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?

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?

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?

Introduction
Main Results
Concluding Remarks
Reasoning About Actions
Goal: inference tasks
Prediction
Explanation
Planning
Ivan José Varzinczak What is a Good Domain Description?

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?

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?

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?

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?

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?

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?

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?

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?

Introduction
Describing Action Theories
Main Results
Unwanted Conclusions
Concluding Remarks
Formalizing Domains
Several base formalisms
Situation calculus [McCarthy & Hayes, 1969]
s Holds loaded s Holds alive do shoot s
¢ £¡ ¢ ¤ ¨ ©§¥
¦ ¢ ¤ ¢ ¤ ¥
¥ ¥
Languages  ,   , etc. [Lifschitz et al., 90’s]
shoot causes alive if loaded ¨
Fluent calculus [Thielscher, 1995]
Poss shoot tk s
¢ ¢ ¤ ¥ ¦ §¥
State do shoot tk s
¢ ¢ ¢ ¤ ¥ ¥
 ¥ State s¢  ¥ dead tk ¢ !¥ alive tk¢ ¥
...
Ivan José Varzinczak What is a Good Domain Description?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
What About the Frame Problem?
In our example
If we had an action wait
loaded wait loaded
¡ ’ “ ¢¤
£” h
PDL
¤ ¤ ¤  ¦ i
Definition
Dependence relation [Castilho et al. 99]: Fª©•&$§¦¥
% D C ¨ % # " ˆ
Example
shoot Q «¥ alive, tease ¥ walking, tease ¬¥ alive
From wait Q «¥
¬ loaded conclude loaded e † wait loaded
f
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
What About the Frame Problem?
In our example
If we had an action wait
loaded wait loaded
¡ ’ “ ¢¤
£” h
PDL
¤ ¤ ¤  ¦ i
Definition
Dependence relation [Castilho et al. 99]: Fª©•&$§¦¥
% D C ¨ % # " ˆ
Example
shoot Q «¥ alive, tease ¥ walking, tease ¬¥ alive
From wait Q «¥
¬ loaded conclude loaded e † wait loaded
f
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
What About the Frame Problem?
In our example
If we had an action wait
loaded wait loaded
¡ ’ “ ¢¤
£” h
PDL
¤ ¤ ¤  ¦ i
Definition
Dependence relation [Castilho et al. 99]: Fª©•&$§¦¥
% D C ¨ % # " ˆ
Example
shoot Q «¥ alive, tease ¥ walking, tease ¬¥ alive
From wait Q «¥
¬ loaded conclude loaded e † wait loaded
f
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
What About the Frame Problem?
In our example
If we had an action wait
loaded wait loaded
¡ ’ “ ¢¤
£” h
PDL
¤ ¤ ¤  ¦ i
Definition
Dependence relation [Castilho et al. 99]: Fª©•&$§¦¥
% D C ¨ % # " ˆ
Example
shoot Q «¥ alive, tease ¥ walking, tease ¬¥ alive
From wait Q «¥
¬ loaded conclude loaded e † wait loaded
f
Ivan José Varzinczak What is a Good Domain Description?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Example
tease walking
l
walking alive
‘ e f 1
loaded shoot alive
) 0' •i4
• 1 ' 1
e † Q gf o
tease alive tease
r
– ) 0' „ s ‘i4
— 1 R0'
Q ) e †  gf 4
tease ¥ walking shoot 1 Q «¥ alive
˜
‘
tease ˜ tease tease alive
• 1 – n1 — ‚1 ® '
But alive
‘
'¬
! Postulate PS violated
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Example
tease walking
l
walking alive
‘ e f 1
loaded shoot alive
) 0' •i4
• 1 ' 1
e † Q gf o
tease alive tease
r
– ) 0' „ s ‘i4
— 1 R0'
Q ) e †  gf 4
tease ¥ walking shoot 1 Q «¥ alive
˜
‘
tease ˜ tease tease alive
• 1 – n1 — ‚1 ® '
But alive
‘
'¬
! Postulate PS violated
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Example
tease walking
l
walking alive
‘ e f 1
loaded shoot alive
) 0' •i4
• 1 ' 1
e † Q gf o
tease alive tease
r
– ) 0' „ s ‘i4
— 1 R0'
Q ) e †  gf 4
tease ¥ walking shoot 1 Q «¥ alive
˜
‘
tease ˜ tease tease alive
• 1 – n1 — ‚1 ® '
But alive
‘
'¬
! Postulate PS violated
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Example
tease walking
l
walking alive
‘ e f 1
loaded shoot alive
) 0' •i4
• 1 ' 1
e † Q gf o
tease alive tease
r
– ) 0' „ s ‘i4
— 1 R0'
Q ) e †  gf 4
tease ¥ walking shoot 1 Q «¥ alive
˜
‘
tease ˜ tease tease alive
• 1 – n1 — ‚1 ® '
But alive
‘
'¬
! Postulate PS violated
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Idea of algorithm
For each a
r
tc „ s
1 find e †‘c
e a entailed by the theory
 gf
if is consistent with
‘
2 ‘©´c
e c ‚
¸!8q(¨
¥ · µ ¶ µ ¢ is possibly an implicit law
Result: the set of all implicit static laws
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Idea of algorithm
For each a
r
tc „ s
1 find e †‘c
e a entailed by the theory
 gf
if is consistent with
‘
2 ‘©´c
e c ‚
¸!8q(¨
¥ · µ ¶ µ ¢ is possibly an implicit law
Result: the set of all implicit static laws
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Algorithm 1: Finding all implicit static laws induced by a
a a a
input: ‚•¸¹
¼ » º and ½ » ¾ F»
¿
À
a a a
output: imp* , the set of all implicit static laws of
º &•¸¹
¼ » º ½ €» ¾ 5»
¿
calls: NewCons PI PI ÇXFÃÁ
Æ Å Ä Â aXËÊqÂ
Ì Å Ä É È ÇqÂ
Å È
º imp* := Í
repeat
imp :=
º Í
a
for all a ¹do
¦ÏÈ
Î
Ñ Ò‚¿
Ð
½
a a a
for all do Ó Ô Ãf ¼
Õ
¾
a
a := Ö i
×È i a i Ø nuÙ
È Ú È Û Ü ¦Î Ä £Ý
Ñ
Ó Þ ¸f
a
a := Ä i Öi a i Ø ßuÙ
Ä Ú È Û Ü ¦Î Ä £Ý
Ñ
Ó Þ ¸f
for all NewCons a do à
Ñ
ÇF!á
Ö Ä Â Å Ø
if imp* a and li
º
Õ
º
Õ
׀–pÚ
Ö È » Èt‚Ø
à â » ä gÞ
ã å
Ñ
» à a æÀ li then
imp := imp a
Õ Þ ÇtéÉ Ø
º º ÈèÉÊÈqÂçnÚ
â Ö Å à â
imp* := imp* imp
Õ
º º º
until imp º Í UÆ
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Algorithm 1: Finding all implicit static laws induced by a
a a a
input: ‚•¸¹
¼ » º and ½ » ¾ F»
¿
À
a a a
output: imp* , the set of all implicit static laws of
º &•¸¹
¼ » º ½ €» ¾ 5»
