on action theory change: semantics for contraction and its properties
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On Action Theory Change:Semantics for Contraction and its Properties
Ivan Jose Varzinczak
Knowledge Representation and Reasoning
Meraka Institute, CSIR
Pretoria, South Africa
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 1 / 29
Motivation
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 2 / 29
Motivation
Knowledge Base
A coffee is a hot drink
With a token I can buy coffee
After buying I have a hot drink
. . .
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 2 / 29
Motivation
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b b
b
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 2 / 29
Motivation
Observations
I have got a cold coffee
I cannot buy
I bought and I got no hot drink
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 2 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 2 / 29
Motivation
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b b
b
Need for changing the laws about the behavior of actions
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 2 / 29
Motivation
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
c,¬h
b b
b
Need for changing the laws about the behavior of actions
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 2 / 29
Motivation
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b b
b
Need for changing the laws about the behavior of actions
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 2 / 29
Motivation
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b
b
Need for changing the laws about the behavior of actions
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 2 / 29
Motivation
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b b
b
Need for changing the laws about the behavior of actions
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 2 / 29
Motivation
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b b
b
b
Need for changing the laws about the behavior of actions
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 2 / 29
Outline
1 PreliminariesAction Theories
2 Contracting Action LawsSemanticsAlgorithmsProperties
3 ConclusionContributionsFuture Work
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 3 / 29
Outline
1 PreliminariesAction Theories
2 Contracting Action LawsSemanticsAlgorithmsProperties
3 ConclusionContributionsFuture Work
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 3 / 29
Outline
1 PreliminariesAction Theories
2 Contracting Action LawsSemanticsAlgorithmsProperties
3 ConclusionContributionsFuture Work
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 3 / 29
Outline
1 PreliminariesAction Theories
2 Contracting Action LawsSemanticsAlgorithmsProperties
3 ConclusionContributionsFuture Work
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 4 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 5 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 5 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 5 / 29
Action Theories in Multimodal Logic
Multimodal Logic
Propositional logic + modal operators
I [a] : every a-arrow
I 〈a〉 : some a-arrow
Well defined semantics
I Possible worlds models
Expressive
I Actions, state constraints, nondeterminism
Decidable
I EXPTIME-complete, though
More elegant than FOL
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 6 / 29
Action Theories in Multimodal Logic
Multimodal Logic
Propositional logic + modal operators
I [a] : every a-arrow
I 〈a〉 : some a-arrow
Well defined semantics
I Possible worlds models
Expressive
I Actions, state constraints, nondeterminism
Decidable
I EXPTIME-complete, though
More elegant than FOL
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 6 / 29
Action Theories in Multimodal Logic
Multimodal Logic
Propositional logic + modal operators
I [a] : every a-arrow
I 〈a〉 : some a-arrow
Well defined semantics
I Possible worlds models
Expressive
I Actions, state constraints, nondeterminism
Decidable
I EXPTIME-complete, though
More elegant than FOL
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 6 / 29
Action Theories in Multimodal Logic
Multimodal Logic
Propositional logic + modal operators
I [a] : every a-arrow
I 〈a〉 : some a-arrow
Well defined semantics
I Possible worlds models
Expressive
I Actions, state constraints, nondeterminism
Decidable
I EXPTIME-complete, though
More elegant than FOL
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 6 / 29
Action Theories in Multimodal Logic
Multimodal Logic
Propositional logic + modal operators
I [a] : every a-arrow
I 〈a〉 : some a-arrow
Well defined semantics
I Possible worlds models
Expressive
I Actions, state constraints, nondeterminism
Decidable
I EXPTIME-complete, though
More elegant than FOL
