Strategize a Smooth Tenant-to-tenant Migration and Copilot Takeoff
What Is a Good Domain Description? Evaluating & Revising Action Theories in Dynamic Logic
1. Introduction
Main Results
Concluding Remarks
What is a Good Domain Description?
Evaluating & Revising Action Theories in Dynamic Logic
Ivan José Varzinczak
IRIT – Université Paul Sabatier
October 27th 2006
Ivan José Varzinczak What is a Good Domain Description?
2. Introduction
Main Results
Concluding Remarks
Reasoning About Actions
Problem: describing domains by logical formulas
Actions and their effects
Executabilities of actions
Inexecutabilities of actions
Domain constraints
Example
A turkey that walks is alive
Teasing a turkey makes it walk
It is always possible to tease a turkey
A dead turkey remains dead after teasing it
Ivan José Varzinczak What is a Good Domain Description?
3. Introduction
Main Results
Concluding Remarks
Reasoning About Actions
Problem: describing domains by logical formulas
Actions and their effects
Executabilities of actions
Inexecutabilities of actions
Domain constraints
Example
A turkey that walks is alive
Teasing a turkey makes it walk
It is always possible to tease a turkey
A dead turkey remains dead after teasing it
Ivan José Varzinczak What is a Good Domain Description?
4. Introduction
Main Results
Concluding Remarks
Reasoning About Actions
Goal: inference tasks
Prediction
Explanation
Planning
Ivan José Varzinczak What is a Good Domain Description?
5. Introduction
Main Results
Concluding Remarks
Reasoning About Actions
Prediction: reasoning about the future
?
Initial actions Result
state state
After shooting, the turkey stops walking
Ivan José Varzinczak What is a Good Domain Description?
6. Introduction
Main Results
Concluding Remarks
Reasoning About Actions
Explanation: reasoning about the past
?
Initial actions Current
state state
After shooting, the turkey is dead: the gun was loaded
Ivan José Varzinczak What is a Good Domain Description?
7. Introduction
Main Results
Concluding Remarks
Reasoning About Actions
Planning: what to do to achieve a goal
?
Current actions Desired
state state
To have the turkey dead: load the gun, then shoot
Ivan José Varzinczak What is a Good Domain Description?
8. Introduction
Main Results
Concluding Remarks
Reasoning About Actions
Other important tasks
Consistency check
Test of executability/inexecutability
Theory change
...
Ivan José Varzinczak What is a Good Domain Description?
9. Introduction
Main Results
Concluding Remarks
Outline
1 Introduction
Describing Action Theories
Unwanted Conclusions
2 Main Results
Decomposing Theories
Logical Modularity
Exploiting Modularity
Theory Change
3 Concluding Remarks
Ivan José Varzinczak What is a Good Domain Description?
10. Introduction
Main Results
Concluding Remarks
Outline
1 Introduction
Describing Action Theories
Unwanted Conclusions
2 Main Results
Decomposing Theories
Logical Modularity
Exploiting Modularity
Theory Change
3 Concluding Remarks
Ivan José Varzinczak What is a Good Domain Description?
11. Introduction
Main Results
Concluding Remarks
Outline
1 Introduction
Describing Action Theories
Unwanted Conclusions
2 Main Results
Decomposing Theories
Logical Modularity
Exploiting Modularity
Theory Change
3 Concluding Remarks
Ivan José Varzinczak What is a Good Domain Description?
12. Introduction
Describing Action Theories
Main Results
Unwanted Conclusions
Concluding Remarks
Outline
1 Introduction
Describing Action Theories
Unwanted Conclusions
2 Main Results
Decomposing Theories
Logical Modularity
Exploiting Modularity
Theory Change
3 Concluding Remarks
Ivan José Varzinczak What is a Good Domain Description?
14. Introduction
Describing Action Theories
Main Results
Unwanted Conclusions
Concluding Remarks
Formalizing Domains
In this work. . .
we have chosen Modal Logic
Weak version of Propositional Dynamic Logic (PDL)
Simple and decidable
With a tableaux-based theorem prover: Lotrec
Ivan José Varzinczak What is a Good Domain Description?