¿
calls: NewCons PI PI ÇXFÃÁ
Æ Å Ä Â aXËÊqÂ
Ì Å Ä É È ÇqÂ
Å È
º imp* := Í
repeat
imp :=
º Í
a
for all a ¹do
¦ÏÈ
Î
Ñ Ò‚¿
Ð
½
a a a
for all do Ó Ô Ãf ¼
Õ
¾
a
a := Ö i
×È i a i Ø nuÙ
È Ú È Û Ü ¦Î Ä £Ý
Ñ
Ó Þ ¸f
a
a := Ä i Öi a i Ø ßuÙ
Ä Ú È Û Ü ¦Î Ä £Ý
Ñ
Ó Þ ¸f
for all NewCons a do à
Ñ
ÇF!á
Ö Ä Â Å Ø
if imp* a and li
º
Õ
º
Õ
׀–pÚ
Ö È » Èt‚Ø
à â » ä gÞ
ã å
Ñ
» à a æÀ li then
imp := imp a
Õ Þ ÇtéÉ Ø
º º ÈèÉÊÈqÂçnÚ
â Ö Å à â
imp* := imp* imp
Õ
º º º
until imp º Í UÆ
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Algorithm 1: Finding all implicit static laws induced by a
a a a
input: ‚•¸¹
¼ » º and ½ » ¾ F»
¿
À
a a a
output: imp* , the set of all implicit static laws of
º &•¸¹
¼ » º ½ €» ¾ 5»
¿
calls: NewCons PI PI ÇXFÃÁ
Æ Å Ä Â aXËÊqÂ
Ì Å Ä É È ÇqÂ
Å È
º imp* := Í
repeat
imp :=
º Í
a
for all a ¹do
¦ÏÈ
Î
Ñ Ò‚¿
Ð
½
a a a
for all do Ó Ô Ãf ¼
Õ
¾
a
a := Ö i
×È i a i Ø nuÙ
È Ú È Û Ü ¦Î Ä £Ý
Ñ
Ó Þ ¸f
a
a := Ä i Öi a i Ø ßuÙ
Ä Ú È Û Ü ¦Î Ä £Ý
Ñ
Ó Þ ¸f
for all NewCons a do à
Ñ
ÇF!á
Ö Ä Â Å Ø
if imp* a and li
º
Õ
º
Õ
׀–pÚ
Ö È » Èt‚Ø
à â » ä gÞ
ã å
Ñ
» à a æÀ li then
imp := imp a
Õ Þ ÇtéÉ Ø
º º ÈèÉÊÈqÂçnÚ
â Ö Å à â
imp* := imp* imp
Õ
º º º
until imp º Í UÆ
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Algorithm 1: Finding all implicit static laws induced by a
a a a
input: ‚•¸¹
¼ » º and ½ » ¾ F»
¿
À
a a a
output: imp* , the set of all implicit static laws of
º &•¸¹
¼ » º ½ €» ¾ 5»
¿
calls: NewCons PI PI ÇXFÃÁ
Æ Å Ä Â aXËÊqÂ
Ì Å Ä É È ÇqÂ
Å È
º imp* := Í
repeat
imp :=
º Í
a
for all a ¹do
¦ÏÈ
Î
Ñ Ò‚¿
Ð
½
a a a
for all do Ó Ô Ãf ¼
Õ
¾
a
a := Ö i
×È i a i Ø nuÙ
È Ú È Û Ü ¦Î Ä £Ý
Ñ
Ó Þ ¸f
a
a := Ä i Öi a i Ø ßuÙ
Ä Ú È Û Ü ¦Î Ä £Ý
Ñ
Ó Þ ¸f
for all NewCons a do à
Ñ
ÇF!á
Ö Ä Â Å Ø
if imp* a and li
º
Õ
º
Õ
׀–pÚ
Ö È » Èt‚Ø
à â » ä gÞ
ã å
Ñ
» à a æÀ li then
imp := imp a
Õ Þ ÇtéÉ Ø
º º ÈèÉÊÈqÂçnÚ
â Ö Å à â
imp* := imp* imp
Õ
º º º
until imp º Í UÆ
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Algorithm 1: Finding all implicit static laws induced by a
a a a
input: ‚•¸¹
¼ » º and ½ » ¾ F»
¿
À
a a a
output: imp* , the set of all implicit static laws of
º &•¸¹
¼ » º ½ €» ¾ 5»
¿
calls: NewCons PI PI ÇXFÃÁ
Æ Å Ä Â aXËÊqÂ
Ì Å Ä É È ÇqÂ
Å È
º imp* := Í
repeat
imp :=
º Í
a
for all a ¹do
¦ÏÈ
Î
Ñ Ò‚¿
Ð
½
a a a
for all do Ó Ô Ãf ¼
Õ
¾
a
a := Ö i
×È i a i Ø nuÙ
È Ú È Û Ü ¦Î Ä £Ý
Ñ
Ó Þ ¸f
a
a := Ä i Öi a i Ø ßuÙ
Ä Ú È Û Ü ¦Î Ä £Ý
Ñ
Ó Þ ¸f
for all NewCons a do à
Ñ
ÇF!á
Ö Ä Â Å Ø
if imp* a and li
º
Õ
º
Õ
׀–pÚ
Ö È » Èt‚Ø
à â » ä gÞ
ã å
Ñ
» à a æÀ li then
imp := imp a
Õ Þ ÇtéÉ Ø
º º ÈèÉÊÈqÂçnÚ
â Ö Å à â
imp* := imp* imp
Õ
º º º
until imp º Í UÆ
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Algorithm 1: Finding all implicit static laws induced by a
a a a
input: ‚•¸¹
¼ » º and ½ » ¾ F»
¿
À
a a a
output: imp* , the set of all implicit static laws of
º &•¸¹
¼ » º ½ €» ¾ 5»
¿
calls: NewCons PI PI ÇXFÃÁ
Æ Å Ä Â aXËÊqÂ
Ì Å Ä É È ÇqÂ
Å È
º imp* := Í
repeat
imp :=
º Í
a
for all a ¹do
¦ÏÈ
Î
Ñ Ò‚¿
Ð
½
a a a
for all do Ó Ô Ãf ¼
Õ
¾
a
a := Ö i
×È i a i Ø nuÙ
È Ú È Û Ü ¦Î Ä £Ý
Ñ
Ó Þ ¸f
a
a := Ä i Öi a i Ø ßuÙ
Ä Ú È Û Ü ¦Î Ä £Ý
Ñ
Ó Þ ¸f
for all NewCons a do à
Ñ
ÇF!á
Ö Ä Â Å Ø
if imp* a and li
º
Õ
º
Õ
׀–pÚ
Ö È » Èt‚Ø
à â » ä gÞ
ã å
Ñ
» à a æÀ li then
imp := imp a
Õ Þ ÇtéÉ Ø
º º ÈèÉÊÈqÂçnÚ
â Ö Å à â
imp* := imp* imp
Õ
º º º
until imp º Í UÆ
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Algorithm 1: Finding all implicit static laws induced by a
a a a
input: ‚•¸¹
¼ » º and ½ » ¾ F»
¿
À
a a a
output: imp* , the set of all implicit static laws of
º &•¸¹
¼ » º ½ €» ¾ 5»
¿
calls: NewCons PI PI ÇXFÃÁ
Æ Å Ä Â aXËÊqÂ
Ì Å Ä É È ÇqÂ
Å È
º imp* := Í
repeat
imp :=
º Í
a
for all a ¹do
¦ÏÈ
Î
Ñ Ò‚¿
Ð
½
a a a
for all do Ó Ô Ãf ¼
Õ
¾
a
a := Ö i
×È i a i Ø nuÙ
È Ú È Û Ü ¦Î Ä £Ý
Ñ
Ó Þ ¸f
a
a := Ä i Öi a i Ø ßuÙ
Ä Ú È Û Ü ¦Î Ä £Ý
Ñ
Ó Þ ¸f
for all NewCons a do à
Ñ
ÇF!á
Ö Ä Â Å Ø
if imp* a and li
º
Õ
º
Õ
׀–pÚ
Ö È » Èt‚Ø
à â » ä gÞ
ã å
Ñ
» à a æÀ li then
imp := imp a
Õ Þ ÇtéÉ Ø
º º ÈèÉÊÈqÂçnÚ
â Ö Å à â
imp* := imp* imp
Õ
º º º
until imp º Í UÆ
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Algorithm 1: Finding all implicit static laws induced by a
a a a
input: ‚•¸¹
¼ » º and ½ » ¾ F»
¿
À
a a a
output: imp* , the set of all implicit static laws of
º &•¸¹
¼ » º ½ €» ¾ 5»
¿
calls: NewCons PI PI ÇXFÃÁ
Æ Å Ä Â aXËÊqÂ
Ì Å Ä É È ÇqÂ
Å È
º imp* := Í
repeat
ºimp := Í
a
for all a ¹ ¦ÏÈ
Î do Ñ Ò‚¿
Ð
½
a a a
for all do Ó Ô Ãf ¼
Õ
¾
a
a := Ö ×È i i a i Ø nuÙ
È Ú È Û Ü ¦Î Ä £Ý
Ñ
Ó Þ ¸f
a
a :=
Ä i
Ö i a i
Ø ßuÙ
Ä Ú È Û Ü ¦Î Ä £Ý
Ñ
Ó Þ ¸f
for all NewCons a do à
Ñ
ÇF!á
Ö Ä Â Å Ø
if imp* a º and li Õ
º
Õ
׀–pÚ
Ö È » Èt‚Ø
à â » ä gÞ
ã å
Ñ
» à a æÀ li then
imp := imp a
Õ Þ ÇtéÉ Ø
º º ÈèÉÊÈqÂçnÚ
â Ö Å à â
imp* := imp* imp
Õ
º º º
until imp
º Í UÆ
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Example
tease walking
walking alive
Ü Ý »
loaded shoot alive
Ú ©ƒº
Æ Î ê ϖ» Þ
Æ ¼ »
Ü ¦Î â 5Ý ë
쩆½
¹ Ú Æ tease Ð ‚¿
p©di» Þ
â Ú Æ ¾ alive Ü ¦Î tease Þ •ä Ý
tease À walking shoot » â íÀ alive
For tease and tease walking:
r
„ s e f
NewCons walking j vî k ' alive: tease alive
e f
tease ¬¥ alive: Q alive e { tease alive Q ‚f
Hence alive Q e { tease
˜
 gf
˜
alive : alive
‘ ‘
Q ĠRPI
‚ „ ) 4  Ž' ¬ '¬
alive
‘
imp ) 0' 4
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Example
tease walking
walking alive
Ü Ý »
loaded shoot alive
Ú ©ƒº
Æ Î ê ϖ» Þ
Æ ¼ »
Ü ¦Î â 5Ý ë
¹ ©†½
Ú Æ tease Ð ‚¿
p©di» Þ
â Ú Æ ¾ alive Ü ¦Î tease Þ •ä Ý
tease À walking shoot » â íÀ alive
For tease and tease walking:
r
„ s e f
NewCons walking j vî k ' alive: tease alive
e f
tease ¬¥ alive: Q alive e { tease alive Q ‚f
Hence alive Q e { tease
˜
 gf
˜
alive : alive
‘ ‘
Q ĠRPI
‚ „ ) 4  Ž' ¬ '¬
alive
‘
