On Action Theory Change:
        Semantics for Contraction and its Properties

                                    Ivan Jo...
Motivation




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


                                             Knowledge Base
                                                 ...
Motivation


                                                                            ¬t, c, h

                       ...
Motivation



                                             Observations
                                                  ...
Motivation



                                             Observations
                                                  ...
Motivation


                                                                            ¬t, c, h

                       ...
Motivation


                                                                            ¬t, c, h                   c, ¬h
...
Motivation


                                                                            ¬t, c, h

                       ...
Motivation


                                                                        ¬t, c, h

                           ...
Motivation


                                                                            ¬t, c, h

                       ...
Motivation


                                                                            ¬t, c, h

                       ...
Outline

1   Preliminaries
      Action Theories


2   Contracting Action Laws
      Semantics
      Algorithms
      Prop...
Outline

1   Preliminaries
      Action Theories


2   Contracting Action Laws
      Semantics
      Algorithms
      Prop...
Outline

1   Preliminaries
      Action Theories


2   Contracting Action Laws
      Semantics
      Algorithms
      Prop...
Outline

1   Preliminaries
      Action Theories


2   Contracting Action Laws
      Semantics
      Algorithms
      Prop...
Action Theories
Knowledge bases about the dynamics of the world
       Actions
       Effects
       Preconditions

Usually...
Action Theories
Knowledge bases about the dynamics of the world
       Actions
       Effects
       Preconditions

Usually...
Action Theories
Knowledge bases about the dynamics of the world
       Actions
       Effects
       Preconditions

Usually...
Action Theories in Multimodal Logic
Multimodal Logic
       Propositional logic + modal operators
              [a] : ever...
Action Theories in Multimodal Logic
Multimodal Logic
       Propositional logic + modal operators
              [a] : ever...
Action Theories in Multimodal Logic
Multimodal Logic
       Propositional logic + modal operators
              [a] : ever...
Action Theories in Multimodal Logic
Multimodal Logic
       Propositional logic + modal operators
              [a] : ever...
Action Theories in Multimodal Logic
Multimodal Logic
       Propositional logic + modal operators
              [a] : ever...
Action Theories in Multimodal Logic
Multimodal Logic
       Propositional logic + modal operators
              [a] : ever...
Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = W , R
       W : possible worlds
   ...
Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = W , R
       W : possible worlds
   ...
Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = W , R
       W : possible worlds
   ...
Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = W , R
       W : possible worlds
   ...
Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = W , R
       W : possible worlds
   ...
Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = W , R
       W : possible worlds
   ...
Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = W , R
       W : possible worlds
   ...
Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = W , R
       W : possible worlds
   ...
Action Theories in Multimodal Logic
Example
       Static Law: coffee → hot

       Executability Law: token → buy

       ...
Action Theories in Multimodal Logic
Example
       Static Law: coffee → hot

       Executability Law: token → buy

       ...
Action Theories in Multimodal Logic
Example
                                                                             ...
Action Theories in Multimodal Logic
Example
                                                                             ...
Outline

1   Preliminaries
      Action Theories


2   Contracting Action Laws
      Semantics
      Algorithms
      Prop...
Intuitions about Model Contraction
Contracting a law


                                                  ¬t, c, h

       ...
Intuitions about Model Contraction
Contracting coffee → hot


                                                  ¬t, c, h

 ...
Intuitions about Model Contraction
Contracting coffee → hot


                                                  ¬t, c, h   ...
Intuitions about Model Contraction
Contracting coffee → hot


                          ¬t, c, ¬h                 ¬t, c, h
...
Intuitions about Model Contraction
Contracting coffee → hot


                          ¬t, c, ¬h                 ¬t, c, h ...
Intuitions about Model Contraction
Contracting a law


                                                  ¬t, c, h

       ...
Intuitions about Model Contraction
Contracting token → buy


                                                  ¬t, c, h

 ...
Intuitions about Model Contraction
Contracting token → buy


                                                  ¬t, c, h

 ...
Intuitions about Model Contraction
Contracting token → buy


                                                  ¬t, c, h

 ...
Intuitions about Model Contraction
Contracting token → buy


                                                  ¬t, c, h


...
Intuitions about Model Contraction
Contracting a law


                                                  ¬t, c, h

       ...
Intuitions about Model Contraction
Contracting token → [buy]hot


                                                  ¬t, c,...
Intuitions about Model Contraction
Contracting token → [buy]hot


                                                  ¬t, c,...
Intuitions about Model Contraction
Contracting token → [buy]hot


                                                      ¬t...
Intuitions about Model Contraction
Contracting token → [buy]hot


                                                      ¬t...
Action Theory Change
Principles (Dalal, 1988)

      Maintenance of Consistency                       "
      Primacy of N...
Action Theory Change
Principles (Dalal, 1988)

      Maintenance of Consistency                       "
      Primacy of N...
Action Theory Change
Principles (Dalal, 1988)

      Maintenance of Consistency                       "
      Primacy of N...
Action Theory Change
Principles (Dalal, 1988)