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 6 / 29
Action Theories in Multimodal Logic
Multimodal Logic
Propositional logic + modal operators
I [a] : every a-arrow
I 〈a〉 : some a-arrow
Well defined semantics
I Possible worlds models
Expressive
I Actions, state constraints, nondeterminism
Decidable
I EXPTIME-complete, though
More elegant than FOL
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 6 / 29
Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = 〈W ,R 〉
W : possible worlds
R : accessibility relations
M :
p, q p,¬q
¬p,¬q
a1
a1
a1
a2
a2
a1
Satisfaction in a modelq → p
p → [a1]¬q
p → 〈a1〉>
p → 〈a2〉>
(p ∧ ¬q)→ [a2]⊥
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 7 / 29
Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = 〈W ,R 〉
W : possible worlds
R : accessibility relations
M :
p, q p,¬q
¬p,¬q
a1
a1
a1
a2
a2
a1
Satisfaction in a modelq → p
p → [a1]¬q
p → 〈a1〉>
p → 〈a2〉>
(p ∧ ¬q)→ [a2]⊥
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 7 / 29
Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = 〈W ,R 〉
W : possible worlds
R : accessibility relations
M :
p, q p,¬q
¬p,¬q
a1
a1
a1
a2
a2
a1
Satisfaction in a modelq → p
p → [a1]¬q
p → 〈a1〉>
p → 〈a2〉>
(p ∧ ¬q)→ [a2]⊥
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 7 / 29
Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = 〈W ,R 〉
W : possible worlds
R : accessibility relations
M :
p, q p,¬q
¬p,¬q
a1
a1
a1
a2
a2
a1
Satisfaction in a model
q → p "
p → [a1]¬q
p → 〈a1〉>
p → 〈a2〉>
(p ∧ ¬q)→ [a2]⊥
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 7 / 29
Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = 〈W ,R 〉
W : possible worlds
R : accessibility relations
M :
p, q p,¬q
¬p,¬q
a1
a1
a1
a2
a2
a1
Satisfaction in a model
q → p "
p → [a1]¬q "
p → 〈a1〉>
p → 〈a2〉>
(p ∧ ¬q)→ [a2]⊥
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 7 / 29
Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = 〈W ,R 〉
W : possible worlds
R : accessibility relations
M :
p, q p,¬q
¬p,¬q
a1
a1
a1
a2
a2
a1
Satisfaction in a model
q → p "
p → [a1]¬q "
p → 〈a1〉> "
p → 〈a2〉>
(p ∧ ¬q)→ [a2]⊥
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 7 / 29
Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = 〈W ,R 〉
W : possible worlds
R : accessibility relations
M :
p, q p,¬q
¬p,¬q
a1
a1
a1
a2
a2
a1
Satisfaction in a model
q → p "
p → [a1]¬q "
p → 〈a1〉> "
p → 〈a2〉> %
(p ∧ ¬q)→ [a2]⊥
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 7 / 29
Action Theories in Multimodal Logic
Possible worlds semantics: transition systems M = 〈W ,R 〉
W : possible worlds
R : accessibility relations
M :
p, q p,¬q
¬p,¬q
a1
a1
a1
a2
a2
a1
Satisfaction in a model
q → p "
p → [a1]¬q "
p → 〈a1〉> "
p → 〈a2〉> %
(p ∧ ¬q)→ [a2]⊥ "
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 7 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 8 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 8 / 29
Action Theories in Multimodal Logic
Example
T = S ∪ E ∪ X =
coffee→ hot, token→ 〈buy〉>,
¬coffee→ [buy]coffee, token→ [buy]¬token,¬token→ [buy]⊥,
coffee→ [buy]coffee, hot→ [buy]hot
M :
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b b
b
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 9 / 29
Action Theories in Multimodal Logic
Example
T = S ∪ E ∪ X =
coffee→ hot, token→ 〈buy〉>,
¬coffee→ [buy]coffee, token→ [buy]¬token,¬token→ [buy]⊥,
coffee→ [buy]coffee, hot→ [buy]hot
M :
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b b
b
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 9 / 29
Outline
1 PreliminariesAction Theories
2 Contracting Action LawsSemanticsAlgorithmsProperties
3 ConclusionContributionsFuture Work
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 10 / 29
Intuitions about Model Contraction
Contracting a law
M :
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b b
b
Make the law false in the model
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 11 / 29
Intuitions about Model Contraction
Contracting coffee→ hot
M :
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b b
b
Make coffee ∧ ¬hot true in one world
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 11 / 29
Intuitions about Model Contraction
Contracting coffee→ hot
M :
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
t, c,¬h
b b
b
Make coffee ∧ ¬hot true in one world
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 11 / 29
Intuitions about Model Contraction
Contracting coffee→ hot
M :
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
¬t, c,¬h
b b
b
Make coffee ∧ ¬hot true in one world
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 11 / 29
Intuitions about Model Contraction
Contracting coffee→ hot
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
b b
b
Make coffee ∧ ¬hot true in one world
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 11 / 29