15. Introduction
Describing Action Theories
Main Results
Unwanted Conclusions
Concluding Remarks
Logical Preliminaries
Ontology
Actions: ) 0($
' % # a 1 a2
1 53331
4 2 2 2
Atomic propositions: ) 0BA386
' @ 9 7 p 1 p2 1 53331
4 2 2 2
Literals: RP$H38GFEC
Q ) I @ 9 7 6 ' % D p p S H38UT
@ 9 7 6 4
Classical formulas: Rba`XV
c ) ' Y W 1 c 1 2 53331
4 2 2 2
Action operators
For each a , a modal operator a
$dT
% # e f
ea : “after execution of a, is true”
c gf c
a : “a is inexecutable”
h
p qi
a a
r
' ts
c def e uQ vgf
c Q
a : “a is executable”
w
y €x
Complex formulas: 1 1 2 3331
2 2 2
Ivan José Varzinczak What is a Good Domain Description?
16. Introduction
Describing Action Theories
Main Results
Unwanted Conclusions
Concluding Remarks
Logical Preliminaries
Ontology
Actions: ) 0($
' % # a 1 a2
1 53331
4 2 2 2
Atomic propositions: ) 0BA386
' @ 9 7 p 1 p2 1 53331
4 2 2 2
Literals: RP$H38GFEC
Q ) I @ 9 7 6 ' % D p p S H38UT
@ 9 7 6 4
Classical formulas: Rba`XV
c ) ' Y W 1 c 1 2 53331
4 2 2 2
Action operators
For each a , a modal operator a
$dT
% # e f
ea : “after execution of a, is true”
c gf c
a : “a is inexecutable”
h
p qi
a a
r
' ts
c def e uQ vgf
c Q
a : “a is executable”
w
y €x
Complex formulas: 1 1 2 3331
2 2 2
Ivan José Varzinczak What is a Good Domain Description?
17. Introduction
Describing Action Theories
Main Results
Unwanted Conclusions
Concluding Remarks
Logical Preliminaries
Ontology
Actions: ) 0($
' % # a 1 a2
1 53331
4 2 2 2
Atomic propositions: ) 0BA386
' @ 9 7 p 1 p2 1 53331
4 2 2 2
Literals: RP$H38GFEC
Q ) I @ 9 7 6 ' % D p p S H38UT
@ 9 7 6 4
Classical formulas: Rba`XV
c ) ' Y W 1 c 1 2 53331
4 2 2 2
Action operators
For each a , a modal operator a
$dT
% # e f
ea : “after execution of a, is true”
c gf c
a : “a is inexecutable”
h
p qi
a a
r
' ts
c def e uQ vgf
c Q
a : “a is executable”
w
y €x
Complex formulas: 1 1 2 3331
2 2 2
Ivan José Varzinczak What is a Good Domain Description?
18. Introduction
Describing Action Theories
Main Results
Unwanted Conclusions
Concluding Remarks
Logical Preliminaries
Ontology
Actions: ) 0($
' % # a 1 a2
1 53331
4 2 2 2
Atomic propositions: ) 0BA386
' @ 9 7 p 1 p2 1 53331
4 2 2 2
Literals: RP$H38GFEC
Q ) I @ 9 7 6 ' % D p p S H38UT
@ 9 7 6 4
Classical formulas: Rba`XV
c ) ' Y W 1 c 1 2 53331
4 2 2 2
Action operators
For each a , a modal operator a
$dT
% # e f
ea : “after execution of a, is true”
c gf c
a : “a is inexecutable”
h
p qi
a a
r
' ts
c def e uQ vgf
c Q
a : “a is executable”
w
y €x
Complex formulas: 1 1 2 3331
2 2 2
Ivan José Varzinczak What is a Good Domain Description?
19. Introduction
Describing Action Theories
Main Results
Unwanted Conclusions
Concluding Remarks
Logical Preliminaries
Example
Actions: shoot, tease
Propositions: loaded, alive, walking
Formulas: alive walking, tease ,
r
Q ƒ‚ „ s
loaded e shoot alive
†… Q gf
Ivan José Varzinczak What is a Good Domain Description?
