Work presented at the IJCAI'09 workshop on Nonmonotonic Reasoning, Action and Change (NRAC'09).

1. On the Revision of Action Laws
An Algorithmic Approach
Ivan Jos´ Varzinczak
e
Knowledge Systems Group
Meraka Institute
CSIR Pretoria, South Africa
NRAC’2009
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 1 / 25

2. Motivation
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 2 / 25

3. Motivation
Knowledge Base
‘A coffee is a hot drink’
‘With a token I can buy coffee’
‘Without a token I cannot buy’
‘After buying I have a hot drink’
...
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 2 / 25

4. Motivation
k, ¬t, c, h
b b
b
b k, t, c, h k, t, ¬c, h
b
b
k, t, ¬c, ¬h
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 2 / 25

5. Motivation
Observations
‘Only coffee on the machine’
‘After buying, I lose my token’
‘Coffee is for free’
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 2 / 25

6. Motivation
Observations
‘Only coffee on the machine’
‘After buying, I lose my token’
‘Coffee is for free’
Need for change the laws about the behavior of actions
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 2 / 25

7. Motivation
k, ¬t, c, h
b b
b
b k, t, c, h k, t, ¬c, h
b
b
k, t, ¬c, ¬h
Need for change the laws about the behavior of actions
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 2 / 25

8. Motivation
¬k, ¬t, c, h k, ¬t, c, h
b
b k, t, c, h
b
b
k, t, ¬c, ¬h
Need for change the laws about the behavior of actions
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 2 / 25

9. Motivation
k, ¬t, c, h
b b
b
b k, t, c, h k, t, ¬c, h
b
b
k, t, ¬c, ¬h
Need for change the laws about the behavior of actions
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 2 / 25

10. Motivation
k, ¬t, c, h
b b
k, t, c, h k, t, ¬c, h
b
k, t, ¬c, ¬h
Need for change the laws about the behavior of actions
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 2 / 25

11. Motivation
k, ¬t, c, h
b b
b
b k, t, c, h k, t, ¬c, h
b
b
k, t, ¬c, ¬h
Need for change the laws about the behavior of actions
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 2 / 25

12. Motivation
b
k, ¬t, c, h
b b
b
b k, t, c, h k, t, ¬c, h
b
b
k, t, ¬c, ¬h
Need for change the laws about the behavior of actions
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 2 / 25

13. Outline
Preliminaries
Action Theories in Multimodal Logic
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 3 / 25

14. Outline
Preliminaries
Action Theories in Multimodal Logic
Revision of Laws
Semantics of Revision
Algorithms
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 3 / 25

15. Outline
Preliminaries
Action Theories in Multimodal Logic
Revision of Laws
Semantics of Revision
Algorithms
Conclusion
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 3 / 25

16. Preliminaries Action Theories in Multimodal Logic
Outline
Preliminaries
Action Theories in Multimodal Logic
Revision of Laws
Semantics of Revision
Algorithms
Conclusion
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 4 / 25

17. Preliminaries Action Theories in Multimodal Logic
Action Theories in Multimodal Logic
Multimodal Logic
◮ Well defined semantics
◮ Expressive
◮ Decidable
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 5 / 25

18. Preliminaries Action Theories in Multimodal Logic
Action Theories in Multimodal Logic
Multimodal Logic
◮ Well defined semantics
◮ Possible worlds models
◮ Expressive
◮ Decidable
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 5 / 25

19. Preliminaries Action Theories in Multimodal Logic
Action Theories in Multimodal Logic
Multimodal Logic
◮ Well defined semantics
◮ Possible worlds models
◮ Expressive
◮ Actions, state constraints, nondeterminism
◮ Decidable
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 5 / 25

20. Preliminaries Action Theories in Multimodal Logic
Action Theories in Multimodal Logic
Multimodal Logic
◮ Well defined semantics
◮ Possible worlds models
◮ Expressive
◮ Actions, state constraints, nondeterminism
◮ Decidable
◮ exptime-complete, though
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 5 / 25

