Changing Legal Systems: Abrogation and Annulment Part II: - - PowerPoint PPT Presentation

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Changing Legal Systems: Abrogation and Annulment Part II: - - PowerPoint PPT Presentation

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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

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SLIDE 1

Changing Legal Systems: Abrogation and Annulment

Part II: Temporalised Defeasible Logic Guido Governatori and Antonino Rotolo

NICTA and CIRSFID

15 July 2008

c NICTA 2008 1 / 1

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SLIDE 2

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.

c NICTA 2008 2 / 1

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SLIDE 3

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.

c NICTA 2008 2 / 1

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SLIDE 4

Tax Dilemma

The new norm annulls the old one: refund already paid taxes

c NICTA 2008 3 / 1

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SLIDE 5

Tax Dilemma

The new norm annulls the old one: refund already paid taxes The new norm abrogates the old one: no refunds

c NICTA 2008 3 / 1

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SLIDE 6

Tax Dilemma

The new norm annulls the old one: refund already paid taxes The new norm abrogates the old one: no refunds Italian solution:

c NICTA 2008 3 / 1

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SLIDE 7

Tax Dilemma

The new norm annulls the old one: refund already paid taxes The new norm abrogates the old one: no refunds Italian solution:

c NICTA 2008 3 / 1

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SLIDE 8

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!

c NICTA 2008 3 / 1

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SLIDE 9

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:

c NICTA 2008 3 / 1

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SLIDE 10

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!

c NICTA 2008 3 / 1

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SLIDE 11

Normative Systems

LS(t1),LS(t2),...,LS(tj),... t0 t′ LS(t′) t′′ LS(t′′)

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SLIDE 12

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

1

+∆q, which means that q is strictly provable in D;

2

−∆q, which means that q is not strictly provable in D;

3

+∂q, which means that q is defeasibly provable in D;

4

−∂q, which means that q is not defeasibly provable in D.

c NICTA 2008 5 / 1

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SLIDE 13

Rules

A rule is identified by a unique label and gives conditions to derive a (legal) provision at a particular time.

c NICTA 2008 6 / 1

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SLIDE 14

Rules

A rule is identified by a unique label and gives conditions to derive a (legal) provision at a particular time.

r1 : (IncomeThreshold31Jan ⇒ HighMarginalRate(28Feb,τ))(1Jan,π)@(31Dec,π) r2 : (HighMarginalRate28Feb ⇒ Pay50%(1March,π))(1Jan,π)@(31Dec,π)

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SLIDE 15

Meta-Rules

A meta-rule gives conditions to establish that a rule is effective (and when it is), with respect to a particular time.

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SLIDE 16

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 : (JoinEU21March ⇒ r1 : (IncomeThreshold31Jan ⇒ HighMarginalRate(28Feb,τ))(1Jan,π))@(1Jan,π)

c NICTA 2008 7 / 1

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SLIDE 17

Temporal Model

t0

t0 t0 t′ t′′ t′ t′′

t′ LS(t′) t′′ LS(t′′)

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SLIDE 18

Rule Persistence

t0

t0 t0 t′ t′′ t′ t′′

t′ LS(t′) t′′ LS(t′′) r : t′′′@t′ r : t′′′@t′′

t′′′

r

t′′′

r

c NICTA 2008 9 / 1

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SLIDE 19

Conclusion Persistence

t0

t0 t0 t′ t′′ t′ t′′

t′ LS(t′) t′′ LS(t′′)

t

′′′

t′′′

+∂a +∂a

c NICTA 2008 10 / 1

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SLIDE 20

Persistence in Normative Systems

Given a10 r1 : (a10 ⇒ b(20,π))(5,?)@v1 When can we prove b?

c NICTA 2008 11 / 1

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SLIDE 21

Persistence in Normative Systems

Given a10 r1 : (a10 ⇒ b(20,π))(5,?)@v1 When can we prove b?

1 Can we prove b20 from viewpoint 4? c NICTA 2008 11 / 1

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SLIDE 22

Persistence in Normative Systems

Given a10 r1 : (a10 ⇒ b(20,π))(5,?)@v1 When can we prove b?

1 Can we prove b20 from viewpoint 4? No c NICTA 2008 11 / 1

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SLIDE 23

Persistence in Normative Systems

Given a10 r1 : (a10 ⇒ b(20,π))(5,?)@v1 When can we prove b?

1 Can we prove b20 from viewpoint 4? No 2 Can we prove b20 from viewpoint 5? c NICTA 2008 11 / 1

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SLIDE 24

Persistence in Normative Systems

Given a10 r1 : (a10 ⇒ b(20,π))(5,?)@v1 When can we prove b?

1 Can we prove b20 from viewpoint 4? No 2 Can we prove b20 from viewpoint 5? Yes c NICTA 2008 11 / 1

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SLIDE 25

Persistence in Normative Systems

Given a10 r1 : (a10 ⇒ b(20,π))(5,?)@v1 When can we prove b?

