An analytial deomp osition of trust in terms of mental - PowerPoint PPT Presentation

An analyti al de omp osition of trust in terms of mental attitudes (w o rk in p rogress) 1 Rob ert Demolomb e 1 Institut de Re her he en Info rmatique de T oulouse June 2012 Demolomb e An analyti al de omp osition of trust in terms of mental attitudes (w o rk in p rogress)

Assumption (� la Castelfran hi et al.): the truster b elieves that if he has some pa rti ula r goal, then this goal will b e rea hed Analysis of p ossible supp o rts fo r trust: Empiri al truster's observations info rmation from trusted sour es Analyti al trust in something an b e supp o rted b y trust in other things ◮ ◮ 2 ◮ ◮ ◮

Obje tive of this w o rk: systemati analysis of the p ossible so ial relationships b et w een the truster and the trustees Metho d: fo rmalization in mo dal logi no analysis of the logi al p rop erties of the involved mo dalities: b elief, a tion, intention, obligation, ... trust has the from of onditional p rop erties ◮ ◮ 3 ◮

Mo dalities and op erato rs : φ entails ψ Bel : i b elieves φ i φ Goal : i 's goal is φ i φ A ttempt : i attempts to b ring it ab out that φ i φ Int : i 's intention is to b ring it ab out that φ i φ Obg φ : it is obligato ry that φ F o rb φ : it is fo rbidden that φ def F o rb φ Obg ¬ φ Ask : i asks j to b ring it ab out that φ φ ⇒ ψ i , j φ Commit : i has ommitted himself to b ring it ab out that φ i ( φ | ψ ) if ψ holds : φ holds no w and alw a ys in the future : φ will hold at some moment in the future def = 4 � φ ♦ φ = ¬ � ¬ φ ♦ φ

Logi al p rop erties Bel ob eys a K system i Prop erties of the onditionals (su� ient) (EQUIV) Si ⊢ φ ↔ φ ′ et ⊢ ψ ↔ ψ ′ , alo rs ⊢ ( φ ⇒ ψ ) → ( φ ′ ⇒ ψ ′ ) (PROPG) ( φ 1 ∧ φ 2 ⇒ φ 3 ) → ( φ 1 ∧ φ 2 ⇒ φ 1 ∧ φ 3 ) (TRANS) ( φ 1 ⇒ φ 2 ) ∧ ( φ 2 ⇒ φ 3 ) → ( φ 1 ⇒ φ 3 ) (DIST) ( φ 1 ∧ ( φ 1 ⇒ φ 2 ) ∧ ψ ) ⇒ ( φ 2 ∧ ψ ) (MA TIMP) ( φ ⇒ ψ ) → ( φ → ψ ) 5

Initial fo rm of trust i 's goal: to rea h a state of a�airs Example: i b elieves that if he has no ash ( ¬ φ ) and his goal is to get ash ( ♦ φ ), then he will get ash ( ♦ φ ) (F1) Bel Goal i ( ¬ φ ∧ i ♦ φ ⇒ ♦ φ ) 6

Initial fo rm of trust i 's goal: to rea h a state of a�airs Example: i b elieves that if he has no ash ( ¬ φ ) and his goal is to get ash ( ♦ φ ), then he will get ash ( ♦ φ ) (F1) Bel Goal i ( ¬ φ ∧ i ♦ φ ⇒ ♦ φ ) i 's goal: to maintain a state of a�airs Example: i b elieves that if his a r w oks w ell ( φ ) and his goal is that it still w o rks w ell ( � φ ), then it still w o rks w ell ( � φ ) (M1) Bel Goal i ( φ ∧ i � φ ⇒ � φ ) 7

Analysis of trust supp o rt to rea h If there is some agent j who holds some p rop ert y Prop ( j , φ ) su h that: (F2) Bel Goal i ♦ φ ⇒ ∃ jProp ( j , φ )) ∧ ( ∃ jProp ( j , φ ) ⇒ ♦ φ )) i (( ¬ φ ∧ (F2) is a supp o rt fo r (F1) (F1) Bel Goal i ( ¬ φ ∧ i ♦ φ ⇒ ♦ φ ) b e ause (F2) entails (F1) 8

