Talk given at the Université de Toulouse 1 Sciences Sociales, Toulouse, France.

1. On Action Theory Change:
Semantics for Contraction and its Properties
Ivan Jos´ Varzinczak
e
Knowledge Representation and Reasoning
Meraka Institute, CSIR
Pretoria, South Africa
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 1 / 29

2. Motivation
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 2 / 29

3. Motivation
Knowledge Base
A coffee is a hot drink
With a token I can buy coffee
After buying I have a hot drink
...
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 2 / 29

4. Motivation
¬t, c, h
b b
t, c, h b t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 2 / 29

5. Motivation
Observations
I have got a cold coffee
I cannot buy
I bought and I got no hot drink
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 2 / 29

6. Motivation
Observations
I have got a cold coffee
I cannot buy
I bought and I got no hot drink
Need for changing the laws about the behavior of actions
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 2 / 29

7. Motivation
¬t, c, h
b b
t, c, h b t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Need for changing the laws about the behavior of actions
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 2 / 29

8. Motivation
¬t, c, h c, ¬h
b b
t, c, h b t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Need for changing the laws about the behavior of actions
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 2 / 29

9. Motivation
¬t, c, h
b b
t, c, h b t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Need for changing the laws about the behavior of actions
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 2 / 29

10. Motivation
¬t, c, h
b
t, c, h b t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Need for changing the laws about the behavior of actions
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 2 / 29

11. Motivation
¬t, c, h
b b
t, c, h b t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Need for changing the laws about the behavior of actions
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 2 / 29

12. Motivation
¬t, c, h
b b
t, c, h b t, ¬c, h
b
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Need for changing the laws about the behavior of actions
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 2 / 29

13. Outline
1 Preliminaries
Action Theories
2 Contracting Action Laws
Semantics
Algorithms
Properties
3 Conclusion
Contributions
Future Work
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 3 / 29

14. Outline
1 Preliminaries
Action Theories
2 Contracting Action Laws
Semantics
Algorithms
Properties
3 Conclusion
Contributions
Future Work
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 3 / 29

15. Outline
1 Preliminaries
Action Theories
2 Contracting Action Laws
Semantics
Algorithms
Properties
3 Conclusion
Contributions
Future Work
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 3 / 29

16. Outline
1 Preliminaries
Action Theories
2 Contracting Action Laws
Semantics
Algorithms
Properties
3 Conclusion
Contributions
Future Work
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 4 / 29

17. Action Theories
Knowledge bases about the dynamics of the world
Actions
Effects
Preconditions
Usually 3 types of laws
Static laws : ‘a coffee is a hot drink’
Effect laws : ‘after buying I get a coffee’
Executability laws : ‘if I have a token, I can buy’
Reasoning tasks
Projection : ‘do I have a hot drink after I buy?’
Explanation : ‘I hold a coffee. I bought. Did I have a token?’
Planning : ‘how to get a hot drink?’
...
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 5 / 29

18. Action Theories
Knowledge bases about the dynamics of the world
Actions
Effects
Preconditions
Usually 3 types of laws
Static laws : ‘a coffee is a hot drink’
Effect laws : ‘after buying I get a coffee’
Executability laws : ‘if I have a token, I can buy’
Reasoning tasks
Projection : ‘do I have a hot drink after I buy?’
Explanation : ‘I hold a coffee. I bought. Did I have a token?’
Planning : ‘how to get a hot drink?’
...
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 5 / 29

19. Action Theories
Knowledge bases about the dynamics of the world
Actions
Effects
Preconditions
Usually 3 types of laws
Static laws : ‘a coffee is a hot drink’
Effect laws : ‘after buying I get a coffee’
Executability laws : ‘if I have a token, I can buy’
Reasoning tasks
Projection : ‘do I have a hot drink after I buy?’
Explanation : ‘I hold a coffee. I bought. Did I have a token?’
Planning : ‘how to get a hot drink?’
...
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 5 / 29