21. Preliminaries Action Theories in Multimodal Logic
Action Theories in Multimodal Logic
Multimodal Logic
◮ Well defined semantics
◮ Possible worlds models
◮ Expressive
◮ Actions, state constraints, nondeterminism
◮ Decidable
◮ exptime-complete, though
But of course
◮ I have nothing against Situation Calculus, Fluent Calculus, . . .
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 5 / 25

22. Preliminaries Action Theories in Multimodal Logic
Action Theories in Multimodal Logic
Possible worlds semantics: Transition Systems M = W , R
◮ W : possible worlds
◮ R : accessibility relation
a1
p1 , ¬p2 p1 , p2 a2
M : a2
a1
¬p1 , p2
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 6 / 25

23. Preliminaries Action Theories in Multimodal Logic
Action Theories in Multimodal Logic
Describing Laws
In RAA: 3 types of laws
◮ Static Laws: ϕ
◮ Ex.: p1 ∨ p2
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 7 / 25

24. Preliminaries Action Theories in Multimodal Logic
Action Theories in Multimodal Logic
Describing Laws
In RAA: 3 types of laws
◮ Static Laws: ϕ
◮ Ex.: p1 ∨ p2
◮ Executability Laws: ϕ → a ⊤
◮ Ex.: p2 → a2 ⊤
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 7 / 25

25. Preliminaries Action Theories in Multimodal Logic
Action Theories in Multimodal Logic
Describing Laws
In RAA: 3 types of laws
◮ Static Laws: ϕ
◮ Ex.: p1 ∨ p2
◮ Executability Laws: ϕ → a ⊤
◮ Ex.: p2 → a2 ⊤
◮ Effect Laws: ϕ → [a]ψ
◮ Ex.: p1 → [a1 ]p2
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 7 / 25

26. Preliminaries Action Theories in Multimodal Logic
Action Theories in Multimodal Logic
Describing Laws
In RAA: 3 types of laws
◮ Static Laws: ϕ
◮ Ex.: p1 ∨ p2
◮ Executability Laws: ϕ → a ⊤
◮ Ex.: p2 → a2 ⊤
◮ Effect Laws: ϕ → [a]ψ
◮ Ex.: p1 → [a1 ]p2
◮ Frame axioms: ℓ → [a]ℓ
◮ Inexecutability laws: ϕ → [a]⊥
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 7 / 25

27. Preliminaries Action Theories in Multimodal Logic
Action Theories in Multimodal Logic
Formulas that hold in M
a1
p1 , ¬p2 p1 , p2 a2
◮ p1 ∨ p2
M : a2
a1 ◮ p1 → [a1 ]p2
◮ p2 → a 2 ⊤
¬p1 , p2 ◮ ¬p1 → a1 ⊤
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 8 / 25

28. Preliminaries Action Theories in Multimodal Logic
Action Theories in Multimodal Logic
Formulas that hold in M
a1
p1 , ¬p2 p1 , p2 a2
◮ p1 ∨ p2
M : a2
a1 ◮ p1 → [a1 ]p2
◮ p2 → a 2 ⊤
¬p1 , p2 ◮ ¬p1 → a1 ⊤
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 8 / 25

29. Preliminaries Action Theories in Multimodal Logic
Action Theories in Multimodal Logic
Formulas that hold in M
a1
p1 , ¬p2 p1 , p2 a2
◮ p1 ∨ p2
M : a2
a1 ◮ p1 → [a1 ]p2
◮ p2 → a 2 ⊤
¬p1 , p2 ◮ ¬p1 → a1 ⊤
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 8 / 25

30. Preliminaries Action Theories in Multimodal Logic
Action Theories in Multimodal Logic
Formulas that hold in M
a1
p1 , ¬p2 p1 , p2 a2
◮ p1 ∨ p2
M : a2
a1 ◮ p1 → [a1 ]p2
◮ p2 → a 2 ⊤
¬p1 , p2
◮ ¬p1 → a1 ⊤
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 8 / 25

