declarative LPPN for transitions p11 p r o d u c e s t4 e n t a i l s ● E q u i v a l e n t t o t4 :- t2, p8. t3 :- t2, p9. t2. A S P / P r o l o g : → → (t2 ∧ p8 t4) ∧ (t2 ∧ p9 t4) ∧ t2 F O L :
Evaluating the LPPN notation
Evaluating the LPPN notation ● N o r m a t i v e m o d e l i n g i s o n e o f t h e p u r p o s e s o f t h e n o t a t i o n . We u s e d i t t o m o d e l w e l l - k n o w n p r o b l e m s d e fj n e d b y t h e d e o n t i c l o g i c c o m m u n i t y .
Evaluating the LPPN notation ● N o r m a t i v e m o d e l i n g i s o n e o f t h e p u r p o s e s o f t h e n o t a t i o n . We u s e d i t t o m o d e l w e l l - k n o w n p r o b l e m s d e fj n e d b y t h e d e o n t i c l o g i c c o m m u n i t y . ● C o n t r a r y T o D u t y ( C T D ) s t r u c t u r e s : s i t u a t i o n s i n w h i c h a p r i m a r y o b l i g a t i o n e x i s t s , a n d w i t h i t s v i o l a t i o n , a s e c o n d a r y o b l i g a t i o n c o m e s i n t o e x i s t e n c e .
Evaluating the LPPN notation ● N o r m a t i v e m o d e l i n g i s o n e o f t h e p u r p o s e s o f t h e n o t a t i o n . We u s e d i t t o m o d e l w e l l - k n o w n p r o b l e m s d e fj n e d b y t h e d e o n t i c l o g i c c o m m u n i t y . ● C o n t r a r y T o D u t y ( C T D ) s t r u c t u r e s : s i t u a t i o n s i n w h i c h a p r i m a r y o b l i g a t i o n e x i s t s , a n d w i t h i t s v i o l a t i o n , a s e c o n d a r y o b l i g a t i o n c o m e s i n t o e x i s t e n c e . ● C o m m o n i n e . g . c o m p e n s a t o r y n o r m s .
A simple deontic paradox ● Y o u a r e f o r b i d d e n t o c r o s s t h e r o a d . ● I f y o u a r e c r o s s i n g t h e r o a d , ( y o u h a v e t o ) c r o s s t h e r o a d !
A simple deontic paradox ● Y o u a r e f o r b i d d e n t o c r o s s t h e r o a d . ● I f y o u a r e c r o s s i n g t h e r o a d , ( y o u h a v e t o ) c r o s s t h e r o a d ! ● Y o u a r e c r o s s i n g .
A simple deontic paradox ● Y o u a r e f o r b i d d e n t o c r o s s t h e r o a d . ● I f y o u a r e c r o s s i n g t h e r o a d , ( y o u h a v e t o ) c r o s s t h e r o a d ! ● Y o u a r e c r o s s i n g . obl(not cross) obl(not cross) if cross then obl(cross) obl(cross) cross contradiction
You mustn't cross the road. If you are crossing the road, cross the road! ● U s u a l s o l u t i o n : p r e f e r e n c e s a m o n s t p o s s i b l e w o r l d s .
You mustn't cross the road. If you are crossing the road, cross the road! ● U s u a l s o l u t i o n : p r e f e r e n c e s a m o n s t p o s s i b l e w o r l d s . ● A l t e r n a t i v e s o l u t i o n : – i m p l i c i t t e m p o r a l m e a n i n g : i f y o u s t a r t e d c r o s s i n g t h e r o a d , fj n i s h t o c r o s s t h e r o a d ! → L e t u s i n c r e a s e g r a n u l a r i t y o f t h e m o d e l . . .
You mustn't cross the road. V e r s i o n 1 If you are crossing the road, cross the road!
You mustn't cross the road. V e r s i o n 1 ● Y o u s t a r t c r o s s i n g . If you are crossing the road, cross the road! source firing
You mustn't cross the road. V e r s i o n 1 ● Y o u s t a r t c r o s s i n g . If you are crossing the road, cross the road! propagation
You mustn't cross the road. V e r s i o n 1 ● Y o u s t a r t c r o s s i n g . If you are crossing the road, cross the road! consumption production
You mustn't cross the road. V e r s i o n 1 ● Y o u a r e c r o s s i n g . If you are crossing the road, cross the road! ● N o t s o r e a l i s t i c : i n t u i t i v e l y , w e s t i l l h a v e s u c h p r o h i b i t i o n .
You mustn't cross the road. V e r s i o n 1 ● Y o u fj n i s h c r o s s i n g . If you are crossing the road, cross the road! ● N o t s o r e a l i s t i c : i n t u i t i v e l y , w e s t i l l h a v e s u c h p r o h i b i t i o n .