Intuitions about Model Contraction
Contracting a law
M :
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b b
b
Make the law false in the model
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 11 / 29
Intuitions about Model Contraction
Contracting token→ 〈buy〉>
M :
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b b
b
Make token ∧ [buy]⊥ true in one world
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 11 / 29
Intuitions about Model Contraction
Contracting token→ 〈buy〉>
M :
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b
b
Make token ∧ [buy]⊥ true in one world
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 11 / 29
Intuitions about Model Contraction
Contracting token→ 〈buy〉>
M :
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b b
Make token ∧ [buy]⊥ true in one world
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 11 / 29
Intuitions about Model Contraction
Contracting token→ 〈buy〉>
M :
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
Make token ∧ [buy]⊥ true in one world
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 11 / 29
Intuitions about Model Contraction
Contracting a law
M :
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b b
b
Make the law false in the model
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 11 / 29
Intuitions about Model Contraction
Contracting token→ [buy]hot
M :
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b b
b
Make token ∧ 〈buy〉¬hot true in one world
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 11 / 29
Intuitions about Model Contraction
Contracting token→ [buy]hot
M :
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b b
b
b
Make token ∧ 〈buy〉¬hot true in one world
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 11 / 29
Intuitions about Model Contraction
Contracting token→ [buy]hot
M :
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b b
b
b
Make token ∧ 〈buy〉¬hot true in one world
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 11 / 29
Intuitions about Model Contraction
Contracting token→ [buy]hot
M :
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b b
b
b
b b
Make token ∧ 〈buy〉¬hot true in one world
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 11 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 12 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 12 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 12 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 12 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 13 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 13 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 13 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 14 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 14 / 29
Choosing Models
Contracting coffee→ hot
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
t, c,¬h
b b
b �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
b b
b
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 15 / 29
Choosing Models
Contracting coffee→ hot
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
t, c,¬h
b b
b
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
¬t, c,¬h
b b
b
Incomparable
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 15 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 16 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 16 / 29
Choosing Models
Contracting token→ 〈buy〉>
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b
b �M
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 17 / 29
Choosing Models
Contracting token→ 〈buy〉>
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b
b
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b b
Incomparable
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 17 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 18 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 18 / 29
Choosing Models
Contracting token→ [buy]hot
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b b
b
b
�M
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b b
b
b
b
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 19 / 29
Choosing Models
Contracting token→ [buy]hot
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b b
b
b
¬t, c, h
t, c, h t,¬c, h
t,¬c,¬h¬t,¬c,¬h ¬t,¬c, h
b b
b
b
Incomparable
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 19 / 29
Outline
1 PreliminariesAction Theories
2 Contracting Action LawsSemanticsAlgorithmsProperties
3 ConclusionContributionsFuture Work
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 20 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 21 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 21 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 21 / 29
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 Jose Varzinczak (KRR–Meraka) On Action Theory Change 21 / 29