20. Introduction
Describing Action Theories
Main Results
Unwanted Conclusions
Concluding Remarks
Semantics
Multimodal logic K [Popkorn 94,Blackburn et al. 2001].
Definition
Models W R where
r
‡ ' 1 s
W ˆ 2 g‘‰
“ ’ : set of possible worlds (states)
R: –•$
… ” % # 2W — W
Definition
˜
p (p is true at world w of model ) iff p w
w
™ A' ˜ ‡ ˜ T
a iff for every w such that wRa w ,
w w
™ A' e df e e ™ A'
f
the usual truth conditions for the other connectives
Ivan José Varzinczak What is a Good Domain Description?
21. Introduction
Describing Action Theories
Main Results
Unwanted Conclusions
Concluding Remarks
Semantics
Multimodal logic K [Popkorn 94,Blackburn et al. 2001].
Definition
Models W R where
r
‡ ' 1 s
W ˆ 2 g‘‰
“ ’ : set of possible worlds (states)
R: –•$
… ” % # 2W — W
Definition
˜
p (p is true at world w of model ) iff p w
w
™ A' ˜ ‡ ˜ T
a iff for every w such that wRa w ,
w w
™ A' e df e e ™ A'
f
the usual truth conditions for the other connectives
Ivan José Varzinczak What is a Good Domain Description?
22. Introduction
Describing Action Theories
Main Results
Unwanted Conclusions
Concluding Remarks
Semantics
Example
If a1 a2 , and p 1 p2 , W R , where
r
) b($
' % # 1 4 ) 0gH386
' @ 9 7 1 4 ‡ ' 1 s
W hb'
) ) p 1 p2
1 ) i4
1 p1 Q 1 p2 Q R) i4
1 p1 p2 1 ih4
1 4
p1 p2 p 1 p2 p 1 p2 p 1 p2
l
R a1
) mj 1 ) i4
1 Q 1 ) mj nR4
1 k 1 Q R) i4
1 1 nR4
1 k
p1 p2 p1 p2 p 1 p2 p1 p2
j k '
Rmj
Q ) 1 Q R) i4
1 1 Rmj nR4
Q ) 1 k 1 ) i4
1 Q 1 o tR4
k
R a2
j k mi0'
) j ) p1 p2
1 ) i4
1 p1 Q 1 p2 ) mj nR4
1 k p1 Q 1 p2 ) i4
1 p1 Q 1 p2 pR4
4 k
is a model
Ivan José Varzinczak What is a Good Domain Description?
23. Introduction
Describing Action Theories
Main Results
Unwanted Conclusions
Concluding Remarks
Semantics
Example
a1
a1
p1 p2 p1 p2
p1 p2
q r s w A uv
a2
x
p1 a2 p2
w uv
‡ : a1 a1 z {y } g|
p1 a1
w A uv
} ~ {y €
p1 p2 p2 a1
w uv
} z †y ‚|
r ts
a2
Ivan José Varzinczak What is a Good Domain Description?
24. Introduction
Describing Action Theories
Main Results
Unwanted Conclusions
Concluding Remarks
Semantics
Definition ˜ ˜
iff for all w W,
w
™ '˜ ˜ T ™ '
ƒ „A'
™ iff …A'
™ for every ƒ P†
T
Definition
is a consequence of the set of global axioms in all ˜
ƒ
˜
PDL-models (noted
˜
PDL
) iff for every , if , then
ƒ ' ‡ ™ ' ƒ
™ ' .
Ivan José Varzinczak What is a Good Domain Description?
25. Introduction
Describing Action Theories
Main Results
Unwanted Conclusions
Concluding Remarks
Semantics
Definition ˜ ˜
iff for all w W,
w
™ '˜ ˜ T ™ '
ƒ „A'
™ iff …A'
™ for every ƒ P†
T
Definition
is a consequence of the set of global axioms in all ˜
ƒ
˜
PDL-models (noted
˜
PDL
) iff for every , if , then
ƒ ' ‡ ™ ' ƒ
™ ' .
