The document discusses action theory change and contracting action laws. It begins by motivating the need to change laws about the behavior of actions based on observations that contradict the current laws. It then outlines the topics to be covered, including preliminaries on action theories using multimodal logic, contracting action laws through semantics and algorithms, and properties of the contraction approach. The goal is to develop techniques for revising action theory laws in response to observations.

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