Changing Legal Systems: Abrogation and Annulment Part II: Temporalised Defeasible Logic Guido Governatori and Antonino Rotolo NICTA and CIRSFID 15 July 2008 � NICTA 2008 c 1 / 1
Tax Dilemma Provision in force from January 1 If the taxable income of a person is in excess of 100,000$, then the top marginal rate computed at February 28 is 50% of the total taxable income. � NICTA 2008 c 2 / 1
Tax Dilemma Provision in force from January 1 If the taxable income of a person is in excess of 100,000$, then the top marginal rate computed at February 28 is 50% of the total taxable income. Provision in force from February 15 If the taxable income of a person is in excess of 120,000$, then the top marginal rate computed at February 28 is 30% of the total taxable income. � NICTA 2008 c 2 / 1
Tax Dilemma The new norm annulls the old one: refund already paid taxes � NICTA 2008 c 3 / 1
Tax Dilemma The new norm annulls the old one: refund already paid taxes The new norm abrogates the old one: no refunds � NICTA 2008 c 3 / 1
Tax Dilemma The new norm annulls the old one: refund already paid taxes The new norm abrogates the old one: no refunds Italian solution: � NICTA 2008 c 3 / 1
Tax Dilemma The new norm annulls the old one: refund already paid taxes The new norm abrogates the old one: no refunds Italian solution: � NICTA 2008 c 3 / 1
Tax Dilemma The new norm annulls the old one: refund already paid taxes The new norm abrogates the old one: no refunds Italian solution: Don’t pay taxes! � NICTA 2008 c 3 / 1
Tax Dilemma The new norm annulls the old one: refund already paid taxes The new norm abrogates the old one: no refunds Italian solution: Don’t pay taxes! US solution: � NICTA 2008 c 3 / 1
Tax Dilemma The new norm annulls the old one: refund already paid taxes The new norm abrogates the old one: no refunds Italian solution: Don’t pay taxes! US solution: Lend money! � NICTA 2008 c 3 / 1
Normative Systems LS ( t 1 ) , LS ( t 2 ) ,..., LS ( t j ) ,... LS ( t ′ ) LS ( t ′′ ) t 0 t ′ t ′′ � NICTA 2008 c 4 / 1
Defeasible Logic Derive (plausible) conclusions with the minimum amount of information. Definite conclusions Defeasible conclusions Defeasible Theory Facts Strict rules ( A → B ) Defeasible rules ( A ⇒ B ) Defeaters ( A ❀ B ) Superiority relation over rules Conclusions +∆ q , which means that q is strictly provable in D ; 1 − ∆ q , which means that q is not strictly provable in D ; 2 + ∂ q , which means that q is defeasibly provable in D ; 3 − ∂ q , which means that q is not defeasibly provable in D . 4 � NICTA 2008 c 5 / 1
Rules A rule is identified by a unique label and gives conditions to derive a (legal) provision at a particular time. � NICTA 2008 c 6 / 1
Rules A rule is identified by a unique label and gives conditions to derive a (legal) provision at a particular time. r 1 : ( IncomeThreshold 31 Jan ⇒ HighMarginalRate (28 Feb , τ ) ) (1 Jan , π ) @(31 Dec , π ) r 2 : ( HighMarginalRate 28 Feb ⇒ Pay50 % ( 1March , π ) ) (1 Jan , π ) @(31 Dec , π ) � NICTA 2008 c 6 / 1