      Maintenance of Consistency                       "
      Primacy of N...
Choosing Models
Distance between models

       Prefer models closest to the original one
       Hamming/Dalal distance, e...
Choosing Models
Distance between models

       Prefer models closest to the original one
       Hamming/Dalal distance, e...
Choosing Models
Distance between models

       Prefer models closest to the original one
       Hamming/Dalal distance, e...
Choosing Models
Contracting ϕ

Definition
M is a candidate iff
       W ⊆W
       R =R
       There is w ∈ W falsifying ϕ

T...
Choosing Models
Contracting ϕ

Definition
M is a candidate iff
       W ⊆W
       R =R
       There is w ∈ W falsifying ϕ

T...
Choosing Models
Contracting coffee → hot


                               ¬t, c, h                   t, c, ¬h              ...
Choosing Models
Contracting coffee → hot


                               ¬t, c, h                   t, c, ¬h              ...
Choosing Models
Contracting ϕ → a

Definition
M is a candidate iff
       W =W
       R ⊆R
       There is w ∈ W falsifying ...
Choosing Models
Contracting ϕ → a

Definition
M is a candidate iff
       W =W
       R ⊆R
       There is w ∈ W falsifying ...
Choosing Models
Contracting token → buy


                           ¬t, c, h                                             ...
Choosing Models
Contracting token → buy


                           ¬t, c, h                                             ...
Choosing Models
Contracting ϕ → [a]ψ

Definition
M is a candidate iff
       W =W
       R ⊆R
       If (w , w ) ∈ R  R , th...
Choosing Models
Contracting ϕ → [a]ψ

Definition
M is a candidate iff
       W =W
       R ⊆R
       If (w , w ) ∈ R  R , th...
Choosing Models
Contracting token → [buy]hot


                               ¬t, c, h                                    ...
Choosing Models
Contracting token → [buy]hot


                               ¬t, c, h                                    ...
Outline

1   Preliminaries
      Action Theories


2   Contracting Action Laws
      Semantics
      Algorithms
      Prop...
Quick look: Algorithms
We have defined algorithms that contract T giving T

Theorem
The algorithms are correct w.r.t. our s...
Quick look: Algorithms
We have defined algorithms that contract T giving T

Theorem
The algorithms are correct w.r.t. our s...
Quick look: Algorithms
We have defined algorithms that contract T giving T

Theorem
The algorithms are correct w.r.t. our s...
Quick look: Algorithms
We have defined algorithms that contract T giving T

Theorem
The algorithms are correct w.r.t. our s...
Outline

1   Preliminaries
      Action Theories


2   Contracting Action Laws
      Semantics
      Algorithms
      Prop...
Properties

Monotonicity
T |= T


Preservation
If T |= α, then T ≡ T


Success
If T |= ⊥ and |= α, then T |= α




Ivan Jo...
Properties

Monotonicity
T |= T


Preservation
If T |= α, then T ≡ T


Success
If T |= ⊥ and |= α, then T |= α




Ivan Jo...
Properties

Monotonicity
T |= T


Preservation
If T |= α, then T ≡ T


Success
If T |= ⊥ and |= α, then T |= α




Ivan Jo...
Properties

Equivalences
Contracting with equivalent formulas give the same result


Recovery
T ∪ {α} |= T




Ivan Jos´ V...
Properties

Equivalences
Contracting with equivalent formulas give the same result


Recovery
T ∪ {α} |= T




Ivan Jos´ V...
Outline

1   Preliminaries
      Action Theories


2   Contracting Action Laws
      Semantics
      Algorithms
      Prop...
Contributions
       Approach for action theory change
              Contraction: falsifying a law
              Revision:...
Contributions
       Approach for action theory change
              Contraction: falsifying a law
              Revision:...
Contributions
       Approach for action theory change
              Contraction: falsifying a law
              Revision:...
Contributions
       Approach for action theory change
              Contraction: falsifying a law
              Revision:...
Outline

1   Preliminaries
      Action Theories


2   Contracting Action Laws
      Semantics
      Algorithms
      Prop...
Future (rather outstanding) Work
       More ‘orthodox’ approach to non-classical revision
              Other distances
 ...
Future (rather outstanding) Work
       More ‘orthodox’ approach to non-classical revision
              Other distances
 ...
Future (rather outstanding) Work
       More ‘orthodox’ approach to non-classical revision
              Other distances
 ...
Reference
       I.J. Varzinczak. On Action Theory Change. Journal of Artificial
       Intelligence Research (JAIR) vol. 3...
Reference
       I.J. Varzinczak. On Action Theory Change. Journal of Artificial
       Intelligence Research (JAIR) vol. 3...
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On Action Theory Change: Semantics for Contraction and its Properties

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On Action Theory Change: Semantics for Contraction and its Properties

  1. 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. 2. Motivation Ivan Jos´ Varzinczak (KRR–Meraka) e On Action Theory Change 2 / 29
  3. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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

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