imp ) 0' 4
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Example
tease walking
walking alive
Ü Ý »
loaded shoot alive
Ú ©ƒº
Æ Î ê ϖ» Þ
Æ ¼ »
Ü ¦Î â 5Ý ë
¹ ©†½
Ú Æ tease Ð ‚¿
p©di» Þ
â Ú Æ ¾ alive Ü ¦Î tease Þ •ä Ý
tease À walking shoot » â íÀ alive
For tease and tease walking:
r
„ s e f
NewCons walking j vî k ' alive: tease alive
e f
tease ¬¥ alive: Q alive e { tease alive Q ‚f
Hence alive Q e { tease
˜
 gf
˜
alive : alive
‘ ‘
Q ĠRPI
‚ „ ) 4  Ž' ¬ '¬
alive
‘
imp ) 0' 4
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Example
tease walking
walking alive
Ü Ý »
loaded shoot alive
Ú ©ƒº
Æ Î ê ϖ» Þ
Æ ¼ »
Ü ¦Î â 5Ý ë
¹ ©†½
Ú Æ tease Ð ‚¿
p©di» Þ
â Ú Æ ¾ alive Ü ¦Î tease Þ •ä Ý
tease À walking shoot » â íÀ alive
For tease and tease walking:
r
„ s e f
NewCons walking j vî k ' alive: tease alive
e f
tease ¬¥ alive: Q alive e { tease alive Q ‚f
Hence alive Q e { tease
˜
 gf
˜
alive : alive
‘ ‘
Q ĠRPI
‚ „ ) 4  Ž' ¬ '¬
alive
‘
imp ) 0' 4
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Example
tease walking
walking alive
Ü Ý »
loaded shoot alive
Ú ©ƒº
Æ Î ê ϖ» Þ
Æ ¼ »
Ü ¦Î â 5Ý ë
¹ ©†½
Ú Æ tease Ð ‚¿
p©di» Þ
â Ú Æ ¾ alive Ü ¦Î tease Þ •ä Ý
tease À walking shoot » â íÀ alive
For tease and tease walking:
r
„ s e f
NewCons walking j vî k ' alive: tease alive
e f
tease ¬¥ alive: Q alive e { tease alive Q ‚f
Hence alive Q e { tease
˜
 gf
˜
alive : alive
‘ ‘
Q ĠRPI
‚ „ ) 4  Ž' ¬ '¬
alive
‘
imp ) 0' 4
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Example
tease walking
walking alive
Ü Ý »
loaded shoot alive
Ú ©ƒº
Æ Î ê ϖ» Þ
Æ ¼ »
Ü ¦Î â 5Ý ë
¹ ©†½
Ú Æ tease Ð ‚¿
p©di» Þ
â Ú Æ ¾ alive Ü ¦Î tease Þ •ä Ý
tease À walking shoot » â íÀ alive
For tease and tease walking:
r
„ s e f
NewCons walking j vî k ' alive: tease alive
e f
tease ¬¥ alive: Q alive e { tease alive Q ‚f
Hence alive Q e { tease
˜
 gf
˜
alive : alive
‘ ‘
Q ĠRPI
‚ „ ) 4  Ž' ¬ '¬
alive
‘
imp ) 0' 4
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Example
tease walking
walking alive
Ü Ý »
loaded shoot alive
Ú ©ƒº
Æ Î ê ϖ» Þ
Æ ¼ »
Ü ¦Î â 5Ý ë
¹ ©†½
Ú Æ tease Ð ‚¿
p©di» Þ
â Ú Æ ¾ alive Ü ¦Î tease Þ •ä Ý
tease À walking shoot » â íÀ alive
For tease and tease walking:
r
„ s e f
NewCons walking j vî k ' alive: tease alive
e f
tease ¬¥ alive: Q alive e { tease alive Q ‚f
Hence alive Q e { tease
˜
 gf
˜
alive : alive
‘ ‘
Q ĠRPI
‚ „ ) 4  Ž' ¬ '¬
alive
‘
imp ) 0' 4
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Example (cont.)
Alternatives for repairing:
:= alive
‘ ‘
) ©I 4
add tease ¥ alive
weaken tease walking: alive
e f e † tease walking
f
weaken tease : alive tease
r r
„ s „ s
contraction of action theories (addressed later)
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Example (cont.)
Alternatives for repairing:
:= alive
‘ ‘
) ©I 4
add tease ¥ alive
weaken tease walking: alive
e f e † tease walking
f
weaken tease : alive tease
r r
„ s „ s
contraction of action theories (addressed later)
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Example (cont.)
Alternatives for repairing:
:= alive
‘ ‘
) ©I 4
add tease ¥ alive
weaken tease walking: alive
e f e † tease walking
f
weaken tease : alive tease
r r
„ s „ s
contraction of action theories (addressed later)
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Theorem
‘ r
a a a and satisfy Postulate PS iff
‘
.
• 1 – n1 — ‚1 s ¥ imp* ï ð'
Theorem
Let imp* be the output of Algorithm 1 on input
‘ ‘ r
a a a s
• 1 – n1 — ‚1
and . Then ¥
‘ r ‘
a a a has no implicit static law.
imp*
˜
I • 1 – n1 — ‚1 s
a a a
imp* .
‘ ‘
• 1 – n1 — ‚1 ñ ³® '
Corollary ˜ ˜
For all ,
‘
a a a iff
‘ ‘
.
Y `Xdòc
W V T • 1 – n1 — ‚1 ® ' c I imp* c Ž'
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Theorem
‘ r
a a a and satisfy Postulate PS iff
‘
.
• 1 – n1 — ‚1 s ¥ imp* ï ð'
Theorem
Let imp* be the output of Algorithm 1 on input
‘ ‘ r
a a a s
• 1 – n1 — ‚1
and . Then ¥
‘ r ‘
a a a has no implicit static law.
imp*
˜
I • 1 – n1 — ‚1 s
a a a
imp* .
‘ ‘
• 1 – n1 — ‚1 ñ ³® '
Corollary ˜ ˜
For all ,
‘
a a a iff
‘ ‘
.
Y `Xdòc
W V T • 1 – n1 — ‚1 ® ' c I imp* c Ž'
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Static Laws
Theorem
‘ r
a a a and satisfy Postulate PS iff
‘
.
• 1 – n1 — ‚1 s ¥ imp* ï ð'
Theorem
Let imp* be the output of Algorithm 1 on input
‘ ‘ r
a a a s
• 1 – n1 — ‚1
and . Then ¥
‘ r ‘
a a a has no implicit static law.
imp*
˜
I • 1 – n1 — ‚1 s
a a a
imp* .
‘ ‘
• 1 – n1 — ‚1 ñ ³® '
Corollary ˜ ˜
For all ,
‘
a a a iff
‘ ‘
.
Y `Xdòc
W V T • 1 – n1 — ‚1 ® ' c I imp* c Ž'
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Example
tease walking
walking alive
Ü Ý »
loaded shoot alive
Ú ©ƒº
Æ Î Æ Ï–» Þ
¼ ê »
Ü ¦Î â 5Ý ë
ìƒ`Bó½
» Í Æ ¾ Æ
˜
tease À walking shoot » â ôÀ alive
‘
tease tease alive
• 1 e õß' ˜
® f
‘
tease alive tease alive (from tease
‚f ˜ alive)
• 1 ® ' Q e † Q ¬¥
Thus
‘
tease ˜ tease tease alive tease
• 1 – n1 — ‚1 ® ' Q e †  gf
But
‘
tease alive tease
PDL
— ‚1 '¬ Q e †  gf
! Postulate PI violated
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Example
tease walking
walking alive
Ü Ý »
loaded shoot alive
Ú ©ƒº
Æ Î Æ Ï–» Þ
¼ ê »
Ü ¦Î â 5Ý ë
ìƒ`Bó½
» Í Æ ¾ Æ
˜
tease À walking shoot » â ôÀ alive
‘
tease tease alive
• 1 e õß' ˜
® f
‘
tease alive tease alive (from tease
‚f ˜ alive)
• 1 ® ' Q e † Q ¬¥
Thus
‘
tease ˜ tease tease alive tease
• 1 – n1 — ‚1 ® ' Q e †  gf
But
‘
tease alive tease
PDL
— ‚1 '¬ Q e †  gf
! Postulate PI violated
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Example
tease walking
walking alive
Ü Ý »
loaded shoot alive
Ú ©ƒº
Æ Î Æ Ï–» Þ
¼ ê »
Ü ¦Î â 5Ý ë
ìƒ`Bó½
» Í Æ ¾ Æ
˜
tease À walking shoot » â ôÀ alive
‘
tease tease alive
• 1 e õß' ˜
® f
‘