Analysis of trust supp o rt to rea h If there is some agent j who holds some p rop ert y Prop ( j , φ ) su h that: (F2) Bel Goal i ♦ φ ⇒ ∃ jProp ( j , φ )) ∧ ( ∃ jProp ( j , φ ) ⇒ ♦ φ )) i (( ¬ φ ∧ (F2) is a supp o rt fo r (F1) (F1) Bel Goal i ( ¬ φ ∧ i ♦ φ ⇒ ♦ φ ) b e ause (F2) entails (F1) to maintain If there is no agent who holds some p rop ert y Prop ′ ( j , φ ) su h that: (M2) Bel Goal i � φ ⇒ ¬∃ jProp ′ ( j , φ )) ∧ ( ¬∃ jProp ′ ( j , φ ) ⇒ � φ )) i (( φ ∧ (M2) is a supp o rt fo r (M1) i 's assumption: the only w a y to hange φ is that there is an agent j su h that Prop ′ ( j , φ ) 9

T rust in abilit y (F2) Bel Goal i ♦ φ ⇒ ∃ jProp ( j , φ )) ∧ ( ∃ jProp ( j , φ ) ⇒ ♦ φ )) i (( ¬ φ ∧ Abilit y def Able A ttempt j φ j φ ⇒ ♦ φ T rust in abilit y: Bel Able i j φ def Prop j , φ ) A ttempt A ttempt 1 ( j φ ∧ ( j φ ⇒ ♦ φ ) = = 10

T rust in abilit y (F2) Bel Goal i ♦ φ ⇒ ∃ jProp ( j , φ )) ∧ ( ∃ jProp ( j , φ ) ⇒ ♦ φ )) i (( ¬ φ ∧ Abilit y def Able A ttempt j φ j φ ⇒ ♦ φ T rust in abilit y: Bel Able i j φ def Prop j , φ ) A ttempt A ttempt 1 ( j φ ∧ ( j φ ⇒ ♦ φ ) i 's b elief: ∃ j ( A ttempt Able j φ ∧ j φ ) ⇒ ♦ φ If Prop ( j , φ ) is Prop j , φ ) , (F2) holds 1 ( = = 11

T rust in abilit y (M2) Bel Goal i � φ ⇒ ¬∃ jProp ′ ( j , φ )) ∧ ( ¬∃ jProp ′ ( j , φ ) ⇒ � φ )) i (( φ ∧ Abilit y def Prop ′ j , φ ) A ttempt A ttempt j ¬ φ ∧ ( j ¬ φ ⇒ ♦ ¬ φ ) 1 ( = 12

T rust in abilit y (M2) Bel Goal i � φ ⇒ ¬∃ jProp ′ ( j , φ )) ∧ ( ¬∃ jProp ′ ( j , φ ) ⇒ � φ )) i (( φ ∧ Abilit y def Prop ′ j , φ ) A ttempt A ttempt j ¬ φ ∧ ( j ¬ φ ⇒ ♦ ¬ φ ) 1 ( Logi al p rop erties: ⊢ ∃ jProp ′ j , φ ) → ♦ ¬ φ 1 ( ⊢ � φ → ¬∃ jProp ′ j , φ ) 1 ( i 's b elief: ¬∃ j ( A ttempt Able j ¬ φ ∧ j ¬ φ ) ⇒ � φ If Prop ′ ( j , φ ) is Prop ′ j , φ ) , (M2) holds 1 ( = 13

A tive j 's intention triggers j 's a tion def A tive Int A ttempt j φ j φ ⇒ j φ def Prop j , φ ) Int Int A ttempt Able 2 ( j φ ∧ ( j φ ⇒ j φ ) ∧ j φ = = 14

A tive j 's intention triggers j 's a tion def A tive Int A ttempt j φ j φ ⇒ j φ def Prop j , φ ) Int Int A ttempt Able 2 ( j φ ∧ ( j φ ⇒ j φ ) ∧ j φ Logi al p rop ert y: ⊢ ∃ jProp j , φ ) → ♦ φ 2 ( i 's b elief: ∃ j ( Int A tive Able j φ ∧ j φ ∧ j φ ) ⇒ ♦ φ = = 15