20. Action Theories in Multimodal Logic
Multimodal Logic
Propositional logic + modal operators
[a] : every a-arrow
a : some a-arrow
Well defined semantics
Possible worlds models
Expressive
Actions, state constraints, nondeterminism
Decidable
EXPTIME-complete, though
More elegant than FOL
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 6 / 29

21. Action Theories in Multimodal Logic
Multimodal Logic
Propositional logic + modal operators
[a] : every a-arrow
a : some a-arrow
Well defined semantics
Possible worlds models
Expressive
Actions, state constraints, nondeterminism
Decidable
EXPTIME-complete, though
More elegant than FOL
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 6 / 29

22. Action Theories in Multimodal Logic
Multimodal Logic
Propositional logic + modal operators
[a] : every a-arrow
a : some a-arrow
Well defined semantics
Possible worlds models
Expressive
Actions, state constraints, nondeterminism
Decidable
EXPTIME-complete, though
More elegant than FOL
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 6 / 29

23. Action Theories in Multimodal Logic
Multimodal Logic
Propositional logic + modal operators
[a] : every a-arrow
a : some a-arrow
Well defined semantics
Possible worlds models
Expressive
Actions, state constraints, nondeterminism
Decidable
EXPTIME-complete, though
More elegant than FOL
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 6 / 29

24. Action Theories in Multimodal Logic
Multimodal Logic
Propositional logic + modal operators
[a] : every a-arrow
a : some a-arrow
Well defined semantics
Possible worlds models
Expressive
Actions, state constraints, nondeterminism
Decidable
EXPTIME-complete, though
More elegant than FOL
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 6 / 29

25. Action Theories in Multimodal Logic
Multimodal Logic
Propositional logic + modal operators
[a] : every a-arrow
a : some a-arrow
Well defined semantics
Possible worlds models
Expressive
Actions, state constraints, nondeterminism
Decidable
EXPTIME-complete, though
More elegant than FOL
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 6 / 29

26. Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = W , R
W : possible worlds
R : accessibility relations
a1
Satisfaction in a model
p, q
a1
p, ¬q q→p
p → [a1 ]¬q
a2
a1
p → a1
M : a1
p → a2
¬p, ¬q
(p ∧ ¬q) → [a2 ]⊥
a2
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 7 / 29

27. Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = W , R
W : possible worlds
R : accessibility relations
a1
Satisfaction in a model
p, q
a1
p, ¬q q→p
p → [a1 ]¬q
a2
a1
p → a1
M : a1
p → a2
¬p, ¬q
(p ∧ ¬q) → [a2 ]⊥
a2
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 7 / 29

28. Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = W , R
W : possible worlds
R : accessibility relations
a1
Satisfaction in a model
p, q
a1
p, ¬q q→p
p → [a1 ]¬q
a2
a1
p → a1
M : a1
p → a2
¬p, ¬q
(p ∧ ¬q) → [a2 ]⊥
a2
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 7 / 29

29. Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = W , R
W : possible worlds
R : accessibility relations
a1
Satisfaction in a model
p, q
a1
p, ¬q q→p "
p → [a1 ]¬q
a2
M : a1 a1 p → a1
p → a2
¬p, ¬q
(p ∧ ¬q) → [a2 ]⊥
a2
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 7 / 29

30. Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = W , R
W : possible worlds
R : accessibility relations
a1
Satisfaction in a model
p, q
a1
p, ¬q q→p "
a2
p → [a1 ]¬q "
M : a1 a1 p → a1
p → a2
¬p, ¬q
(p ∧ ¬q) → [a2 ]⊥
a2
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 7 / 29

31. Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = W , R
W : possible worlds
R : accessibility relations
a1
Satisfaction in a model
p, q
a1
p, ¬q q→p "
a2
p → [a1 ]¬q "
M : a1 a1 p → a1 "
p → a2
¬p, ¬q
(p ∧ ¬q) → [a2 ]⊥
a2
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 7 / 29

32. Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = W , R
W : possible worlds
R : accessibility relations
a1
Satisfaction in a model
p, q
a1
p, ¬q q→p "
a2
p → [a1 ]¬q "
M : a1 a1 p → a1 "
¬p, ¬q
p → a2 %
(p ∧ ¬q) → [a2 ]⊥
a2
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 7 / 29

33. Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = W , R
W : possible worlds
R : accessibility relations
a1
Satisfaction in a model
p, q
a1
p, ¬q q→p "
a2
p → [a1 ]¬q "
M : a1 a1 p → a1 "
¬p, ¬q
p → a2 %
(p ∧ ¬q) → [a2 ]⊥ "
a2
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 7 / 29

34. Action Theories in Multimodal Logic
Example
Static Law: coffee → hot
Executability Law: token → buy
Effect Law: ¬coffee → [buy]coffee, ¬token → [buy]⊥, hot → [buy]hot
Definition
Action Theory T = S ∪ E ∪ X
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 8 / 29

35. Action Theories in Multimodal Logic
Example
Static Law: coffee → hot
Executability Law: token → buy
Effect Law: ¬coffee → [buy]coffee, ¬token → [buy]⊥, hot → [buy]hot
Definition
Action Theory T = S ∪ E ∪ X
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 8 / 29

36. Action Theories in Multimodal Logic
Example
 
coffee → hot, token → buy ,

 

¬coffee → [buy]coffee, token → [buy]¬token,
 
T =S ∪E ∪X =

 ¬token → [buy]⊥, 

coffee → [buy]coffee, hot → [buy]hot
 
¬t, c, h
b b
M : t, c, h b t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 9 / 29

37. Action Theories in Multimodal Logic
Example
 
coffee → hot, token → buy ,

 

¬coffee → [buy]coffee, token → [buy]¬token,
 
T =S ∪E ∪X =

 ¬token → [buy]⊥, 

coffee → [buy]coffee, hot → [buy]hot
 
¬t, c, h
b b
M : t, c, h b t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 9 / 29

38. Outline
1 Preliminaries
Action Theories
2 Contracting Action Laws
Semantics
Algorithms
Properties
3 Conclusion
Contributions
Future Work
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 10 / 29

39. Intuitions about Model Contraction
Contracting a law
¬t, c, h
b b
M : t, c, h b t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Make the law false in the model
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 11 / 29

40. Intuitions about Model Contraction
Contracting coffee → hot
¬t, c, h
b b
M : t, c, h b t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Make coffee ∧ ¬hot true in one world
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 11 / 29

41. Intuitions about Model Contraction
Contracting coffee → hot
¬t, c, h t, c, ¬h
b b
M : t, c, h b t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Make coffee ∧ ¬hot true in one world
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 11 / 29

42. Intuitions about Model Contraction
Contracting coffee → hot
¬t, c, ¬h ¬t, c, h
b b
M : t, c, h b t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Make coffee ∧ ¬hot true in one world
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 11 / 29

43. Intuitions about Model Contraction
Contracting coffee → hot
¬t, c, ¬h ¬t, c, h t, c, ¬h
b b
M : t, c, h b t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Make coffee ∧ ¬hot true in one world
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 11 / 29

44. Intuitions about Model Contraction
Contracting a law
¬t, c, h
b b
M : t, c, h b t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Make the law false in the model
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 11 / 29

45. Intuitions about Model Contraction
Contracting token → buy
¬t, c, h
b b
M : t, c, h b t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Make token ∧ [buy]⊥ true in one world
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 11 / 29

46. Intuitions about Model Contraction
Contracting token → buy
¬t, c, h
b
M : t, c, h b t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Make token ∧ [buy]⊥ true in one world
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 11 / 29

47. Intuitions about Model Contraction
Contracting token → buy
¬t, c, h
b b
M : t, c, h t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Make token ∧ [buy]⊥ true in one world
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 11 / 29

48. Intuitions about Model Contraction
Contracting token → buy
¬t, c, h
M : t, c, h t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Make token ∧ [buy]⊥ true in one world
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 11 / 29