tease alive tease alive (from tease
‚f ˜ alive)
• 1 ® ' Q e † Q ¬¥
Thus
‘
tease ˜ tease tease alive tease
• 1 – n1 — ‚1 ® ' Q e †  gf
But
‘
tease alive tease
PDL
— ‚1 '¬ Q e †  gf
! Postulate PI violated
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Example
tease walking
walking alive
Ü Ý »
loaded shoot alive
Ú ©ƒº
Æ Î Æ Ï–» Þ
¼ ê »
Ü ¦Î â 5Ý ë
ìƒ`Bó½
» Í Æ ¾ Æ
˜
tease À walking shoot » â ôÀ alive
‘
tease tease alive
• 1 e õß' ˜
® f
‘
tease alive tease alive (from tease
‚f ˜ alive)
• 1 ® ' Q e † Q ¬¥
Thus
‘
tease ˜ tease tease alive tease
• 1 – n1 — ‚1 ® ' Q e †  gf
But
‘
tease alive tease
PDL
— ‚1 '¬ Q e †  gf
! Postulate PI violated
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Example
tease walking
walking alive
Ü Ý »
loaded shoot alive
Ú ©ƒº
Æ Î Æ Ï–» Þ
¼ ê »
Ü ¦Î â 5Ý ë
ìƒ`Bó½
» Í Æ ¾ Æ
˜
tease À walking shoot » â ôÀ alive
‘
tease tease alive
• 1 e õß' ˜
® f
‘
tease alive tease alive (from tease
‚f ˜ alive)
• 1 ® ' Q e † Q ¬¥
Thus
‘
tease ˜ tease tease alive tease
• 1 – n1 — ‚1 ® ' Q e †  gf
But
‘
tease alive tease
PDL
— ‚1 '¬ Q e †  gf
! Postulate PI violated
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Example
tease walking
walking alive
Ü Ý »
loaded shoot alive
Ú ©ƒº
Æ Î Æ Ï–» Þ
¼ ê »
Ü ¦Î â 5Ý ë
ìƒ`Bó½
» Í Æ ¾ Æ
˜
tease À walking shoot » â ôÀ alive
‘
tease tease alive
• 1 e õß' ˜
® f
‘
tease alive tease alive (from tease
‚f ˜ alive)
• 1 ® ' Q e † Q ¬¥
Thus
‘
tease ˜ tease tease alive tease
• 1 – n1 — ‚1 ® ' Q e †  gf
But
‘
tease alive tease
PDL
— ‚1 '¬ Q e †  gf
! Postulate PI violated
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Idea of algorithm
For each combination of effect laws
1 find inconsistent consequents
2 mark it as an implicit inexecutability
Result: the set of all implicit inexecutabilities
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Idea of algorithm
For each combination of effect laws
1 find inconsistent consequents
2 mark it as an implicit inexecutability
Result: the set of all implicit inexecutabilities
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Algorithm 2: Finding implicit inexecutability laws for a
input: a
‘ r
a and s ¥
• 1 — ‚1
output: imp a , the set of implicit inexecutability laws for a
—
calls: NewCons PI PI ‚çö
÷ j k ' ÷ ´U€j
‚ c ø §k c €j k
a :=
— imp ï
for all a a do
•
e ˆ •
a i a
ù a :=
§c f i i ñ c R) c aS e † ÷ df T •
e
4
a i a
ù a :=
(÷ f i i ñ ÷ ì) c ÃS e † ÷ df T •
e
4
for all NewCons a do T òú î ª‚j
ù ÷ k f
if li a li and a a then
‘
a
ü
û ú UT 1 ¬¥ — ‚1 ‘€j
ù c f (ƒ‚
ú Q k e †  gf
a := a a
a
imp imp — — ‘€iPI
ù c j ) f ªU‚
ú Q k e †  gf 4
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Algorithm 2: Finding implicit inexecutability laws for a
input: a
‘ r
a and s ¥
• 1 — ‚1
output: imp a , the set of implicit inexecutability laws for a
—
calls: NewCons PI PI ‚çö
÷ j k ' ÷ ´U€j
‚ c ø §k c €j k
a :=
— imp ï
for all a a do
•
e ˆ •
a i a
ù a :=
§c f i i ñ c R) c aS e † ÷ df T •
e
4
a i a
ù a :=
(÷ f i i ñ ÷ ì) c ÃS e † ÷ df T •
e
4
for all NewCons a do T òú î ª‚j
ù ÷ k f
if li a li and a a then
‘
a
ü
û ú UT 1 ¬¥ — ‚1 ‘€j
ù c f (ƒ‚
ú Q k e †  gf
a := a a
a
imp imp — — ‘€iPI
ù c j ) f ªU‚
ú Q k e †  gf 4
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Algorithm 2: Finding implicit inexecutability laws for a
input: a
‘ r
a and s ¥
• 1 — ‚1
output: imp a , the set of implicit inexecutability laws for a
—
calls: NewCons PI PI ‚çö
÷ j k ' ÷ ´U€j
‚ c ø §k c €j k
a :=
— imp ï
for all a a do
•
e ˆ •
a i a
ù a :=
§c f i i ñ c R) c aS e † ÷ df T •
e
4
a i a
ù a :=
(÷ f i i ñ ÷ ì) c ÃS e † ÷ df T •
e
4
for all NewCons a do T òú î ª‚j
ù ÷ k f
if li a li and a a then
‘
a
ü
û ú UT 1 ¬¥ — ‚1 ‘€j
ù c f (ƒ‚
ú Q k e †  gf
a := a a
a
imp imp — — ‘€iPI
ù c j ) f ªU‚
ú Q k e †  gf 4
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Algorithm 2: Finding implicit inexecutability laws for a
input: a
‘ r
a and s ¥
• 1 — ‚1
output: imp a , the set of implicit inexecutability laws for a
—
calls: NewCons PI PI ‚çö
÷ j k ' ÷ ´U€j
‚ c ø §k c €j k
a :=
— imp ï
for all a a do
•
e ˆ •
a i a
ù a :=
§c f i i ñ c R) c aS e † ÷ df T •
e
4
a i a
ù a :=
(÷ f i i ñ ÷ ì) c ÃS e † ÷ df T •
e
4
for all NewCons a do T òú î ª‚j
ù ÷ k f
if li a li and a a then
‘
a
ü
û ú UT 1 ¬¥ — ‚1 ‘€j
ù c f (ƒ‚
ú Q k e †  gf
a := a a
a
imp imp — — ‘€iPI
ù c j ) f ªU‚
ú Q k e †  gf 4
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Algorithm 2: Finding implicit inexecutability laws for a
input: a
‘ r
a and s ¥
• 1 — ‚1
output: imp a , the set of implicit inexecutability laws for a
—
calls: NewCons PI PI ‚çö
÷ j k ' ÷ ´U€j
‚ c ø §k c €j k
a :=
— imp ï
for all a a do
•
e ˆ •
a i a
ù a :=
§c f i i ñ c R) c aS e † ÷ df T •
e
4
a i a
ù a :=
(÷ f i i ñ ÷ ì) c ÃS e † ÷ df T •
e
4
for all NewCons a do T òú î ª‚j
ù ÷ k f
if li a li and a a then
‘
a
ü
û ú UT 1 ¬¥ — ‚1 ‘€j
ù c f (ƒ‚
ú Q k e †  gf
a := a a
a
imp imp — — ‘€iPI
ù c j ) f ªU‚
ú Q k e †  gf 4
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Algorithm 2: Finding implicit inexecutability laws for a
input: a
‘ r
a and s ¥
• 1 — ‚1
output: imp a , the set of implicit inexecutability laws for a
—
calls: NewCons PI PI ‚çö
÷ j k ' ÷ ´U€j
‚ c ø §k c €j k
a :=
— imp ï
for all a a do
•
e ˆ •
a i a
ù a :=
§c f i i ñ c R) c aS e † ÷ df T •
e
4
a i a
ù a :=
(÷ f i i ñ ÷ ì) c ÃS e † ÷ df T •
e
4
for all NewCons a do T òú î ª‚j
ù ÷ k f
if li a li and a a then
‘
a
ü
û ú UT 1 ¬¥ — ‚1 ‘€j
ù c f (ƒ‚
ú Q k e †  gf
a := a a
a
imp imp — — ‘€iPI
ù c j ) f ªU‚
ú Q k e †  gf 4
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Algorithm 2: Finding implicit inexecutability laws for a
input: a
‘ r
a and s ¥
• 1 — ‚1