Ivan José Varzinczak What is a Good Domain Description?
26. Introduction
Describing Action Theories
Main Results
Unwanted Conclusions
Concluding Remarks
Outline
1 Introduction
Describing Action Theories
Unwanted Conclusions
2 Main Results
Decomposing Theories
Logical Modularity
Exploiting Modularity
Theory Change
3 Concluding Remarks
Ivan José Varzinczak What is a Good Domain Description?
27. Introduction
Describing Action Theories
Main Results
Unwanted Conclusions
Concluding Remarks
The Tale Again
Example
A turkey that walks is alive: walking … alive
Teasing a turkey makes it to walk: e tease walking
f
It is always possible to tease a turkey: tease
r
„ s
A dead turkey remains dead after teasing it
alive tease alive
h
¨ ¦ ¨ Fi
If the gun is loaded, shooting kills the turkey
loaded shoot alive
h
¦ ¨ di
Teasing does not unload the gun
loaded tease loaded
h
¦ i
Ivan José Varzinczak What is a Good Domain Description?
28. Introduction
Describing Action Theories
Main Results
Unwanted Conclusions
Concluding Remarks
The Tale Again
Example
‡ˆ
ˆ
ˆ
ˆ
ˆ ˆ
ˆ ˆ
ˆ ˆ
ˆ ˆ
tease
r ‹ ˜
tease alive
„ s 1
ˆ
ˆ
ˆ walking alive … 1
ˆ
ˆ
ˆ
'˜ e f
tease walking alive tease alive alive
ˆ ‰ ˆ
Œˆ
ˆ
ˆ e f ˆ
1 Q Ž' ˜ e †… j €f Q ƒ‚
loaded shoot alive
k
alive tease
e {… Q gf 1
alive tease alive
Q Ž' ˜ e {… ‚f
Q e †… Q gf
alive
1
loaded tease loaded
Š
e †… f '
N.B.: Such a description is consistent
What is the problem?
Ivan José Varzinczak What is a Good Domain Description?
29. Introduction
Describing Action Theories
Main Results
Unwanted Conclusions
Concluding Remarks
The Tale Again
Example
‡ˆ
ˆ
ˆ
ˆ
ˆ ˆ
ˆ ˆ
ˆ ˆ
ˆ ˆ
tease
r ‹ ˜
tease alive
„ s 1
ˆ
ˆ
ˆ walking alive … 1
ˆ
ˆ
ˆ
'˜ e f
tease walking alive tease alive alive
ˆ ‰ ˆ
Œˆ
ˆ
ˆ e f ˆ
1 Q Ž' ˜ e †… j €f Q ƒ‚
loaded shoot alive
k
alive tease
e {… Q gf 1
alive tease alive
Q Ž' ˜ e {… ‚f
Q e †… Q gf
alive
1
loaded tease loaded
Š
e †… f '
N.B.: Such a description is consistent
What is the problem?
Ivan José Varzinczak What is a Good Domain Description?
30. Introduction
Describing Action Theories
Main Results
Unwanted Conclusions
Concluding Remarks
The Tale Again
Example
‡ˆ
ˆ
ˆ
ˆ
ˆ ˆ
ˆ ˆ
ˆ ˆ
ˆ ˆ
tease
r ‹ ˜
tease alive
„ s 1
ˆ
ˆ
ˆ walking alive … 1
ˆ
ˆ
ˆ
'˜ e f
tease walking alive tease alive alive
ˆ ‰ ˆ
Œˆ
ˆ
ˆ e f ˆ
1 '˜ Q e †… j €f Q ƒ‚
loaded shoot alive
k
alive tease
e {… Q gf 1
alive tease alive
Q Ž' ˜ e {… ‚f
Q e †… Q gf
alive
1
loaded tease loaded
Š
e †… f '
N.B.: Such a description is consistent
What is the problem?
Ivan José Varzinczak What is a Good Domain Description?