49. Intuitions about Model Contraction
Contracting a law
¬t, c, h
b b
M : t, c, h b t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Make the law false in the model
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 11 / 29

50. Intuitions about Model Contraction
Contracting token → [buy]hot
¬t, c, h
b b
M : t, c, h b t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Make token ∧ buy ¬hot true in one world
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 11 / 29

51. Intuitions about Model Contraction
Contracting token → [buy]hot
¬t, c, h
b b
M : t, c, h b t, ¬c, h
b
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Make token ∧ buy ¬hot true in one world
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 11 / 29

52. Intuitions about Model Contraction
Contracting token → [buy]hot
¬t, c, h
b b
M : t, c, h b t, ¬c, h
b
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Make token ∧ buy ¬hot true in one world
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 11 / 29

53. Intuitions about Model Contraction
Contracting token → [buy]hot
¬t, c, h
b b
M : t, c, h b t, ¬c, h
b b
b
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Make token ∧ buy ¬hot true in one world
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 11 / 29

54. Action Theory Change
Principles (Dalal, 1988)
Maintenance of Consistency "
Primacy of New Information "
Persistence of Prior Knowledge "
Fairness "
Irrelevance of Syntax +−
Assumptions in Reasoning about Actions (Shanahan, 1997)
Status of static laws "
Focus on the effect laws "
Executability laws: very difficult "
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 12 / 29

55. Action Theory Change
Principles (Dalal, 1988)
Maintenance of Consistency "
Primacy of New Information "
Persistence of Prior Knowledge "
Fairness "
Irrelevance of Syntax +−
Assumptions in Reasoning about Actions (Shanahan, 1997)
Status of static laws "
Focus on the effect laws "
Executability laws: very difficult "
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 12 / 29

56. Action Theory Change
Principles (Dalal, 1988)
Maintenance of Consistency "
Primacy of New Information "
Persistence of Prior Knowledge "
Fairness "
Irrelevance of Syntax +−
Assumptions in Reasoning about Actions (Shanahan, 1997)
Status of static laws "
Focus on the effect laws "
Executability laws: very difficult "
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 12 / 29

57. Action Theory Change
Principles (Dalal, 1988)
Maintenance of Consistency "
Primacy of New Information "
Persistence of Prior Knowledge "
Fairness "
Irrelevance of Syntax +−
Assumptions in Reasoning about Actions (Shanahan, 1997)
Status of static laws "
Focus on the effect laws "
Executability laws: very difficult "
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 12 / 29

58. Choosing Models
Distance between models
Prefer models closest to the original one
Hamming/Dalal distance, etc
Distance dependent on the type of law retracted
Static law: look at the set of worlds
Action laws: look at the set of arrows
Definition
M is as close to M as M iff
˙
either W −W ⊆ W −W ˙
˙ ˙ ˙ ˙
or W −W = W −W and R −R ⊆ R −R
Notation: M M M
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 13 / 29

59. Choosing Models
Distance between models
Prefer models closest to the original one
Hamming/Dalal distance, etc
Distance dependent on the type of law retracted
Static law: look at the set of worlds
Action laws: look at the set of arrows
Definition
M is as close to M as M iff
˙
either W −W ⊆ W −W ˙
˙ ˙ ˙ ˙
or W −W = W −W and R −R ⊆ R −R
Notation: M M M
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 13 / 29

60. Choosing Models
Distance between models
Prefer models closest to the original one
Hamming/Dalal distance, etc
Distance dependent on the type of law retracted
Static law: look at the set of worlds
Action laws: look at the set of arrows
Definition
M is as close to M as M iff
˙
either W −W ⊆ W −W ˙
˙ ˙ ˙ ˙
or W −W = W −W and R −R ⊆ R −R
Notation: M M M
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 13 / 29

61. Choosing Models
Contracting ϕ
Definition
M is a candidate iff
W ⊆W
R =R
There is w ∈ W falsifying ϕ
Take the models that are minimal w.r.t. M
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 14 / 29