output: imp a , the set of implicit inexecutability laws for a
—
calls: NewCons PI PI ‚çö
÷ j k ' ÷ ´U€j
‚ c ø §k c €j k
a :=
— imp ï
for all a a do
•
e ˆ •
a i a
ù a :=
§c f i i ñ c R) c aS e † ÷ df T •
e
4
a i a
ù a :=
(÷ f i i ñ ÷ ì) c ÃS e † ÷ df T •
e
4
for all NewCons a do T òú î ª‚j
ù ÷ k f
if li a li and a a then
‘
a
ü
û ú UT 1 ¬¥ — ‚1 ‘€j
ù c f (ƒ‚
ú Q k e †  gf
a := a a
a
imp imp — — ‘€iPI
ù c j ) f ªU‚
ú Q k e †  gf 4
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Example
tease walking
walking alive
Ü Ý »
loaded shoot alive
Ú ©ƒº
Æ Î ê ϖ» Þ
Æ ¼ »
Ü ¦Î â 5Ý ë
ìUdg†½
» Í Æ ¾ Æ tease À walking shoot » â ôÀ alive
For action tease:
NewCons walking j vî k ' alive: tease alive
e f
tease ¬¥ alive: Q alive e { tease alive Q ‚f
Then alive Q
˜
e † tease  gf
‘
tease alive tease
PDL
— ‚1 '¬ Q e †  gf
tease alive tease
— imp R0'
Q ) e †  ‚f 4
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Example
tease walking
walking alive
Ü Ý »
loaded shoot alive
Ú ©ƒº
Æ Î ê ϖ» Þ
Æ ¼ »
Ü ¦Î â 5Ý ë
ìUdg†½
» Í Æ ¾ Æ tease À walking shoot » â ôÀ alive
For action tease:
NewCons walking j vî k ' alive: tease alive
e f
tease ¬¥ alive: Q alive e { tease alive Q ‚f
Then alive Q
˜
e † tease  gf
‘
tease alive tease
PDL
— ‚1 '¬ Q e †  gf
tease alive tease
— imp R0'
Q ) e †  ‚f 4
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Example
tease walking
walking alive
Ü Ý »
loaded shoot alive
Ú ©ƒº
Æ Î ê ϖ» Þ
Æ ¼ »
Ü ¦Î â 5Ý ë
ìUdg†½
» Í Æ ¾ Æ tease À walking shoot » â ôÀ alive
For action tease:
NewCons walking j vî k ' alive: tease alive
e f
tease ¬¥ alive: Q alive e { tease alive Q ‚f
Then alive Q
˜
e † tease  gf
‘
tease alive tease
PDL
— ‚1 '¬ Q e †  gf
tease alive tease
— imp R0'
Q ) e †  ‚f 4
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Example
tease walking
walking alive
Ü Ý »
loaded shoot alive
Ú ©ƒº
Æ Î ê ϖ» Þ
Æ ¼ »
Ü ¦Î â 5Ý ë
ìUdg†½
» Í Æ ¾ Æ tease À walking shoot » â ôÀ alive
For action tease:
NewCons walking j vî k ' alive: tease alive
e f
tease ¬¥ alive: Q alive e { tease alive Q ‚f
Then alive Q
˜
e † tease  gf
‘
tease alive tease
PDL
— ‚1 '¬ Q e †  gf
tease alive tease
— imp R0'
Q ) e †  ‚f 4
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Example
tease walking
walking alive
Ü Ý »
loaded shoot alive
Ú ©ƒº
Æ Î ê ϖ» Þ
Æ ¼ »
Ü ¦Î â 5Ý ë
ìUdg†½
» Í Æ ¾ Æ tease À walking shoot » â ôÀ alive
For action tease:
NewCons walking j vî k ' alive: tease alive
e f
tease ¬¥ alive: Q alive e { tease alive Q ‚f
Then alive Q
˜
e † tease  gf
‘
tease alive tease
PDL
— ‚1 '¬ Q e †  gf
tease alive tease
— imp R0'
Q ) e †  ‚f 4
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Example
tease walking
walking alive
Ü Ý »
loaded shoot alive
Ú ©ƒº
Æ Î ê ϖ» Þ
Æ ¼ »
Ü ¦Î â 5Ý ë
ìUdg†½
» Í Æ ¾ Æ tease À walking shoot » â ôÀ alive
For action tease:
NewCons walking j vî k ' alive: tease alive
e f
tease ¬¥ alive: Q alive e { tease alive Q ‚f
Then alive Q
˜
e † tease  gf
‘
tease alive tease
PDL
— ‚1 '¬ Q e †  gf
tease alive tease
— imp R0'
Q ) e †  ‚f 4
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Example
tease walking
walking alive
Ü Ý »
loaded shoot alive
Ú ©ƒº
Æ Î ê ϖ» Þ
Æ ¼ »
Ü ¦Î â 5Ý ë
ìUdg†½
» Í Æ ¾ Æ tease À walking shoot » â ôÀ alive
For action tease:
NewCons walking j vî k ' alive: tease alive
e f
tease ¬¥ alive: Q alive e { tease alive Q ‚f
Then alive Q
˜
e † tease  gf
‘
tease alive tease
PDL
— ‚1 '¬ Q e †  gf
tease alive tease
— imp R0'
Q ) e †  ‚f 4
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
No Implicit Inexecutability Laws
Theorem
If a
‘ r
a aands satisfy Postulate PS, then
¥
• 1 – n1 — ‚1
‘ r
a a a s and satisfy Postulate PI iff imp
¥ ï ð' .
• 1 – n1 — ‚1 —
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Generalizing the Postulates
Postulate
PS* (No implicit static laws):
˜ ˜
if , then
‘ ‘
PDL
‚ýnŸ1
— 1 – 1 • c ³'
® ' c
Theorem
‘ r
and s satisfy PS* iff
¥
‘ r
a a a s and ¥
‚ nŸ1
— 1 – 1 • • 1 – n1 — ‚1
satisfy PS for all a . &$UT
% # "
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Generalizing the Postulates
Postulate
PS* (No implicit static laws):
˜ ˜
if , then
‘ ‘
PDL
‚ýnŸ1
— 1 – 1 • c ³'
® ' c
Theorem
‘ r
and s satisfy PS* iff
¥
‘ r
a a a s and ¥
‚ nŸ1
— 1 – 1 • • 1 – n1 — ‚1
satisfy PS for all a . &$UT
% # "
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Generalizing the Postulates
Postulate ˜
PC* (Logical consistency):
‘
‚ýnŸ1
— 1 – 1 • ® '¬ 
Theorem
If and satisfy PS*, then and
‘ r ‘ r
‚ nŸ1
— 1 – 1 • s ¥ ‚tnŸ1
— 1 – 1 • s ¥
satisfy PC* iff
‘ r
a a a and
s ¥ satisfies PC for all a &$UT
% # " .
• 1 – n1 — ‚1
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Generalizing the Postulates
Postulate ˜
PC* (Logical consistency):
‘
‚ýnŸ1
— 1 – 1 • ® '¬ 
Theorem
If and satisfy PS*, then and
‘ r ‘ r
‚ nŸ1
— 1 – 1 • s ¥ ‚tnŸ1
— 1 – 1 • s ¥
satisfy PC* iff
‘ r
a a a and
s ¥ satisfies PC for all a &$UT
% # " .
• 1 – n1 — ‚1
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Generalizing the Postulates
Postulate
PI* (No implicit inexecutability laws):
˜ ˜
if a , then a
‘ ‘
PDL
‚ nŸ1
— 1 – 1 • e †tþ'
c ®  ‚f — ‚1 ' e †tc
 gf
Theorem
Let and satisfy PS*. and
‘ r ‘ r
‚ nŸ1
— 1 – 1 • s ¥ ‚ nŸ1
— 1 – 1 • s ¥
satisfy PI* iff
‘ r
a a a ands ¥ satisfy PI for all a &$dT
% # " .
• 1 – n1 — ‚1
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Generalizing the Postulates
Postulate
PI* (No implicit inexecutability laws):
˜ ˜
if a , then a
‘ ‘
PDL
‚ nŸ1
— 1 – 1 • e †tþ'
c ®  ‚f — ‚1 ' e †tc
 gf
Theorem
Let and satisfy PS*. and
‘ r ‘ r
‚ nŸ1
— 1 – 1 • s ¥ ‚ nŸ1
— 1 – 1 • s ¥
satisfy PI* iff
‘ r
a a a ands ¥ satisfy PI for all a &$dT
% # " .
• 1 – n1 — ‚1
Ivan José Varzinczak What is a Good Domain Description?

