Enforcement is a kind of Update Enforcement in Argumentation is a kind of Update an axiomatic approach of enforcement P . Bisquert, C. Cayrol, F . Dupin de Saint-Cyr, MC. Lagasquie IRIT, Toulouse University, France July 2013 F. Dupin de Saint-Cyr Sintelnet workshop: Believing, planning, acting, revising July 2013 1 / 30 Sintelnet workshop: Believing, planning, acting, revising
Enforcement is a kind of Update A lawyer during a trial a c b blabla . . . my client d innocent . . . . . . blabla . . . guilty audience Lawyer Opposite party A lawyer makes her final address to an audience ; O (opposite party) knows the corresponding argumentation system (AS). O can compute the accepted arguments in AS. F. Dupin de Saint-Cyr Sintelnet workshop: Believing, planning, acting, revising July 2013 2 / 30
Enforcement is a kind of Update Lawyer’s example a c b d e attacks c audience Lawyer Opposite party O wants to force the audience to accept specific arguments. She has to make a change to the public system : ◮ by adding an argument F. Dupin de Saint-Cyr Sintelnet workshop: Believing, planning, acting, revising July 2013 3 / 30
Enforcement is a kind of Update Lawyer’s example e a c b d e attacks c audience Lawyer Opposite party O wants to force the audience to accept specific arguments. She has to make a change to the public system : ◮ by adding an argument F. Dupin de Saint-Cyr Sintelnet workshop: Believing, planning, acting, revising July 2013 3 / 30
Enforcement is a kind of Update Lawyer’s example a c b d objection against c audience Lawyer Opposite party O wants to force the audience to accept specific arguments. She has to make a change to the public system : ◮ by adding an argument ◮ or by doing an objection about an argument (to remove it) F. Dupin de Saint-Cyr Sintelnet workshop: Believing, planning, acting, revising July 2013 3 / 30
Enforcement is a kind of Update Lawyer’s example a b d objection against c audience Lawyer Opposite party O wants to force the audience to accept specific arguments. She has to make a change to the public system : ◮ by adding an argument ◮ or by doing an objection about an argument (to remove it) F. Dupin de Saint-Cyr Sintelnet workshop: Believing, planning, acting, revising July 2013 3 / 30
Enforcement is a kind of Update a ( d ) ∧ on ( b ) e ∧¬ on ( e ) a 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 ◮ agent should respect some constraints ⇒ notion of executable operation Target = public argumentation system (state of the dialog) F. Dupin de Saint-Cyr Sintelnet workshop: Believing, planning, acting, revising July 2013 4 / 30
Enforcement is a kind of Update Summary Framework 1 Towards Generalized Enforcement 2 Generalized Update Postulates 3 Concluding Remarks 4 F. Dupin de Saint-Cyr Sintelnet workshop: Believing, planning, acting, revising July 2013 5 / 30
Enforcement is a kind of Update Summary Framework 1 Abstract argumentation Goals Change in Argumentation Towards Generalized Enforcement 2 Generalized Update Postulates 3 Concluding Remarks 4 F. Dupin de Saint-Cyr Sintelnet workshop: Believing, planning, acting, revising July 2013 6 / 30
Enforcement is a kind of Update Abstract argumentation A universe � Arg , Rel � = all arguments and their interactions. Mr. X is not guilty of the murder of Mrs. X 0 Universe 0 F. Dupin de Saint-Cyr Sintelnet workshop: Believing, planning, acting, revising July 2013 7 / 30
Enforcement is a kind of Update Abstract argumentation A universe � Arg , Rel � = 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 F. Dupin de Saint-Cyr Sintelnet workshop: Believing, planning, acting, revising July 2013 7 / 30
Enforcement is a kind of Update Abstract argumentation A universe � Arg , Rel � = 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 F. Dupin de Saint-Cyr Sintelnet workshop: Believing, planning, acting, revising July 2013 7 / 30
Enforcement is a kind of Update Abstract argumentation A universe � Arg , Rel � = 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. Mr. X associate’s testimony is suspicious due to 3 their close working business relationship 3 1 2 0 F. Dupin de Saint-Cyr Sintelnet workshop: Believing, planning, acting, revising July 2013 7 / 30
Enforcement is a kind of Update Abstract argumentation A universe � Arg , Rel � = 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. Mr. X associate’s testimony is suspicious due to 3 their close working business relationship 4 Mr. X loves his wife. A man who loves his wife 4 cannot be her killer. 3 1 2 0 F. Dupin de Saint-Cyr Sintelnet workshop: Believing, planning, acting, revising July 2013 7 / 30
Enforcement is a kind of Update Abstract argumentation A universe � Arg , Rel � = 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 met him at the time of the murder. Mr. X associate’s testimony is suspicious due to 3 their close working business relationship 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 2 0 F. Dupin de Saint-Cyr Sintelnet workshop: Believing, planning, acting, revising July 2013 7 / 30
Enforcement is a kind of Update Abstract argumentation A universe � Arg , Rel � = 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 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 was 6 2 0 not the beneficiary of her life insurance F. Dupin de Saint-Cyr Sintelnet workshop: Believing, planning, acting, revising July 2013 7 / 30
Enforcement is a kind of Update Abstract argumentation A universe � Arg , Rel � = 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 was 6 2 0 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. F. Dupin de Saint-Cyr Sintelnet workshop: Believing, planning, acting, revising July 2013 7 / 30
Enforcement is a kind of Update Abstract argumentation A universe � Arg , Rel � = all arguments and their interactions. Definition (Argumentation graph (AS)) Universe An argumentation graph G is a pair ( A , R ) 5 7 A ⊆ Arg arguments (finite) R ⊆ Rel ∩ ( A × A ) 6 4 Γ = all argumentation graphs w.r.t. the universe. 3 1 2 2 7 4 1 0 4 1 0 2 0 G 1 G 2 F. Dupin de Saint-Cyr Sintelnet workshop: Believing, planning, acting, revising July 2013 7 / 30
Enforcement is a kind of Update Argumentation graph example Agent O knows all the arguments of the universe. But O is not sure about the content of the jury’s system. She hesitates between two graphs : 2 2 7 4 1 0 4 1 0 G 1 G 2 F. Dupin de Saint-Cyr Sintelnet workshop: Believing, planning, acting, revising July 2013 8 / 30
Enforcement is a kind of Update Acceptability of an argument “semantics” : way to compute particular sets of arguments ( extensions ) ◮ a set of arguments Y defends an argument x , denoted x ∈ F ( Y ) iff ∀ y s.t. ( y , x ) ∈ R , ∃ z ∈ Y s.t. ( z , y ) ∈ R . ◮ a grounded extension : conflict free set of arguments = the least (wrt inclusion) fix point for F ◮ a preferred extension : conflict free set of arguments defending all its elements and maximal (wrt inclusion) ◮ a stable extension S : conflict free set of arguments attacking each arguments outside of it. x is accepted if it belongs to the extension(s) ( x ∈ E ) F. Dupin de Saint-Cyr Sintelnet workshop: Believing, planning, acting, revising July 2013 9 / 30
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