Meta-Rules A meta-rule gives conditions to establish that a rule is effective (and when it is), with respect to a particular time. � NICTA 2008 c 7 / 1
Meta-Rules A meta-rule gives conditions to establish that a rule is effective (and when it is), with respect to a particular time. mr : ( JoinEU 21 March ⇒ r 1 : ( IncomeThreshold 31 Jan ⇒ HighMarginalRate (28 Feb , τ ) ) (1 Jan , π ) )@(1 Jan , π ) � NICTA 2008 c 7 / 1
Temporal Model t 0 t 0 t ′ t ′′ t ′ t ′′ LS ( t ′ ) LS ( t ′′ ) t 0 t ′ t ′′ � NICTA 2008 c 8 / 1
Rule Persistence r r t 0 t 0 t ′ t ′′′ t ′′ t ′ t ′′′ t ′′ LS ( t ′ ) LS ( t ′′ ) t 0 r : t ′′′ @ t ′ r : t ′′′ @ t ′′ t ′ t ′′ � NICTA 2008 c 9 / 1
Conclusion Persistence + ∂ a + ∂ a t 0 t 0 t ′ ′′′ t ′′ t ′ t ′′′ t ′′ t LS ( t ′ ) LS ( t ′′ ) t 0 t ′ t ′′ � NICTA 2008 c 10 / 1
Persistence in Normative Systems Given a 10 r 1 : ( a 10 ⇒ b (20 , π ) ) (5 , ?) @ v 1 When can we prove b ? � NICTA 2008 c 11 / 1
Persistence in Normative Systems Given a 10 r 1 : ( a 10 ⇒ b (20 , π ) ) (5 , ?) @ v 1 When can we prove b ? 1 Can we prove b 20 from viewpoint 4? � NICTA 2008 c 11 / 1
Persistence in Normative Systems Given a 10 r 1 : ( a 10 ⇒ b (20 , π ) ) (5 , ?) @ v 1 When can we prove b ? 1 Can we prove b 20 from viewpoint 4? No � NICTA 2008 c 11 / 1
Persistence in Normative Systems Given a 10 r 1 : ( a 10 ⇒ b (20 , π ) ) (5 , ?) @ v 1 When can we prove b ? 1 Can we prove b 20 from viewpoint 4? No 2 Can we prove b 20 from viewpoint 5? � NICTA 2008 c 11 / 1
Persistence in Normative Systems Given a 10 r 1 : ( a 10 ⇒ b (20 , π ) ) (5 , ?) @ v 1 When can we prove b ? 1 Can we prove b 20 from viewpoint 4? No 2 Can we prove b 20 from viewpoint 5? Yes � NICTA 2008 c 11 / 1
Persistence in Normative Systems Given a 10 r 1 : ( a 10 ⇒ b (20 , π ) ) (5 , ?) @ v 1 When can we prove b ? 1 Can we prove b 20 from viewpoint 4? No 2 Can we prove b 20 from viewpoint 5? Yes 3 Can we prove b 25 from viewpoint 5? � NICTA 2008 c 11 / 1
Persistence in Normative Systems Given a 10 r 1 : ( a 10 ⇒ b (20 , π ) ) (5 , ?) @ v 1 When can we prove b ? 1 Can we prove b 20 from viewpoint 4? No 2 Can we prove b 20 from viewpoint 5? Yes 3 Can we prove b 25 from viewpoint 5? Yes � NICTA 2008 c 11 / 1
Persistence in Normative Systems Given a 10 r 1 : ( a 10 ⇒ b (20 , π ) ) (5 , ?) @ v 1 When can we prove b ? 1 Can we prove b 20 from viewpoint 4? No 2 Can we prove b 20 from viewpoint 5? Yes 3 Can we prove b 25 from viewpoint 5? Yes 4 Can we prove b 20 from viewpoint 10? � NICTA 2008 c 11 / 1
Persistence in Normative Systems Given a 10 r 1 : ( a 10 ⇒ b (20 , π ) ) (5 , ?) @ v 1 When can we prove b ? 1 Can we prove b 20 from viewpoint 4? No 2 Can we prove b 20 from viewpoint 5? Yes 3 Can we prove b 25 from viewpoint 5? Yes 4 Can we prove b 20 from viewpoint 10? Yes, if ? is “ π ” � NICTA 2008 c 11 / 1