31. Preliminaries Action Theories in Multimodal Logic
Action Theories in Multimodal Logic
Formulas that hold in M
a1
p1 , ¬p2 p1 , p2 a2
◮ p1 ∨ p2
M : a2
a1 ◮ p1 → [a1 ]p2
◮ p2 → a 2 ⊤
¬p1 , p2
◮ ¬p1 → a1 ⊤ ±
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 8 / 25

32. Preliminaries Action Theories in Multimodal Logic
Action Theories in Multimodal Logic
In our example
◮ Static Law: ◮ coffee → hot
◮ Executability Law: ◮ token → buy ⊤
◮ Effect Law: ◮ ¬coffee → [buy]coffee
◮ Inexecutability Law: ◮ ¬token → [buy]⊥
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 9 / 25

33. Preliminaries Action Theories in Multimodal Logic
Action Theories in Multimodal Logic
In our example
◮ Static Law: ◮ coffee → hot
◮ Executability Law: ◮ token → buy ⊤
◮ Effect Law: ◮ ¬coffee → [buy]coffee
◮ Inexecutability Law: ◮ ¬token → [buy]⊥
Action Theory T = S ∪ E ∪ X
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 9 / 25

34. Preliminaries Action Theories in Multimodal Logic
Action Theories in Multimodal Logic
In our example
◮ Static Law: ◮ coffee → hot
◮ Executability Law: ◮ token → buy ⊤
◮ Effect Law: ◮ ¬coffee → [buy]coffee
◮ Inexecutability Law: ◮ ¬token → [buy]⊥
Action Theory T = S ∪ E ∪ X
What about the Frame, Ramification and Qualification Problems?
◮ No particular solution to the frame problem
◮ Assume we have all relevant frame axioms
◮ Qualification problem: motivation for revision
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 9 / 25

35. Preliminaries Action Theories in Multimodal Logic
Action Theories in Multimodal Logic
In our example
 
coffee → hot, token → buy ⊤,
 
T =S ∪E ∪X = ¬coffee → [buy]coffee, ¬token → [buy]⊥,
coffee → [buy]coffee, hot → [buy]hot
 
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 10 / 25

36. Preliminaries Action Theories in Multimodal Logic
Action Theories in Multimodal Logic
In our example
 
coffee → hot, token → buy ⊤,
 
T =S ∪E ∪X = ¬coffee → [buy]coffee, ¬token → [buy]⊥,
coffee → [buy]coffee, hot → [buy]hot
 
k, ¬t, c, h
b b
b
b k, t, c, h k, t, ¬c, h
b
b
k, t, ¬c, ¬h
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 10 / 25

37. Preliminaries Action Theories in Multimodal Logic
Action Theories in Multimodal Logic
Supra-Models
Definition
M = W , R is a big frame of T iff
◮ W = val(S )
◮ R = a∈Act R a , where
M M
R a = {(w , w ′ ) : ∀.ϕ → [a]ψ ∈ Ea , if |= ϕ then |= ′ ψ}
w w
Definition
M
M is a supra-model of T iff |= T and M is a big frame of T.
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 11 / 25

38. Preliminaries Action Theories in Multimodal Logic
Action Theories in Multimodal Logic
Supra-Models
 
coffee → hot, token → buy ⊤,
 
T =S ∪E ∪X = ¬coffee → [buy]coffee, ¬token → [buy]⊥,
coffee → [buy]coffee, hot → [buy]hot
 
¬k, ¬t, c, h k, ¬t, c, h
b b
b
b k, t, c, h k, t, ¬c, h
b
b
k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 12 / 25

39. Revision of Laws Semantics of Revision
Outline
Preliminaries
Action Theories in Multimodal Logic
Revision of Laws
Semantics of Revision
Algorithms
Conclusion
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 13 / 25

40. Revision of Laws Semantics of Revision
Intuitions About Model Revision
Revision by a law
¬k, ¬t, c, h k, ¬t, c, h
b b
b
b k, t, c, h k, t, ¬c, h
b
b
k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h
Make the law true in the model
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 14 / 25