A tive def Prop ′ j , φ ) Int Int A ttempt Able j ¬ φ ∧ ( j ¬ φ ⇒ j ¬ φ ) ∧ j ¬ φ 2 ( Logi al p rop ert y: ⊢ ∃ jProp ′ j , φ ) → ♦ ¬ φ 2 ( i 's b elief: ¬∃ j ( Int A tive Able j ¬ φ ∧ j ¬ φ ∧ j ¬ φ ) ⇒ � φ = 16

Intention adoption No rms ful�llment T o a hieve If j b elieves that he is obliged to do something, then he intends to do that thing def Ob ey Bel ObgInt Int j φ j j φ ⇒ j φ def Prop j , φ ) Bel ObgInt Bel ObgInt Int 3 . 1 ( j j φ ∧ ( j j φ ⇒ j φ ) ∧ A tive Able j φ ∧ j φ = = 17

Intention adoption No rms ful�llment T o a hieve If j b elieves that he is obliged to do something, then he intends to do that thing def Ob ey Bel ObgInt Int j φ j j φ ⇒ j φ def Prop j , φ ) Bel ObgInt Bel ObgInt Int 3 . 1 ( j j φ ∧ ( j j φ ⇒ j φ ) ∧ A tive Able j φ ∧ j φ Logi al p rop ert y: ⊢ ∃ jProp j , φ ) → ♦ φ 3 . 1 ( i 's b elief: ∃ j ( ObgInt Ob ey A tive Able j φ ∧ j φ ∧ j φ ∧ j φ ) ⇒ ♦ φ = = 18

No rms ful�llment and institutional p o w er If i asks j to b ring it ab out that φ , then j b elieves that it is obligato ry that he adopts the intention to b ring it ab out that φ Example: p oli eman i asks j to stop his a r def InstP o w er Ask Bel ObgInt i , j φ i , j φ ⇒ j j φ def Prop j , φ ) Ask Ask Bel ObgInt 4 . 1 ( i , j φ ∧ ( i , j φ ⇒ j j φ ) ∧ Ob ey A tive Able j φ ∧ j φ ∧ j φ = = 19

No rms ful�llment and institutional p o w er If i asks j to b ring it ab out that φ , then j b elieves that it is obligato ry that he adopts the intention to b ring it ab out that φ Example: p oli eman i asks j to stop his a r def InstP o w er Ask Bel ObgInt i , j φ i , j φ ⇒ j j φ def Prop j , φ ) Ask Ask Bel ObgInt 4 . 1 ( i , j φ ∧ ( i , j φ ⇒ j j φ ) ∧ Ob ey A tive Able j φ ∧ j φ ∧ j φ Logi al p rop ert y: ⊢ ∃ jProp j , φ ) → ♦ φ 4 . 1 ( i 's b elief: ∃ j ( Ask Ob ey InstP o w er A tive Able i , j φ ∧ j φ ∧ i , j φ ∧ j φ ∧ j φ ) ⇒ ♦ φ = = 20

No rms ful�llment T o maintain def Prop ′ j , φ ) Bel ObgInt Bel ObgInt Int j j ¬ φ ∧ ( j j ¬ φ ⇒ j ¬ φ ) ∧ 3 . 1 ( A tive Able j ¬ φ ∧ j ¬ φ = 21

No rms ful�llment T o maintain def Prop ′ j , φ ) Bel ObgInt Bel ObgInt Int j j ¬ φ ∧ ( j j ¬ φ ⇒ j ¬ φ ) ∧ 3 . 1 ( A tive Able j ¬ φ ∧ j ¬ φ Logi al p rop ert y: ⊢ ∃ jProp ′ j , φ ) → ♦ ¬ φ 3 . 1 ( i 's b elief: ¬∃ j ( Bel ObgInt Ob ey A tive Able j j ¬ φ ∧ j ¬ φ ∧ j ¬ φ ∧ j ¬ φ ) ⇒ � φ ¬∃ jProp ′ j , φ ) : no agent who ful�lls the no rms b elieves that 3 . 1 ( ObgInt j ¬ φ def Prop ′′ j , φ ) = Bel F o rbInt Bel F o rbInt Int j j ¬ φ ∧ ( j j ¬ φ ⇒ j ¬ φ ) ∧ 3 . 1 ( A tive Able j ¬ φ ∧ j ¬ φ ¬∃ jProp ′ j , φ ) : no agent who violates the no rms b elieves that 3 . 1 ( F o rbInt j ¬ φ 22 =