALLA BRA 2015 7 / 38

  13. Universe A universe ( A U , R U ) = all arguments and their interactions. Mr. X is not guilty of the murder of Mrs. X 0 Mr. X is guilty of the murder of Mrs. X 1 Universe Mr. X ’s business associate has sworn that he 2 met him at the time of the murder. 1 2 0 P. Bisquert YALLA BRA 2015 7 / 38

  14. Universe A universe ( A U , R U ) = all arguments and their interactions. Mr. X is not guilty of the murder of Mrs. X 0 Mr. X is guilty of the murder of Mrs. X 1 Universe Mr. X ’s business associate has sworn that he 2 5 7 met him at the time of the murder. Mr. X associate’s testimony is suspicious due to 3 their close working business relationship 6 4 Mr. X loves his wife. A man who loves his wife 4 cannot be her killer. 3 1 Mr. X has a reputation for being promiscuous. 5 Mr. X had no interest to kill Mrs. X , since he 6 2 0 was not the beneficiary of her life insurance Mr. X is known to be venal and his “love” for a 7 very rich woman could be only lure of profit. P. Bisquert YALLA BRA 2015 7 / 38

  15. Universe A universe ( A U , R U ) = all arguments and their interactions. Definition (Argumentation graph) Universe An argumentation graph G is a pair ( A , R ) 5 7 A ⊆ A U arguments (finite) R ⊆ R U ∩ ( A × A ) 6 4 Γ = all argumentation graphs w.r.t. the universe. 3 1 5 6 3 2 0 4 1 0 4 1 0 G 1 G 2 P. Bisquert YALLA BRA 2015 7 / 38

  16. Argumentation Graph Example Agent L knows some of the arguments of the universe ( G L ⊆ Γ): 5 6 3 2 6 3 2 7 4 1 0 7 4 1 0 Universe G L P. Bisquert YALLA BRA 2015 8 / 38

  17. Argumentation Graph Example Agent L knows some of the arguments of the universe ( G L ⊆ Γ): 5 6 3 2 6 3 2 7 4 1 0 7 4 1 0 Universe G L on ( { 0 , 1 , 2 , 3 , 4 , 6 , 7 } ) ∧ ¬ ( on ( { 5 } )) ∧ ( { 1 } ⊲ { 0 } ) ∧ ( { 4 } ⊲ { 1 } ) ∧ . . . ∧ ¬ ( { 5 } ⊲ { 4 } ) P. Bisquert YALLA BRA 2015 8 / 38

  18. Argumentation Graph Example But L is not sure about the content of the jury’s system. She hesitates between two graphs: 3 3 2 7 4 1 0 7 4 1 0 G J 1 G J 2 on ( { 0 , 1 , 3 , 4 , 7 } ) ∧ ¬ ( on ( { 5 } )) ∧ ¬ ( on ( { 6 } )) ∧ . . . ∧ ( ¬ ( on ( { 2 } )) ∧ ¬ ( { 2 } ⊲ { 1 } ) ∧ ¬ ( { 3 } ⊲ { 2 } )) � � ∨ ( on ( { 2 } ) ∧ ( { 2 } ⊲ { 1 } ) ∧ ( { 3 } ⊲ { 2 } )) P. Bisquert YALLA BRA 2015 9 / 38

  19. Outline YALLA and Abstract Argumentation 1 Dung Framework Semantics YALLA and Argumentation Dynamics 2 Concluding Remarks 3 P. Bisquert YALLA BRA 2015 10 / 38

  20. Semantics Criteria A set S is conflict-free iff there do not exist a , b ∈ S such that a attacks b ◮ F ( t ) ⇐ ⇒ on ( t ) ∧ ( ¬ ( t ⊲ t )) S 1 defends each argument of S 2 iff each attacker of an argument of S 2 is attacked by an argument of S ◮ t 1 ⊲ ⊲ t 2 ⇐ ⇒ ( ∀ t 3 (( singl ( t 3 ) ∧ ( t 3 ⊲ t 2 )) = ⇒ ( t 1 ⊲ t 3 ))) S is an admissible set iff it is conflict-free and it defends all its elements ◮ A ( t ) ⇐ ⇒ ( F ( t ) ∧ ( t ⊲ ⊲ t )) P. Bisquert YALLA BRA 2015 11 / 38