62. Choosing Models
Contracting ϕ
Definition
M is a candidate iff
W ⊆W
R =R
There is w ∈ W falsifying ϕ
Take the models that are minimal w.r.t. M
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 14 / 29

63. Choosing Models
Contracting coffee → hot
¬t, c, h t, c, ¬h ¬t, c, ¬h ¬t, c, h t, c, ¬h
b b b b
t, c, h b t, ¬c, h M t, c, h b t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h ¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 15 / 29

64. Choosing Models
Contracting coffee → hot
¬t, c, h t, c, ¬h ¬t, c, ¬h ¬t, c, h
b b b b
t, c, h b t, ¬c, h t, c, h b t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h ¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Incomparable
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 15 / 29

65. Choosing Models
Contracting ϕ → a
Definition
M is a candidate iff
W =W
R ⊆R
There is w ∈ W falsifying ϕ → a
Take the models that are minimal w.r.t. M
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 16 / 29

66. Choosing Models
Contracting ϕ → a
Definition
M is a candidate iff
W =W
R ⊆R
There is w ∈ W falsifying ϕ → a
Take the models that are minimal w.r.t. M
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 16 / 29

67. Choosing Models
Contracting token → buy
¬t, c, h ¬t, c, h
b
t, c, h b t, ¬c, h M t, c, h t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h ¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 17 / 29

68. Choosing Models
Contracting token → buy
¬t, c, h ¬t, c, h
b b b
t, c, h b t, ¬c, h t, c, h t, ¬c, h
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h ¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Incomparable
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 17 / 29

69. Choosing Models
Contracting ϕ → [a]ψ
Definition
M is a candidate iff
W =W
R ⊆R
If (w , w ) ∈ R R , then w is a target (details in the JAIR paper)
There is w ∈ W falsifying ϕ → [a]ψ
Take the models that are minimal w.r.t. M
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 18 / 29

70. Choosing Models
Contracting ϕ → [a]ψ
Definition
M is a candidate iff
W =W
R ⊆R
If (w , w ) ∈ R R , then w is a target (details in the JAIR paper)
There is w ∈ W falsifying ϕ → [a]ψ
Take the models that are minimal w.r.t. M
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 18 / 29

71. Choosing Models
Contracting token → [buy]hot
¬t, c, h ¬t, c, h
b b b b
t, c, h b t, ¬c, h M t, c, h b t, ¬c, h
b
b b
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h ¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 19 / 29

72. Choosing Models
Contracting token → [buy]hot
¬t, c, h ¬t, c, h
b b b b
t, c, h b t, ¬c, h t, c, h b t, ¬c, h
b
b
¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h ¬t, ¬c, ¬h t, ¬c, ¬h ¬t, ¬c, h
Incomparable
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 19 / 29

73. Outline
1 Preliminaries
Action Theories
2 Contracting Action Laws
Semantics
Algorithms
Properties
3 Conclusion
Contributions
Future Work
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 20 / 29

74. Quick look: Algorithms
We have defined algorithms that contract T giving T
Theorem
The algorithms are correct w.r.t. our semantics (details in the JAIR paper)
Theorem
Complexity is exponential, though
Nevertheless
Theorem
The algorithms always terminate
Theorem
Size of T is linear in that of T
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 21 / 29

75. Quick look: Algorithms
We have defined algorithms that contract T giving T
Theorem
The algorithms are correct w.r.t. our semantics (details in the JAIR paper)
Theorem
Complexity is exponential, though
Nevertheless
Theorem
The algorithms always terminate
Theorem
Size of T is linear in that of T
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 21 / 29

76. Quick look: Algorithms
We have defined algorithms that contract T giving T
Theorem
The algorithms are correct w.r.t. our semantics (details in the JAIR paper)
Theorem
Complexity is exponential, though
Nevertheless
Theorem
The algorithms always terminate
Theorem
Size of T is linear in that of T
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 21 / 29