31. Introduction
Describing Action Theories
Main Results
Unwanted Conclusions
Concluding Remarks
The Tale Again
Example
‡ˆ
ˆ
ˆ
ˆ
ˆ ˆ
ˆ ˆ
ˆ ˆ
ˆ ˆ
tease
r ‹ ˜
tease alive
„ s 1
ˆ
ˆ
ˆ walking alive … 1
ˆ
ˆ
ˆ
e ' ˜ f
tease walking alive tease alive alive
ˆ ‰ ˆ
Œˆ
ˆ
ˆ e f ˆ
1 Q Ž' ˜ e †… j €f Q ƒ‚
loaded shoot alive
k
alive tease
e {… Q gf 1
alive tease alive
Q Ž' ˜ e {… ‚f
Q e †… Q gf
alive
1
loaded tease loaded
Š
e †… f '
N.B.: Such a description is consistent
What is the problem?
Ivan José Varzinczak What is a Good Domain Description?
32. Introduction
Describing Action Theories
Main Results
Unwanted Conclusions
Concluding Remarks
The Tale Again
Example
‡ˆ
ˆ
ˆ
ˆ
ˆ ˆ
ˆ ˆ
ˆ ˆ
ˆ ˆ
tease
r ‹ ˜
tease alive
„ s 1
ˆ
ˆ
ˆ walking alive … 1
ˆ
ˆ
ˆ
e ' ˜ f
tease walking alive tease alive alive
ˆ ‰ ˆ
Œˆ
ˆ
ˆ e f ˆ
1 Q Ž' ˜ e †… j €f Q ƒ‚
loaded shoot alive
k
alive tease
e {… Q gf 1
alive tease alive
Q Ž' ˜ e {… ‚f
Q e †… Q gf
alive
1
loaded tease loaded
Š
e †… f '
N.B.: Such a description is consistent
What is the problem?
Ivan José Varzinczak What is a Good Domain Description?
33. Introduction
Describing Action Theories
Main Results
Unwanted Conclusions
Concluding Remarks
The Tale Again
Example
‡ˆ
ˆ
ˆ
ˆ
ˆ ˆ
ˆ ˆ
ˆ ˆ
ˆ ˆ
tease
r ‹ ˜
tease alive
„ s 1
ˆ
ˆ
ˆ walking alive … 1
ˆ
ˆ
ˆ
e ' ˜ f
tease walking alive tease alive alive
ˆ ‰ ˆ
Œˆ
ˆ
ˆ e f ˆ
1 Q Ž' ˜ e †… j €f Q ƒ‚
loaded shoot alive
k
alive tease
e {… Q gf 1
alive tease alive
Q Ž' ˜ e {… ‚f
Q e †… Q gf
alive
1
loaded tease loaded
Š
e †… f '
N.B.: Such a description is consistent
What is the problem?
Ivan José Varzinczak What is a Good Domain Description?
34. Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Outline
1 Introduction
Describing Action Theories
Unwanted Conclusions
2 Main Results
Decomposing Theories
Logical Modularity
Exploiting Modularity
Theory Change
3 Concluding Remarks
Ivan José Varzinczak What is a Good Domain Description?
35. Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Natural Modules in Action Theories
Types of domain laws
Static laws : walking … alive
Effect laws : loaded e †… shoot alive
Q ‚f
Executability laws : hasGun shoot
r
… „ s
Inexecutability laws : Q hasGun e †… shoot gf
! only formulas of these types
Ivan José Varzinczak What is a Good Domain Description?
36. Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Natural Modules in Action Theories
Types of domain laws
Static laws : walking … alive
Effect laws : loaded e †… shoot alive
Q ‚f
Executability laws : hasGun shoot
r
… „ s
Inexecutability laws : Q hasGun e †… shoot gf
! only formulas of these types
Ivan José Varzinczak What is a Good Domain Description?
37. Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Natural Modules in Action Theories
Types of domain laws
Static laws : walking … alive
Effect laws : loaded e †… shoot alive
Q ‚f
Executability laws : hasGun shoot
r
… „ s
Inexecutability laws : Q hasGun e †… shoot gf
! only formulas of these types
Ivan José Varzinczak What is a Good Domain Description?
38. Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Natural Modules in Action Theories
Types of domain laws
Static laws : walking … alive
Effect laws : loaded e †… shoot alive
Q ‚f
Executability laws : hasGun shoot
r
… „ s
Inexecutability laws : Q hasGun e †… shoot gf
! only formulas of these types
Ivan José Varzinczak What is a Good Domain Description?
39. Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Natural Modules in Action Theories
Types of domain laws
Static laws : walking … alive
Effect laws : loaded e †… shoot alive
Q ‚f
Executability laws : hasGun shoot
r
… „ s
Inexecutability laws : Q hasGun e †… shoot gf
! only formulas of these types
Ivan José Varzinczak What is a Good Domain Description?
40. Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Natural Modules in Action Theories
Defining modules
: set of static laws
‘
Given a $dT
% #
a
: effect laws for a
’
a
: executability laws for a
“
a
: inexecutability laws for a
”
‘ r
a a a : domain description for a
• 1 – n1 — ‚1 s
a, a, and a
• ˜ Ž'
a • 5R™
œ › š – ˜ '
a – 5R™
œ › š — ˜ Ž'
a — 5ž™
œ › š
: the action theory of a given domain
‘ r
‚ nŸ1
— 1 – 1 • s
Ivan José Varzinczak What is a Good Domain Description?
41. Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Natural Modules in Action Theories
Defining modules
: set of static laws
‘
Given a $dT
% #
a
: effect laws for a
’
a
: executability laws for a
“
a
: inexecutability laws for a
”
‘ r
a a a : domain description for a
• 1 – n1 — ‚1 s
a, a, and a
• ˜ Ž'
a • 5R™
œ › š – ˜ '
a – 5R™
œ › š — ˜ Ž'
a — 5ž™
œ › š
: the action theory of a given domain
‘ r
‚ nŸ1
— 1 – 1 • s
Ivan José Varzinczak What is a Good Domain Description?
42. Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Natural Modules in Action Theories
Defining modules
: set of static laws
‘
Given a $dT
% #
a
: effect laws for a
’
a
: executability laws for a
“
a
: inexecutability laws for a
”
‘ r
a a a : domain description for a
• 1 – n1 — ‚1 s
a, a, and a
• ˜ Ž'
a • 5R™
œ › š – ˜ '
a – 5R™
œ › š — ˜ Ž'
a — 5ž™
œ › š
: the action theory of a given domain
‘ r
‚ nŸ1
— 1 – 1 • s
Ivan José Varzinczak What is a Good Domain Description?
43. Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Natural Modules in Action Theories
Defining modules
: set of static laws
‘
Given a $dT
% #
a
: effect laws for a
’
a
: executability laws for a
“
a
: inexecutability laws for a
”
‘ r
a a a : domain description for a
• 1 – n1 — ‚1 s
a, a, and a
• ˜ Ž'
a • 5R™
œ › š – ˜ '
a – 5R™
œ › š — ˜ Ž'
a — 5ž™
œ › š
: the action theory of a given domain
‘ r
‚ nŸ1
— 1 – 1 • s
Ivan José Varzinczak What is a Good Domain Description?
48. Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
What About the Frame Problem?
Restriction on models
For all wRa w :
˜
e
˜
w
p implies p, if a p
w
™ '¬ ˜ ™ '¬ ˜ ¬¥
f
p implies p, if a p.
w w
™ A' ™ H' Q ¥
¬
f
New logical consequence
˜ ˜
® ' instead of '
PDL
Example ˜
loaded wait loaded
‘
‚ nŸ1
— 1 – 1 • ® ' e ¯… f
Ivan José Varzinczak What is a Good Domain Description?
49. Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
What About the Frame Problem?