Persistence in Normative Systems Given a 10 r 1 : ( a 10 ⇒ b (20 , π ) ) (5 , ?) @ v 1 When can we prove b ? 1 Can we prove b 20 from viewpoint 4? No 2 Can we prove b 20 from viewpoint 5? Yes 3 Can we prove b 25 from viewpoint 5? Yes 4 Can we prove b 20 from viewpoint 10? Yes, if ? is “ π ” 5 What about if r 1 ceases to be effective at 9? Can we still prove b 20 from viewpoint 10, and prove it from viewpoint 5? � NICTA 2008 c 11 / 1
Persistence in Normative Systems Given a 10 r 1 : ( a 10 ⇒ b (20 , π ) ) (5 , ?) @ v 1 When can we prove b ? 1 Can we prove b 20 from viewpoint 4? No 2 Can we prove b 20 from viewpoint 5? Yes 3 Can we prove b 25 from viewpoint 5? Yes 4 Can we prove b 20 from viewpoint 10? Yes, if ? is “ π ” 5 What about if r 1 ceases to be effective at 9? Can we still prove b 20 from viewpoint 10, and prove it from viewpoint 5? ??? � NICTA 2008 c 11 / 1
Persistence in Normative Systems Given a 10 r 1 : ( a 10 ⇒ b (20 , π ) ) (5 , ?) @ v 1 When can we prove b ? 1 Can we prove b 20 from viewpoint 4? No 2 Can we prove b 20 from viewpoint 5? Yes 3 Can we prove b 25 from viewpoint 5? Yes 4 Can we prove b 20 from viewpoint 10? Yes, if ? is “ π ” 5 What about if r 1 ceases to be effective at 9? Can we still prove b 20 from viewpoint 10, and prove it from viewpoint 5? ??? 6 Can we prove b 20 from viewpoint 5 in a successive version of the normative system ( v 2)? and what about if v 2 no longer contains r 1? � NICTA 2008 c 11 / 1
Persistence in Normative Systems Given a 10 r 1 : ( a 10 ⇒ b (20 , π ) ) (5 , ?) @ v 1 When can we prove b ? 1 Can we prove b 20 from viewpoint 4? No 2 Can we prove b 20 from viewpoint 5? Yes 3 Can we prove b 25 from viewpoint 5? Yes 4 Can we prove b 20 from viewpoint 10? Yes, if ? is “ π ” 5 What about if r 1 ceases to be effective at 9? Can we still prove b 20 from viewpoint 10, and prove it from viewpoint 5? ??? 6 Can we prove b 20 from viewpoint 5 in a successive version of the normative system ( v 2)? and what about if v 2 no longer contains r 1? ????? � NICTA 2008 c 11 / 1
Abrogation + ∂ B + ∂ B r r t 0 t 0 t v t v t a t ′ t ′′ t ′ t ′′ LS ( t ′ ) LS ( t ′′ ) abrog ( r ) t a @ t ′′ r t v @ t ′ t 0 t ′ t ′′ � NICTA 2008 c 12 / 1
Annulment + ∂ B r r t 0 t 0 t v t v t a t ′ t ′′ t ′ t ′′ LS ( t ′ ) LS ( t ′′ ) annul ( r ) t a @ t ′′ r t v @ t ′ t 0 t ′ t ′′ � NICTA 2008 c 13 / 1
annul ( r ) + ∂ B t 0 r t 0 r t ′ tv t ′′ t ′ tv ta t ′′ LS ( t ′ ) LS ( t ′′ ) annul ( r ) ta @ t ′′ t 0 rtv @ t ′ t ′ t ′′ R A ⇒ B 0 / r ❀ ∼ B r ∼ A , B ⇒ C s A , ann ( B ) ⇒ ann ( C ) s rep ann ( C ) ❀ ∼ C s ann t t v t a t ′′ T � NICTA 2008 c 14 / 1
Conclusions Logical model to capture modifications in normative systems. It handles retroactivity, time-forking. Model a larger corpus of norm-modifications Experiment with other temporal models (intervals, duration, periodicity), and causality. Study of the complexity and other logical properties. � NICTA 2008 c 15 / 1
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