77. Quick look: Algorithms
We have defined algorithms that contract T giving T
Theorem
The algorithms are correct w.r.t. our semantics (details in the JAIR paper)
Theorem
Complexity is exponential, though
Nevertheless
Theorem
The algorithms always terminate
Theorem
Size of T is linear in that of T
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 21 / 29

78. Outline
1 Preliminaries
Action Theories
2 Contracting Action Laws
Semantics
Algorithms
Properties
3 Conclusion
Contributions
Future Work
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 22 / 29

79. Properties
Monotonicity
T |= T
Preservation
If T |= α, then T ≡ T
Success
If T |= ⊥ and |= α, then T |= α
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 23 / 29

80. Properties
Monotonicity
T |= T
Preservation
If T |= α, then T ≡ T
Success
If T |= ⊥ and |= α, then T |= α
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 23 / 29

81. Properties
Monotonicity
T |= T
Preservation
If T |= α, then T ≡ T
Success
If T |= ⊥ and |= α, then T |= α
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 23 / 29

82. Properties
Equivalences
Contracting with equivalent formulas give the same result
Recovery
T ∪ {α} |= T
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 24 / 29

83. Properties
Equivalences
Contracting with equivalent formulas give the same result
Recovery
T ∪ {α} |= T
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 24 / 29

84. Outline
1 Preliminaries
Action Theories
2 Contracting Action Laws
Semantics
Algorithms
Properties
3 Conclusion
Contributions
Future Work
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 25 / 29

85. Contributions
Approach for action theory change
Contraction: falsifying a law
Revision: making a law valid (details in the NRAC’2009 paper)
Intuitive semantics
Simple operations: add and remove
Distance between models
Minimal change
Syntactic operators (algorithms)
Correct w.r.t. the semantics
Investigation on postulates for action theory change
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 26 / 29

86. Contributions
Approach for action theory change
Contraction: falsifying a law
Revision: making a law valid (details in the NRAC’2009 paper)
Intuitive semantics
Simple operations: add and remove
Distance between models
Minimal change
Syntactic operators (algorithms)
Correct w.r.t. the semantics
Investigation on postulates for action theory change
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 26 / 29

87. Contributions
Approach for action theory change
Contraction: falsifying a law
Revision: making a law valid (details in the NRAC’2009 paper)
Intuitive semantics
Simple operations: add and remove
Distance between models
Minimal change
Syntactic operators (algorithms)
Correct w.r.t. the semantics
Investigation on postulates for action theory change
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 26 / 29

88. Contributions
Approach for action theory change
Contraction: falsifying a law
Revision: making a law valid (details in the NRAC’2009 paper)
Intuitive semantics
Simple operations: add and remove
Distance between models
Minimal change
Syntactic operators (algorithms)
Correct w.r.t. the semantics
Investigation on postulates for action theory change
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 26 / 29

89. Outline
1 Preliminaries
Action Theories
2 Contracting Action Laws
Semantics
Algorithms
Properties
3 Conclusion
Contributions
Future Work
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 27 / 29

90. Future (rather outstanding) Work
More ‘orthodox’ approach to non-classical revision
Other distances
Representation result
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 repair
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 28 / 29

91. Future (rather outstanding) Work
More ‘orthodox’ approach to non-classical revision
Other distances
Representation result
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 repair
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 28 / 29

92. Future (rather outstanding) Work
More ‘orthodox’ approach to non-classical revision
Other distances
Representation result
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 repair
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 28 / 29

93. Reference
I.J. Varzinczak. On Action Theory Change. Journal of Artificial
Intelligence Research (JAIR) vol. 37, 2010.
Thank you!
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 29 / 29

94. Reference
I.J. Varzinczak. On Action Theory Change. Journal of Artificial
Intelligence Research (JAIR) vol. 37, 2010.
Thank you!
Ivan Jos´ Varzinczak (KRR–Meraka)
e On Action Theory Change 29 / 29