This document discusses revising the laws that govern the behavior of actions in action theories. It presents an algorithmic approach to revising action laws based on observations that contradict the existing knowledge base. The document is presented at the NRAC'2009 conference and is divided into sections on preliminaries regarding action theories in multimodal logic, the semantics and algorithms for revising action laws, and a conclusion.

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