41. Revision of Laws Semantics of Revision
Intuitions About Model Revision
Revision by hot → coffee
¬k, ¬t, c, h k, ¬t, c, h
b b
b
b k, t, c, h k, t, ¬c, h
b
b
k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h
Make hot ∧ ¬coffee unsatisfiable
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 14 / 25

42. Revision of Laws Semantics of Revision
Intuitions About Model Revision
Revision by hot → coffee
¬k, ¬t, c, h k, ¬t, c, h
b
b k, t, c, h
b
b
k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h
Make hot ∧ ¬coffee unsatisfiable
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 14 / 25

43. Revision of Laws Semantics of Revision
Intuitions About Model Revision
Revision by hot → coffee
¬k, ¬t, c, h k, ¬t, c, h
b
b k, t, c, h
b
b
k, ¬t, ¬c, ¬h k, t, ¬c, ¬h
Make hot ∧ ¬coffee unsatisfiable
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 14 / 25

44. Revision of Laws Semantics of Revision
Intuitions About Model Revision
Revision by a law
¬k, ¬t, c, h k, ¬t, c, h
b b
b
b k, t, c, h k, t, ¬c, h
b
b
k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h
Make the law true in the model
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 14 / 25

45. Revision of Laws Semantics of Revision
Intuitions About Model Revision
Revision by token → [buy]¬token
¬k, ¬t, c, h k, ¬t, c, h
b b
b
b k, t, c, h k, t, ¬c, h
b
b
k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h
Make token ∧ buy token unsatisfiable
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 14 / 25

46. Revision of Laws Semantics of Revision
Intuitions About Model Revision
Revision by token → [buy]¬token
¬k, ¬t, c, h k, ¬t, c, h
b b
b
b k, t, c, h k, t, ¬c, h
b
k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h
Make token ∧ buy token unsatisfiable
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 14 / 25

47. Revision of Laws Semantics of Revision
Intuitions About Model Revision
Revision by token → [buy]¬token
¬k, ¬t, c, h k, ¬t, c, h
b b
k, t, c, h k, t, ¬c, h
b
k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h
Make token ∧ buy token unsatisfiable
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 14 / 25

48. Revision of Laws Semantics of Revision
Intuitions About Model Revision
Revision by a law
¬k, ¬t, c, h k, ¬t, c, h
b b
b
b k, t, c, h k, t, ¬c, h
b
b
k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h
Make the law true in the model
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 14 / 25

49. Revision of Laws Semantics of Revision
Intuitions About Model Revision
Revision by ¬token → buy ⊤
¬k, ¬t, c, h k, ¬t, c, h
b b
b
b k, t, c, h k, t, ¬c, h
b
b
k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h
Make ¬token ∧ [buy]⊥ unsatisfiable
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 14 / 25

50. Revision of Laws Semantics of Revision
Intuitions About Model Revision
Revision by ¬token → buy ⊤
¬k, ¬t, c, h k, ¬t, c, h
b b b
b
b k, t, c, h k, t, ¬c, h
b
b
k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h
Make ¬token ∧ [buy]⊥ unsatisfiable
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 14 / 25

51. Revision of Laws Semantics of Revision
Intuitions About Model Revision
Revision by ¬token → buy ⊤ b
b ¬k, ¬t, c, h k, ¬t, c, h
b b b b
b
b k, t, c, h k, t, ¬c, h
b
b
k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h
Make ¬token ∧ [buy]⊥ unsatisfiable
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 14 / 25

52. Revision of Laws Semantics of Revision
Minimal Change
Choosing models
◮ Distance between models
◮ Prefer models closest to the original one
◮ Hamming/Dalal distance, etc
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 15 / 25

53. Revision of Laws Semantics of Revision
Minimal Change
Choosing models
◮ Distance between models
◮ Prefer models closest to the original one
◮ Hamming/Dalal distance, etc
◮ Distance dependent on the type of law to make valid
◮ Static law: look at the set of possible states (worlds)
◮ Action laws: look at the set of arrows
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 15 / 25