Outline
1 PreliminariesAction Theories
2 Contracting Action LawsSemanticsAlgorithmsProperties
3 ConclusionContributionsFuture Work
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 22 / 29
Properties
Monotonicity
T |= T ′
Preservation
If T 6|= α, then T ≡ T ′
Success
If T 6|= ⊥ and 6|= α, then T ′ 6|= α
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 23 / 29
Properties
Monotonicity
T |= T ′
Preservation
If T 6|= α, then T ≡ T ′
Success
If T 6|= ⊥ and 6|= α, then T ′ 6|= α
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 23 / 29
Properties
Monotonicity
T |= T ′
Preservation
If T 6|= α, then T ≡ T ′
Success
If T 6|= ⊥ and 6|= α, then T ′ 6|= α
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 23 / 29
Properties
Equivalences
Contracting with equivalent formulas give the same result
Recovery
T ′ ∪ {α} |= T
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 24 / 29
Properties
Equivalences
Contracting with equivalent formulas give the same result
Recovery
T ′ ∪ {α} |= T
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 24 / 29
Outline
1 PreliminariesAction Theories
2 Contracting Action LawsSemanticsAlgorithmsProperties
3 ConclusionContributionsFuture Work
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 25 / 29
Contributions
Approach for action theory change
I Contraction: falsifying a law
I Revision: making a law valid (details in the NRAC’2009 paper)
Intuitive semantics
I Simple operations: add and remove
I Distance between models
I Minimal change
Syntactic operators (algorithms)
I Correct w.r.t. the semantics
Investigation on postulates for action theory change
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 26 / 29
Contributions
Approach for action theory change
I Contraction: falsifying a law
I Revision: making a law valid (details in the NRAC’2009 paper)
Intuitive semantics
I Simple operations: add and remove
I Distance between models
I Minimal change
Syntactic operators (algorithms)
I Correct w.r.t. the semantics
Investigation on postulates for action theory change
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 26 / 29
Contributions
Approach for action theory change
I Contraction: falsifying a law
I Revision: making a law valid (details in the NRAC’2009 paper)
Intuitive semantics
I Simple operations: add and remove
I Distance between models
I Minimal change
Syntactic operators (algorithms)
I Correct w.r.t. the semantics
Investigation on postulates for action theory change
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 26 / 29
Contributions
Approach for action theory change
I Contraction: falsifying a law
I Revision: making a law valid (details in the NRAC’2009 paper)
Intuitive semantics
I Simple operations: add and remove
I Distance between models
I Minimal change
Syntactic operators (algorithms)
I Correct w.r.t. the semantics
Investigation on postulates for action theory change
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 26 / 29
Outline
1 PreliminariesAction Theories
2 Contracting Action LawsSemanticsAlgorithmsProperties
3 ConclusionContributionsFuture Work
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 27 / 29
Future (rather outstanding) Work
More ‘orthodox’ approach to non-classical revision
I Other distances
I Representation result
Revision of general formulas
I Not only ϕ, ϕ→ 〈a〉>, ϕ→ [a]ψ
I More expressive logics: PDL
I Less expressive logics: Causal Theories of Action
Applications in Description Logics
I Ontology repair
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 28 / 29
Future (rather outstanding) Work
More ‘orthodox’ approach to non-classical revision
I Other distances
I Representation result
Revision of general formulas
I Not only ϕ, ϕ→ 〈a〉>, ϕ→ [a]ψ
I More expressive logics: PDL
I Less expressive logics: Causal Theories of Action
Applications in Description Logics
I Ontology repair
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 28 / 29
Future (rather outstanding) Work
More ‘orthodox’ approach to non-classical revision
I Other distances
I Representation result
Revision of general formulas
I Not only ϕ, ϕ→ 〈a〉>, ϕ→ [a]ψ
I More expressive logics: PDL
I Less expressive logics: Causal Theories of Action
Applications in Description Logics
I Ontology repair
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 28 / 29
Reference
I.J. Varzinczak. On Action Theory Change. Journal of ArtificialIntelligence Research (JAIR) vol. 37, 2010.
Thank you!
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 29 / 29
Reference
I.J. Varzinczak. On Action Theory Change. Journal of ArtificialIntelligence Research (JAIR) vol. 37, 2010.
Thank you!
Ivan Jose Varzinczak (KRR–Meraka) On Action Theory Change 29 / 29
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