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?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Reasoning Modularly
If and satisfy Postulate PS*, then
‘ r
‚ nŸ1
— 1 – 1 • s ¥
Theorem ˜ ˜
iff .
‘ ‘
‚ nŸ1
— 1 – 1 • ® '   Ž'
Theorem ˜ ˜
‘
a iff
‘
a a a .
‚ nŸ1
— 1 – 1 • ® ' e †tc
÷ df • 1 — ‚1 ® ' e †tc
÷ qf
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Reasoning Modularly
If and satisfy Postulate PS*, then
‘ r
‚ nŸ1
— 1 – 1 • s ¥
Theorem ˜ ˜
iff .
‘ ‘
‚ nŸ1
— 1 – 1 • ® '   Ž'
Theorem ˜ ˜
‘
a iff
‘
a a a .
‚ nŸ1
— 1 – 1 • ® ' e †tc
÷ df • 1 — ‚1 ® ' e †tc
÷ qf
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Reasoning Modularly
If and satisfy Postulate PS*, then
‘ r
‚ nŸ1
— 1 – 1 • s ¥
Theorem ˜ ˜
a iff a a .
‘ r ‘ r
‚ nŸ1
— 1 – 1 • ® ' tc „ s – n1 ® ' tc „ s
Corollary
PX is a consequence of PS.
Theorem
If and satisfy Postulates PS* and PI*, then
‘ r ˜ ˜
‚ nŸ1
— 1 – 1 • s ¥
‘
a iff a ‘
a .
‚ nŸ1
— 1 – 1 • ® ' e †tc
 gf — ‚1 ® ' e †tc
 ‚f
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Reasoning Modularly
If and satisfy Postulate PS*, then
‘ r
‚ nŸ1
— 1 – 1 • s ¥
Theorem ˜ ˜
a iff a a .
‘ r ‘ r
‚ nŸ1
— 1 – 1 • ® ' tc „ s – n1 ® ' tc „ s
Corollary
PX is a consequence of PS.
Theorem
If and satisfy Postulates PS* and PI*, then
‘ r ˜ ˜
‚ nŸ1
— 1 – 1 • s ¥
‘
a iff a ‘
a .
‚ nŸ1
— 1 – 1 • ® ' e †tc
 gf — ‚1 ® ' e †tc
 ‚f
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Reasoning Modularly
If and satisfy Postulate PS*, then
‘ r
‚ nŸ1
— 1 – 1 • s ¥
Theorem ˜ ˜
a iff a a .
‘ r ‘ r
‚ nŸ1
— 1 – 1 • ® ' tc „ s – n1 ® ' tc „ s
Corollary
PX is a consequence of PS.
Theorem
If and satisfy Postulates PS* and PI*, then
‘ r ˜ ˜
‚ nŸ1
— 1 – 1 • s ¥
‘
a iff a ‘
a .
‚ nŸ1
— 1 – 1 • ® ' e †tc
 gf — ‚1 ® ' e †tc
 ‚f
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Reasoning Modularly
If and satisfy Postulate PS*, then
‘ r
‚ nŸ1
— 1 – 1 • s ¥
Theorem ˜
a1 an iff
‘ ˜
‚ nŸ1
— 1 – 1 • ® ' e †tc
ÿ3331
1 2 2 2 ÷ df
‘
a1 ¢¢¢
¡ ¡ ¡ an a1 ¢¢¢
¡ ¡ ¡ an a1 an .
• 1 — ‚1 ® ' e †tc
ÿ3331
1 2 2 2 ÷ df
Theorem ˜
a1 an iff
‘ r ˜
‚ nŸ1
— 1 – 1 • ® ' tc ÿ3331
1 2 2 2 ÷ €s
a1 an a1 an a1 an a1 an .
‘ r
¢¢¢
¡ ¡ ¡ ¢¢¢
¡ ¡ ¡ ¢¢¢
¡ ¡ ¡
• 1 – n1 — ‚1 ® ' tc ÿ3331
1 2 2 2 ÷ €s
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Reasoning Modularly
If and satisfy Postulate PS*, then
‘ r
‚ nŸ1
— 1 – 1 • s ¥
Theorem ˜
a1 an iff
‘ ˜
‚ nŸ1
— 1 – 1 • ® ' e †tc
ÿ3331
1 2 2 2 ÷ df
‘
a1 ¢¢¢
¡ ¡ ¡ an a1 ¢¢¢
¡ ¡ ¡ an a1 an .
• 1 — ‚1 ® ' e †tc
ÿ3331
1 2 2 2 ÷ df
Theorem ˜
a1 an iff
‘ r ˜
‚ nŸ1
— 1 – 1 • ® ' tc ÿ3331
1 2 2 2 ÷ €s
a1 an a1 an a1 an a1 an .
‘ r
¢¢¢
¡ ¡ ¡ ¢¢¢
¡ ¡ ¡ ¢¢¢
¡ ¡ ¡
• 1 – n1 — ‚1 ® ' tc ÿ3331
1 2 2 2 ÷ €s
Ivan José Varzinczak What is a Good Domain Description?