You mustn't cross the road. V e r s i o n 1 ● Y o u fj n i s h c r o s s i n g . If you are crossing the road, cross the road! ● N o t s o r e a l i s t i c : i n t u i t i v e l y , w e s t i l l h a v e s u c h p r o h i b i t i o n .
You mustn't cross the road. V e r s i o n 2 If you are crossing the road, cross the road!
You mustn't cross the road. ● Y V e r s i o n 2 o u s t a r t c r o s s i n g . If you are crossing the road, cross the road! source firing
You mustn't cross the road. ● Y V e r s i o n 2 o u s t a r t c r o s s i n g . If you are crossing the road, cross the road! propagation
You mustn't cross the road. ● Y V e r s i o n 2 o u s t a r t c r o s s i n g . If you are crossing the road, cross the road! production
You mustn't cross the road. ● Y V e r s i o n 2 o u s t a r t c r o s s i n g . If you are crossing the road, propagation cross the road!
You mustn't cross the road. ● Y V e r s i o n 2 o u a r e c r o s s i n g . If you are crossing the road, propagation cross the road! O b l i g a t i o n h a s h i g h e r p r i o r i t y ( t o p o l o g y c a p t u r e s s a l i e n c e ) .
Gentle murderer [ F o r r e s t e r , 1 9 8 4 ] It is forbidden to kill, but if one kills, one ought to kill gently.
Gentle murderer [ F o r r e s t e r , 1 9 8 4 ] It is forbidden to kill, but if one kills, one ought to kill gently.
Gentle murderer [ F o r r e s t e r , 1 9 8 4 ] It is forbidden to kill, but if one kills, one ought to kill gently. ● H e s t a r t s k i l l i n g .
Gentle murderer [ F o r r e s t e r , 1 9 8 4 ] It is forbidden to kill, but if one kills, one ought to kill gently. ● H e s t a r t s k i l l i n g .
Gentle murderer [ F o r r e s t e r , 1 9 8 4 ] It is forbidden to kill, but if one kills, one ought to kill gently. ● H e s t a r t s k i l l i n g .
Gentle murderer [ F o r r e s t e r , 1 9 8 4 ] It is forbidden to kill, but if one kills, one ought to kill gently. ● H e s t a r t s k i l l i n g . ( e i t h e r h e k i l l s g e n t l y . . . )
Gentle murderer [ F o r r e s t e r , 1 9 8 4 ] It is forbidden to kill, but if one kills, one ought to kill gently. ● H e s t a r t s k i l l i n g . ( e i t h e r h e k i l l s g e n t l y o r n o t . )
There must be no fence. White fence If there is a fence, it must be a white fence. If the cottage is by the sea, there may be a fence. [ P r a k k e n & S e r g o t , 1 9 9 6 ]
There must be no fence. White fence If there is a fence, it must be a white fence. If the cottage is by the sea, there may be a fence. [ P r a k k e n & S e r g o t , 1 9 9 6 ] e x c e p t i o n , i m p l i c i t d e f a u l t
There must be no fence. White fence If there is a fence, it must be a white fence. If the cottage is by the sea, there may be a fence. [ P r a k k e n & S e r g o t , 1 9 9 6 ] default generation
There must be no fence. White fence If there is a fence, it must be a white fence. If the cottage is by the sea, there may be a fence. [ P r a k k e n & S e r g o t , 1 9 9 6 ]
There must be no fence. White fence If there is a fence, it must be a white fence. If the cottage is by the sea, there may be a fence. [ P r a k k e n & S e r g o t , 1 9 9 6 ] ● T h e r e i s a w h i t e f e n c e .
There must be no fence. White fence If there is a fence, it must be a white fence. If the cottage is by the sea, there may be a fence. [ P r a k k e n & S e r g o t , 1 9 9 6 ] ● T h e r e i s a w h i t e f e n c e .
There must be no fence. White fence If there is a fence, it must be a white fence. If the cottage is by the sea, there may be a fence. [ P r a k k e n & S e r g o t , 1 9 9 6 ] ● T h e r e i s a w h i t e f e n c e .
There must be no fence. White fence If there is a fence, it must be a white fence. If the cottage is by the sea, there may be a fence. [ P r a k k e n & S e r g o t , 1 9 9 6 ] ● T h e r e i s a w h i t e f e n c e .
Privacy Act [ G o v e r n a t o r i , 2 0 1 5 ] ● The collection of personal information is forbidden, unless acting on a court order authorising it. ● The destruction of illegally collected personal information before accessing it is a defence against the illegal collection of the personal information. ● The collection of medical information is forbidden, unless the entity collecting the medical information is permitted to collect personal information.