54. Revision of Laws Semantics of Revision
Minimal Change
Choosing models
◮ Distance between models
◮ Prefer models closest to the original one
◮ Hamming/Dalal distance, etc
◮ Distance dependent on the type of law to make valid
◮ Static law: look at the set of possible states (worlds)
◮ Action laws: look at the set of arrows
Definition
Let M = W , R . M ′ = W ′ , R ′ is as close to M as M ′′ = W ′′ , R ′′
iff
◮ either W −W ′ ⊆ W −W ′′
˙ ˙
◮ or W −W = W −W ′′ and R −R ′ ⊆ R −R ′′
˙ ′ ˙ ˙ ˙
Notation: M ′ M M ′′
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 15 / 25

55. Revision of Laws Semantics of Revision
Minimal Change
Choosing models: revising by ϕ
Definition
Let M = W , R . M ′ = W ′ , R ′ ∈ Mϕ iff:
⋆
◮ W ′ = (W val(¬ϕ)) ∪ val(ϕ)
◮ R′ ⊆ R
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 16 / 25

56. Revision of Laws Semantics of Revision
Minimal Change
Choosing models: revising by ϕ
Definition
Let M = W , R . M ′ = W ′ , R ′ ∈ Mϕ iff:
⋆
◮ W ′ = (W val(¬ϕ)) ∪ val(ϕ)
◮ R′ ⊆ R
Definition
revise(M , ϕ) = ⋆
min{Mϕ , M}
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 16 / 25

57. Revision of Laws Semantics of Revision
Minimal Change
Choosing models: revising by hot → coffee
¬k, ¬t, c, h k, ¬t, c, h ¬k, ¬t, c, h k, ¬t, c, h ¬k, t, c, h
b b
b k, t, c, h b k, t, c, h
M
b b
b b
k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, ¬h k, t, ¬c, ¬h
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 17 / 25

58. Revision of Laws Semantics of Revision
Minimal Change
Choosing models: revising by ϕ → [a]ψ
Definition
Let M = W , R . M ′ = W ′ , R ′ ∈ Mϕ→[a]ψ iff:
⋆
◮ W′ = W
◮ R′ ⊆ R
M
◮ If (w , w ′ ) ∈ R R ′ , then |= ϕ
w
M′
◮ |= ϕ → [a]ψ
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 18 / 25

59. Revision of Laws Semantics of Revision
Minimal Change
Choosing models: revising by ϕ → [a]ψ
Definition
Let M = W , R . M ′ = W ′ , R ′ ∈ Mϕ→[a]ψ iff:
⋆
◮ W′ = W
◮ R′ ⊆ R
M
◮ If (w , w ′ ) ∈ R R ′ , then |= ϕ
w
M′
◮ |= ϕ → [a]ψ
Definition
revise(M , ϕ → [a]ψ) = ⋆
min{Mϕ→[a]ψ , M}
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 18 / 25

60. Revision of Laws Semantics of Revision
Minimal Change
Choosing models: revising by token → [buy]¬token
¬k, ¬t, c, h k, ¬t, c, h ¬k, ¬t, c, h k, ¬t, c, h
b b
k, t, c, h k, t, ¬c, h k, t, c, h k, t, ¬c, h
M
b
k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 19 / 25

61. Revision of Laws Semantics of Revision
Minimal Change
Choosing models: revising by ϕ → a ⊤
Definition
Let M = W , R . M ′ = W ′ , R ′ ∈ Mϕ→
⋆
a ⊤ iff:
◮ W′ = W
◮ R ⊆ R′
◮ If (w , w ′ ) ∈ R ′ R , then w ′ ∈ RelTarget(w , ¬(ϕ → [a]⊥))
M′
◮ |= ϕ → a ⊤
RelTarget(.): induces effect laws from the models
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 20 / 25