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?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Another Tale
Example
If the switch is up, the room is lit up
up ¦ light
Toggling the switch changes its position
up toggle up
h
¨ ¦ i
up toggle up
h
¦ ¨ di
It is always possible to toggle the switch
toggle
w
y x
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
The Need for Theory Change
You observe that. . .
even if the switch is up the light is off.
in a blackout, you do not succeed to switch the light on.
despite your efforts you do not manage to toggle the
switch.
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Motivation
Contracting by a static law
You observe that even if the switch is up the light is off
Static law up light must be given up
Can we just contract the static laws of ?
‘
May not be enough: side effects!
Conflict with ½
The contracted law may be an implicit one
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Motivation
Contracting by a static law
You observe that even if the switch is up the light is off
Static law up light must be given up
Can we just contract the static laws of ?
‘
May not be enough: side effects!
Conflict with ½
The contracted law may be an implicit one
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Motivation
Contracting by an effect law
During a blackout you do not succeed to switch the light on
Effect law up
Q e † toggle light must be given up
f
Important issue: give up as few as possible
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Motivation
Contracting by an effect law
During a blackout you do not succeed to switch the light on
Effect law up
Q e † toggle light must be given up
f
Important issue: give up as few as possible
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Motivation
Contracting by an executability law
Despite your efforts you do not manage to toggle the switch
Executability law up toggle must be given up
r
„ s
Side effects?
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Semantics
Playing with models
toggle
£
up q
£
light up light
s
toggle
Semantical contraction produces a set of models:
W R W R
¥ § ¨v
¤ ¦ ¤ ©
~  ~  ©
    