Forbidden A. If C, then Permitted A. Privacy Act If Forbidden A and A, then Obligatory B. Forbidden D. If Permitted A, then Permitted D. [ G o v e r n a t o r i , 2 0 1 5 ] ● The collection of personal information is forbidden, unless acting on a court order authorising it. ● The destruction of illegally collected personal information before accessing it is a defence against the illegal collection of the personal information. ● The collection of medical information is forbidden, unless the entity collecting the medical information is permitted to collect personal information.
Forbidden A. If C, then Permitted A. Privacy Act If Forbidden A and A, then Obligatory B. Forbidden D. If Permitted A, then Permitted D. [ G o v e r n a t o r i , 2 0 1 5 ]
Forbidden A. If C, then Permitted A. Privacy Act If Forbidden A and A, then Obligatory B. Forbidden D. If Permitted A, then Permitted D. [ G o v e r n a t o r i , 2 0 1 5 ]
Forbidden A. If C, then Permitted A. Privacy Act If Forbidden A and A, then Obligatory B. Forbidden D. If Permitted A, then Permitted D. [ G o v e r n a t o r i , 2 0 1 5 ] ● A o c c u r s .
Forbidden A. If C, then Permitted A. Privacy Act If Forbidden A and A, then Obligatory B. Forbidden D. If Permitted A, then Permitted D. [ G o v e r n a t o r i , 2 0 1 5 ] ● A o c c u r s .
Forbidden A. If C, then Permitted A. Privacy Act If Forbidden A and A, then Obligatory B. Forbidden D. If Permitted A, then Permitted D. [ G o v e r n a t o r i , 2 0 1 5 ] institutional realm extra-institutional (“brute”) realm constitutive rules
A bit further into deontic axioms
Factual detachment ∧ → p Obl (q|p) Obl (q)
Deontic detachment ∧ → Obl (p) Obl (q|p) Obl (q) N o t i m p l i e d b y L P P N ! I t d o e s n o t c a p t u r e t h e a n t i c i p a t i o n .
Derived obligations ● Bob’s promise to meet you commits him to meeting you. ● It is obligatory that if Bob promises to meet you, he does so.
Derived obligations ● Bob’s promise to meet you commits him to meeting you. → p Obl (m) ● It is obligatory that if Bob promises to meet you, he does so. → Obl (p m)
Derived obligations ● Bob’s promise to meet you commits him to meeting you. → p Obl (m) ● It is obligatory that if Bob promises to meet you, he does so. → Obl (p m)
Derived obligations ● Bob’s promise to meet you commits him to meeting you. → p Obl (m) ● It is obligatory that if Bob promises to meet you, he does so. → Obl (p m) ● p
Derived obligations ● Bob’s promise to meet you commits him to meeting you. → p Obl (m) ● It is obligatory that if Bob promises to meet you, he does so. → Obl (p m) ● p , ● e i t h e r m . .
Derived obligations ● Bob’s promise to meet you commits him to meeting you. → p Obl (m) ● It is obligatory that if Bob promises to meet you, he does so. → Obl (p m) ● p , ● e i t h e r m , o r ¬ m
Derived obligations ● Bob’s promise to meet you commits him to meeting you. → p Obl (m) ● It is obligatory that if Bob promises to meet you, he does so. → Obl (p m) ● p , ● e i t h e r m , o r ¬ m ● b u t w h a t a b o u t ¬ p ?
Derived obligations ● Bob’s promise to meet you commits him to meeting you. → p Obl (m) ● It is obligatory that if Bob promises to meet you, he does so. → Obl (p m) ● p ∧ ¬ m
Derived obligations ● Bob’s promise to meet you commits him to meeting you. → p Obl (m) ● It is obligatory that if Bob promises to meet you, he does so. → Obl (p m) ● p ∧ ¬ m ● m . . .
Derived obligations ● Bob’s promise to meet you commits him to meeting you. → p Obl (m) ● It is obligatory that if Bob promises to meet you, he does so. → Obl (p m) ● p ∧ ¬ m ● m o r ¬ p
Chisholm’s paradox [ C h i s h o l m , 1 9 6 3 ]
Chisholm’s paradox [ C h i s h o l m , 1 9 6 3 ] ● It ought to be that Jones goes (to the assistance of his neighbors). ● It ought to be that if Jones goes, then he tells them he is coming. ● If Jones doesn’t go, then he ought not tell them he is coming. ● Jones doesn’t go.
Chisholm’s Obl (go) → Obl (go tell) paradox → ¬go Forb(tell) ¬go [ C h i s h o l m , 1 9 6 3 ] ● It ought to be that Jones goes (to the assistance of his neighbors). ● It ought to be that if Jones goes, then he tells them he is coming. ● If Jones doesn’t go, then he ought not tell them he is coming. ● Jones doesn’t go.