62. Revision of Laws Semantics of Revision
Minimal Change
Choosing models: revising by ϕ → a ⊤
Definition
Let M = W , R . M ′ = W ′ , R ′ ∈ Mϕ→
⋆
a ⊤ iff:
◮ W′ = W
◮ R ⊆ R′
◮ If (w , w ′ ) ∈ R ′ R , then w ′ ∈ RelTarget(w , ¬(ϕ → [a]⊥))
M′
◮ |= ϕ → a ⊤
RelTarget(.): induces effect laws from the models
Definition
revise(M , ϕ → a ⊤) = ⋆
min{Mϕ→ a ⊤, M}
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 20 / 25

63. Revision of Laws Semantics of Revision
Minimal Change
Choosing models: revising by ¬token → buy ⊤
◮ coffee: effect of buy, hot: consequence of coffee
◮ token, ¬kitchen: not consequences of coffee
b b
¬k, ¬t, c, h k, ¬t, c, h
b b b b
b
b k, t, c, h k, t, ¬c, h
b
b
k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 21 / 25

64. Revision of Laws Algorithms
Outline
Preliminaries
Action Theories in Multimodal Logic
Revision of Laws
Semantics of Revision
Algorithms
Conclusion
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 22 / 25

65. Revision of Laws Algorithms
Quick look: Revision Algorithms
◮ We have defined algorithms that revise T by Φ, giving T ′
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 23 / 25

66. Revision of Laws Algorithms
Quick look: Revision Algorithms
◮ We have defined algorithms that revise T by Φ, giving T ′
Theorem
If T has supra-models, the algorithms are correct w.r.t. our semantics
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 23 / 25

67. Revision of Laws Algorithms
Quick look: Revision Algorithms
◮ We have defined algorithms that revise T by Φ, giving T ′
Theorem
If T has supra-models, the algorithms are correct w.r.t. our semantics
Theorem (Herzig & Varzinczak, AI Journal 2007)
We can always ensure T has supra-models
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 23 / 25

68. Revision of Laws Algorithms
Quick look: Revision Algorithms
◮ We have defined algorithms that revise T by Φ, giving T ′
Theorem
If T has supra-models, the algorithms are correct w.r.t. our semantics
Theorem (Herzig & Varzinczak, AI Journal 2007)
We can always ensure T has supra-models
Theorem
Size of T ′ is linear in that of T
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 23 / 25

69. Conclusion
Conclusion
Contribution
◮ Semantics for action theory revision
◮ Distance between models
◮ Minimal change
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 24 / 25

70. Conclusion
Conclusion
Contribution
◮ Semantics for action theory revision
◮ Distance between models
◮ Minimal change
◮ Extension of previous work on action theory contraction
◮ Invalidating formulas in a model (KR’2008)
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 24 / 25

71. Conclusion
Conclusion
Contribution
◮ Semantics for action theory revision
◮ Distance between models
◮ Minimal change
◮ Extension of previous work on action theory contraction
◮ Invalidating formulas in a model (KR’2008)
◮ Syntactic operators (algorithms)
◮ Correct w.r.t. the semantics
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 24 / 25

72. Conclusion
Conclusion
Ongoing research and future work
◮ Postulates for action theory revision
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 25 / 25

73. Conclusion
Conclusion
Ongoing research and future work
◮ Postulates for action theory revision
◮ More ‘orthodox’ approach to nonclassical revision
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 25 / 25

74. Conclusion
Conclusion
Ongoing research and future work
◮ Postulates for action theory revision
◮ More ‘orthodox’ approach to nonclassical revision
◮ Revision of general formulas
◮ not only ϕ, ϕ → a ⊤, ϕ → [a]ψ
◮ more expressive logics: PDL
◮ less expressive logics: Causal Theories of Action
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 25 / 25

75. Conclusion
Conclusion
Ongoing research and future work
◮ Postulates for action theory revision
◮ More ‘orthodox’ approach to nonclassical revision
◮ Revision of general formulas
◮ not only ϕ, ϕ → a ⊤, ϕ → [a]ψ
◮ more expressive logics: PDL
◮ less expressive logics: Causal Theories of Action
◮ Applications in Description Logics
◮ ontology evolution/debugging
Ivan Jos´ Varzinczak (KSG - Meraka)
e On the Revision of Action Laws NRAC’2009 25 / 25