1 Can we prove b20 from viewpoint 4? No 2 Can we prove b20 from viewpoint 5? Yes 3 Can we prove b25 from viewpoint 5? c NICTA 2008 11 / 1

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SLIDE 26

Persistence in Normative Systems

Given a10 r1 : (a10 ⇒ b(20,π))(5,?)@v1 When can we prove b?

1 Can we prove b20 from viewpoint 4? No 2 Can we prove b20 from viewpoint 5? Yes 3 Can we prove b25 from viewpoint 5? Yes c NICTA 2008 11 / 1

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SLIDE 27

Persistence in Normative Systems

Given a10 r1 : (a10 ⇒ b(20,π))(5,?)@v1 When can we prove b?

1 Can we prove b20 from viewpoint 4? No 2 Can we prove b20 from viewpoint 5? Yes 3 Can we prove b25 from viewpoint 5? Yes 4 Can we prove b20 from viewpoint 10? c NICTA 2008 11 / 1

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SLIDE 28

Persistence in Normative Systems

Given a10 r1 : (a10 ⇒ b(20,π))(5,?)@v1 When can we prove b?

1 Can we prove b20 from viewpoint 4? No 2 Can we prove b20 from viewpoint 5? Yes 3 Can we prove b25 from viewpoint 5? Yes 4 Can we prove b20 from viewpoint 10? Yes, if ? is “π” c NICTA 2008 11 / 1

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SLIDE 29

Persistence in Normative Systems

Given a10 r1 : (a10 ⇒ b(20,π))(5,?)@v1 When can we prove b?

1 Can we prove b20 from viewpoint 4? No 2 Can we prove b20 from viewpoint 5? Yes 3 Can we prove b25 from viewpoint 5? Yes 4 Can we prove b20 from viewpoint 10? Yes, if ? is “π” 5 What about if r1 ceases to be effective at 9? Can we still

prove b20 from viewpoint 10, and prove it from viewpoint 5?

c NICTA 2008 11 / 1

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SLIDE 30

Persistence in Normative Systems

Given a10 r1 : (a10 ⇒ b(20,π))(5,?)@v1 When can we prove b?

1 Can we prove b20 from viewpoint 4? No 2 Can we prove b20 from viewpoint 5? Yes 3 Can we prove b25 from viewpoint 5? Yes 4 Can we prove b20 from viewpoint 10? Yes, if ? is “π” 5 What about if r1 ceases to be effective at 9? Can we still

prove b20 from viewpoint 10, and prove it from viewpoint 5? ???

c NICTA 2008 11 / 1

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SLIDE 31

Persistence in Normative Systems

Given a10 r1 : (a10 ⇒ b(20,π))(5,?)@v1 When can we prove b?

1 Can we prove b20 from viewpoint 4? No 2 Can we prove b20 from viewpoint 5? Yes 3 Can we prove b25 from viewpoint 5? Yes 4 Can we prove b20 from viewpoint 10? Yes, if ? is “π” 5 What about if r1 ceases to be effective at 9? Can we still

prove b20 from viewpoint 10, and prove it from viewpoint 5? ???

6 Can we prove b20 from viewpoint 5 in a successive version of

the normative system (v2)? and what about if v2 no longer contains r1?

c NICTA 2008 11 / 1

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SLIDE 32

Persistence in Normative Systems

Given a10 r1 : (a10 ⇒ b(20,π))(5,?)@v1 When can we prove b?

1 Can we prove b20 from viewpoint 4? No 2 Can we prove b20 from viewpoint 5? Yes 3 Can we prove b25 from viewpoint 5? Yes 4 Can we prove b20 from viewpoint 10? Yes, if ? is “π” 5 What about if r1 ceases to be effective at 9? Can we still

prove b20 from viewpoint 10, and prove it from viewpoint 5? ???

6 Can we prove b20 from viewpoint 5 in a successive version of

the normative system (v2)? and what about if v2 no longer contains r1? ?????

c NICTA 2008 11 / 1

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SLIDE 33

Abrogation

t0

t0 t0 t′ t′′ t′ t′′

t′ LS(t′) t′′ LS(t′′) rtv @t′ abrog(r)ta@t′′

tv tv ta

r r +∂B +∂B

c NICTA 2008 12 / 1

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SLIDE 34

Annulment

t0

t0 t0 t′ t′′ t′ t′′

t′ LS(t′) t′′ LS(t′′) rtv @t′ annul(r)ta@t′′

tv tv ta

r r +∂B

c NICTA 2008 13 / 1

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SLIDE 35

annul(r)

t0 t0 t0 t ′ t ′′ t ′ t ′′ t ′ LS(t ′) t ′′ LS(t ′′) rtv @t ′

annul(r)ta @t ′′

tv tv ta r r +∂B

R T t tv ta t′′ r r∼ s srep sann A ⇒ B / ❀ ∼B A,B ⇒ C A,ann(B) ⇒ ann(C) ann(C) ❀ ∼C

c NICTA 2008 14 / 1

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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.

c NICTA 2008 15 / 1