Chisholm’s Obl (go) → Obl (go tell) paradox → ¬go Forb(tell) ● Y ¬go o u d o n ' t g o . [ C h i s h o l m , 1 9 6 3 ]
Chisholm’s Obl (go) → Obl (go tell) paradox → ¬go Forb(tell) ● Y ¬go o u d o n ' t g o . [ C h i s h o l m , 1 9 6 3 ]
Chisholm’s Obl (go) → Obl (go tell) paradox → ¬go Forb(tell) ● Y ¬go o u d o n ' t g o . . . [ C h i s h o l m , 1 9 6 3 ] Y o u d o n ' t t e l l . . .
Chisholm’s Obl (go) → Obl (go tell) paradox → ¬go Forb(tell) ● Y ¬go o u d o n ' t g o . . . [ C h i s h o l m , 1 9 6 3 ] Y o u t e l l t h e m . . .
Conclusions
Conclusions ● We p r e s e n t e d e x a m p l e s o f a p p l i c a t i o n o f a n o t a t i o n i n t r o d u c e d f o r w i d e r m o d e l i n g p u r p o s e s , b u t w h i c h c a n b e a p p l i e d f o r n o r m a t i v e s c e n a r i o s :
Conclusions ● We p r e s e n t e d e x a m p l e s o f a p p l i c a t i o n o f a n o t a t i o n i n t r o d u c e d f o r w i d e r m o d e l i n g p u r p o s e s , b u t w h i c h c a n b e a p p l i e d f o r n o r m a t i v e s c e n a r i o s : – p a r a d o x i c a l c a s e s a r e e a s i l y u n v e i l e d
Conclusions ● We p r e s e n t e d e x a m p l e s o f a p p l i c a t i o n o f a n o t a t i o n i n t r o d u c e d f o r w i d e r m o d e l i n g p u r p o s e s , b u t w h i c h c a n b e a p p l i e d f o r n o r m a t i v e s c e n a r i o s : – p a r a d o x i c a l c a s e s a r e e a s i l y u n v e i l e d – d i r e c t l i n k w i t h b u s i n e s s p r o c e s s p r a c t i c e s
Conclusions ● We p r e s e n t e d e x a m p l e s o f a p p l i c a t i o n o f a n o t a t i o n i n t r o d u c e d f o r w i d e r m o d e l i n g p u r p o s e s , b u t w h i c h c a n b e a p p l i e d f o r n o r m a t i v e s c e n a r i o s : – p a r a d o x i c a l c a s e s a r e e a s i l y u n v e i l e d – d i r e c t l i n k w i t h b u s i n e s s p r o c e s s p r a c t i c e s – v i s u a l n o t a t i o n ( a n i m a t i o n o f m o d e l s t h r o u g h s i m u l a t i o n m a k e t h e m i n p r i n c i p l e m o r e a c c e s s i b l e )
Conclusions ● We p r e s e n t e d e x a m p l e s o f a p p l i c a t i o n o f a n o t a t i o n i n t r o d u c e d f o r w i d e r m o d e l i n g p u r p o s e s , b u t w h i c h c a n b e a p p l i e d f o r n o r m a t i v e s c e n a r i o s . ● D e f a u l t s , e x c e p t i o n s , s u s p e n s i o n s r e q u i r e d e x t e n s i o n s .
Conclusions ● We p r e s e n t e d e x a m p l e s o f a p p l i c a t i o n o f a n o t a t i o n i n t r o d u c e d f o r w i d e r m o d e l i n g p u r p o s e s , b u t w h i c h c a n b e a p p l i e d f o r n o r m a t i v e s c e n a r i o s . ● D e f a u l t s , e x c e p t i o n s , s u s p e n s i o n s r e q u i r e d e x t e n s i o n s . ● ~ m i n i m a l c o m m i t m e n t ( c f . i n p u t / o u t p u t l o g i c ) ∧ ∧ O b l ( A ) O b l ( B ) ? ? O b l ( A B )
Conclusions ● We p r e s e n t e d e x a m p l e s o f a p p l i c a t i o n o f a n o t a t i o n i n t r o d u c e d f o r w i d e r m o d e l i n g p u r p o s e s , b u t w h i c h c a n b e a p p l i e d f o r n o r m a t i v e s c e n a r i o s . ● D e f a u l t s , e x c e p t i o n s , s u s p e n s i o n s r e q u i r e d e x t e n s i o n s . ● I n t e r e s t i n g s e m a n t i c c o r r e s p o n d e n c e w i t h l a n g u a g e – n o u n s , ( i m p e r f e c t ) v e r b s ~ p l a c e s / t o k e n s – ( p e r f e c t ) v e r b s ~ t r a n s i t i o n / t r a n s i t i o n e v e n t s
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