Restriction on models
For all wRa w :
˜
e
˜
w
p implies p, if a p
w
™ '¬ ˜ ™ '¬ ˜ ¬¥
f
p implies p, if a p.
w w
™ A' ™ H' Q ¥
¬
f
New logical consequence
˜ ˜
® ' instead of '
PDL
Example ˜
loaded wait loaded
‘
‚ nŸ1
— 1 – 1 • ® ' e ¯… f
Ivan José Varzinczak What is a Good Domain Description?
50. Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
What About the Frame Problem?
Restriction on models
For all wRa w :
˜
e
˜
w
p implies p, if a p
w
™ '¬ ˜ ™ '¬ ˜ ¬¥
f
p implies p, if a p.
w w
™ A' ™ H' Q ¥
¬
f
New logical consequence
˜ ˜
® ' instead of '
PDL
Example ˜
loaded wait loaded
‘
‚ nŸ1
— 1 – 1 • ® ' e ¯… f
Ivan José Varzinczak What is a Good Domain Description?
51. Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
What About the Frame Problem?
The dependence-based approach. . .
solves the frame problem
subsumes Reiter’s regression [Demolombe et al. 2003]
does not entirely solve the ramification problem
e.g. shoot ¨ ±° walking
But is the only approach that works for domains with
actions with both indeterminate and indirect effects
[Castilho et al. 2002], [Herzig Varzinczak 2004]
Ivan José Varzinczak What is a Good Domain Description?
52. Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
What About the Frame Problem?
The dependence-based approach. . .
solves the frame problem
subsumes Reiter’s regression [Demolombe et al. 2003]
does not entirely solve the ramification problem
e.g. shoot ¨ ±° walking
But is the only approach that works for domains with
actions with both indeterminate and indirect effects
[Castilho et al. 2002], [Herzig Varzinczak 2004]
Ivan José Varzinczak What is a Good Domain Description?
53. Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
What About the Frame Problem?
The dependence-based approach. . .
solves the frame problem
subsumes Reiter’s regression [Demolombe et al. 2003]
does not entirely solve the ramification problem
e.g. shoot ¨ ±° walking
But is the only approach that works for domains with
actions with both indeterminate and indirect effects
[Castilho et al. 2002], [Herzig Varzinczak 2004]
Ivan José Varzinczak What is a Good Domain Description?
54. Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Outline
1 Introduction
Describing Action Theories
Unwanted Conclusions
2 Main Results
Decomposing Theories
Logical Modularity
Exploiting Modularity
Theory Change
3 Concluding Remarks
Ivan José Varzinczak What is a Good Domain Description?
55. Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Consistency and More
Postulates ˜
PC (Consistency):
‘
a a a ˜ ˜
• 1 – n1 — ‚1 ® '¬
PS (No implicit static laws): if
‘
a a a , then
‘
• 1 – n1 — ‚1 ® ' c c Ž'
PI (No implicit inexecutability laws):
˜
if
‘
a a a a
˜
,
• 1 – n1 — ‚1 ® ' e {²c
… ‚f
then a ‘
a
PDL — ‚1 ' e †²c
… gf
PX (No implicit executability laws):
˜
if a a a a ,
‘ ˜ r
• 1 – n1 — ‚1 … ²³'
c ® „ s
then a a
‘ r
PDL – n1 ' … tc „ s
Motivation
Better control what is going on
Ivan José Varzinczak What is a Good Domain Description?
56. Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Consistency and More
Postulates ˜
PC (Consistency):
‘
a a a ˜ ˜
• 1 – n1 — ‚1 ® '¬
PS (No implicit static laws): if
‘
a a a , then
‘
• 1 – n1 — ‚1 ® ' c c Ž'
PI (No implicit inexecutability laws):
˜
if
‘
a a a a
˜
,
• 1 – n1 — ‚1 ® ' e {²c
… ‚f
then a ‘
a
PDL — ‚1 ' e †²c
… gf
PX (No implicit executability laws):
˜
if a a a a ,
‘ ˜ r
• 1 – n1 — ‚1 … ²³'
c ® „ s
then a a
‘ r
PDL – n1 ' … tc „ s
Motivation
Better control what is going on
Ivan José Varzinczak What is a Good Domain Description?