  21. Acceptability Semantics E is a complete extension iff E is an admissible set and every acceptable argument wrt E belongs to E ◮ C ( t ) ⇐ ⇒ ( A ( t ) ∧ ∀ t 2 (( singl ( t 2) ∧ ( t ⊲ ⊲ t 2 )) = ⇒ ( t 2 ⊆ t ))) E is the only grounded extension iff E is the smallest complete extension ◮ G ( t ) ⇐ ⇒ ( C ( t ) ∧ ∀ t 2 ( C ( t 2 ) = ⇒ ( t ⊆ t 2 ))) P. Bisquert YALLA BRA 2015 12 / 38

  22. Argumentation Graph Example 3 3 2 7 4 1 0 7 4 1 0 G J 1 G J 2 on ( { 0 , 1 , 3 , 4 , 7 } ) ∧ ¬ ( on ( { 5 } )) ∧ ¬ ( on ( { 6 } )) ∧ . . . ∧ { 7 } ⊲ ⊲ { 1 } ∧ G ( { 1 , 3 , 7 } ) P. Bisquert YALLA BRA 2015 13 / 38

  23. Outline YALLA and Abstract Argumentation 1 YALLA and Argumentation Dynamics 2 Change in Argumentation Update Concepts Applied to Argumentation Specific Update Postulates Concluding Remarks 3 P. Bisquert YALLA BRA 2015 14 / 38

  24. Change in Argumentation ([Cayrol et al., 2010]): four elementary change operations. ◮ adding/removing an argument with related attacks, ◮ adding/removing an attack. Modification to handle multi-agents scenario P. Bisquert YALLA BRA 2015 15 / 38

  25. Change in Argumentation ([Cayrol et al., 2010]): four elementary change operations. ◮ adding/removing an argument with related attacks, ◮ adding/removing an attack. Modification to handle multi-agents scenario P. Bisquert YALLA BRA 2015 15 / 38

  26. Executable Operations: Example Given the universe: 5 6 3 2 7 4 1 0 ( ⊖ , 2 , ∅ ), ( ⊖ , 4 , ∅ ), ( ⊕ , 5 , { (5 , 4) } ) and ( ⊕ , 6 , { (6 , 1) } ) are elementary operations With G L : 6 3 2 7 4 1 0 ( ⊖ , 2 , ∅ ), ( ⊖ , 4 , ∅ ) and ( ⊕ , 6 , { (6 , 1) } ) are allowed for Agent L (arguments she knows). On the target G J 1 : 3 7 4 1 0 ( ⊖ , 4 , ∅ ) and ( ⊕ , 5 , { (5 , 4) } ) are executable by L on G J 1 . P. Bisquert YALLA BRA 2015 16 / 38

  27. Parallel An agent may act on a target argumentation system An agent has a goal An agent has access to some transitions ⇒ Close to belief update P. Bisquert YALLA BRA 2015 17 / 38

  28. Parallel An agent may act on a target argumentation system An agent has a goal An agent has access to some transitions ⇒ Close to belief update Graphs Worlds Formula characterizing Formula characterizing a set of graphs a set of worlds. Arg. Change Update Initial knowledge: Set of AS Set of worlds Input: Goal New info Set of transitions None (every update is Constraints: (executable operations) achievable) P. Bisquert YALLA BRA 2015 17 / 38

  29. Outline YALLA and Abstract Argumentation 1 YALLA and Argumentation Dynamics 2 Change in Argumentation Update Concepts Applied to Argumentation Specific Update Postulates Concluding Remarks 3 P. Bisquert YALLA BRA 2015 18 / 38

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