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Semantics
Playing with models
toggle
£
up q
£
light up light
s
toggle
Semantical contraction produces a set of models:
W R W R
¥ § ¨v
¤ ¦ ¤ ©
~  ~  ©
    
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Semantics
Contracting static laws
W R
r
1 
up
s
light ! "'
Intuition: add some up Q U‚ light-worlds to W
toggle
£
up q
£
light up light
s
toggle
up r ×s
light
Don’t add new arrows to R!
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Semantics
Contracting static laws
W R
r
1 
up
s
light ! "'
Intuition: add some up Q U‚ light-worlds to W
toggle
£
up q
£
light up light
s
toggle
up r ×s
light
Don’t add new arrows to R!
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Semantics
Contracting static laws
Rely on any belief change operator for classical logic
Say PMA, . . .
W R W R , where
r r
1  s
up light ) 0' 1 e 4 s e
W ·  W PMA up ¦ light
R ·  R ˜
N.B.: W R toggle
r r
1 e ' és e
¬ „ s
Executability laws to be weakened!
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Semantics
Contracting static laws
Rely on any belief change operator for classical logic
Say PMA, . . .
W R W R , where
r r
1  s
up light ) 0' 1 e 4 s e
W ·  W PMA up ¦ light
R ·  R ˜
N.B.: W R toggle
r r
1 e ' és e
¬ „ s
Executability laws to be weakened!
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Semantics
Contracting static laws
Rely on any belief change operator for classical logic
Say PMA, . . .
W R W R , where
r r
1  s
up light ) 0' 1 e 4 s e
W ·  W PMA up ¦ light
R ·  R ˜
N.B.: W R toggle
r r
1 e ' és e
¬ „ s
Executability laws to be weakened!
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Semantics
Contracting effect laws
W R
r
1 # s
up $ % toggle light&
! "'
Intuition: add some arrows from up-worlds to Q
Q light-worlds
toggle
toggle
£
up q
£
light up light
s
toggle
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Semantics
Contracting effect laws
W R
r
1 # s
up $ % toggle light &
' ˜
W R Ra Ra w w w up
r
) 1 I S §s e e ˆ j i) 1 k e S Q Ž' 4 h4
Problems:
Don’t link light-worlds
Don’t link all light-worlds ¨
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Semantics
Contracting effect laws
W R
r
1 # s
up $ % toggle light &
' ˜
W R Ra Ra w w w up
r
) 1 I S §s e e ˆ j i) 1 k e S Q Ž' 4 h4
Problems:
Don’t link light-worlds
Don’t link all light-worlds ¨
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Semantics
Contracting executability laws
W R
r
1 up
 s
' ( toggle 0 1)
! "'
Intuition: delete some arrows leaving up-worlds
toggle
£
up q
£
light up light
s
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Semantics
Contracting executability laws
W R
r
1 up
 s
' ( toggle 0 1)
'
˜
W R Ra Ra w w wRa w and w up
r
) 1 ø S §s e e iðˆ
j ) 1 k e S e ' 4 h4
N.B.: if there is no up-world, then contraction is not
successful!
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Semantics
Contracting executability laws
W R
r
1 up
 s
' ( toggle 0 1)
'
˜
W R Ra Ra w w wRa w and w up
r
) 1 ø S §s e e iðˆ
j ) 1 k e S e ' 4 h4
N.B.: if there is no up-world, then contraction is not
successful!
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Syntax
Domain descriptions
Simplification:
‘ r
nŸ1
– 1 • s
Resulting action theory
¡ w ’ “ ¡ w ’ “
¤ ¤ 24
3x  ¤ · ¤ · x ·
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Syntax
Contracting static laws
, where
‘ r ‘ r
nŸ1
– 1 •  s
up light ' – Ÿ1 e
1 • s e
PMA up light light up
¡ ¡
·  ¦ 5 6 ¦ 7
“
· 
up light toggle toggle
w w “
¨ €ž5
¢ ¢ 8 ¥ ‘X϶
¦ ¥ µ ¦ du@€x
µ 9 y A B€x
y 7
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Syntax
Contracting static laws
, where
‘ r ‘ r
nŸ1
– 1 •  s
up light ' – Ÿ1 e
1 • s e
PMA up light light up
¡ ¡
·  ¦ 5 6 ¦ 7
“
· 
up light toggle toggle
w w “
¨ €ž5
¢ ¢ 8 ¥ ‘X϶
¦ ¥ µ ¦ du@€x
µ 9 y A B€x
y 7
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Syntax
Contracting effect laws
, where
‘ r ‘ r
nŸ1
– 1 • # s
up $ ( toggle light
&
' • 1 – n1 e s
up toggle toggle
’ h h ’
· žC
¢ 5 §!¶
¦ ¥ µ ¦ ´uFEi
µ 9 D A GEi
D 7
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Contraction: Syntax
Contracting executability laws
, where
‘ r ‘ r
nŸ1
– 1 • up
 s
' % toggle 0 H)
' – Ÿ1
1 • s e
up toggle toggle
“ w w “
· gžC
¨ ¢ 5 !¶
¦ ¥ µ ¦ du@x
µ 9 y A B€x
y 7
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Soundness
Theorem ˜ ˜
If W R , then W R .
r ‘ r ‘ r
1 s ' ‚ • ‚ – 1 I s ' nŸ1
– 1 • I s
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Incompleteness
Example
, p a , a
‘ r
ï ð' • ) 0' e †  gf 4 – ) 0' „ s 4
Unique model: W R p p p
r r
1 ' Es Rh)
Q ) Rmi) ih4
Q ) j 1 4 Q R) i41 s pR4
4 k
p a p a .
‘ r r r
nŸ1
– 1 • p
 s
' ( a 0 H)
' ï ) 1 e †  ‚f Q R) i4
1 ˜ „ s s 4
Syntactically: successful, as p a .
‘ r
PDL
nŸ1
– 1 • e '¬ „ s
Semantically: contraction is unsuccessful!
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Incompleteness
Example
, p a , a
‘ r
ï ð' • ) 0' e †  gf 4 – ) 0' „ s 4
Unique model: W R p p p
r r
1 ' Es Rh)
Q ) Rmi) ih4
Q ) j 1 4 Q R) i41 s pR4
4 k
p a p a .
‘ r r r
nŸ1
– 1 • p
 s
' ( a 0 H)
' ï ) 1 e †  ‚f Q R) i4
1 ˜ „ s s 4
Syntactically: successful, as p a .
‘ r
PDL
nŸ1
– 1 • e '¬ „ s
Semantically: contraction is unsuccessful!
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Incompleteness
Example
, p a , a
‘ r
ï ð' • ) 0' e †  gf 4 – ) 0' „ s 4
Unique model: W R p p p
r r
1 ' Es Rh)
Q ) Rmi) ih4
Q ) j 1 4 Q R) i41 s pR4
4 k
p a p a .
‘ r r r
nŸ1
– 1 • p
 s
' ( a 0 H)
' ï ) 1 e †  ‚f Q ) i4
1 ˜ „ s s 4
Syntactically: successful, as p a .
‘ r
PDL
nŸ1
– 1 • e '¬ „ s
Semantically: contraction is unsuccessful!
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Incompleteness
Example
, p a , a
‘ r
ï ð' • ) 0' e †  gf 4 – ) 0' „ s 4
Unique model: W R p p p
r r
1 ' Es Rh)
Q ) Rmi) ih4
Q ) j 1 4 Q R) i41 s pR4
4 k
p a p a .
‘ r r r
nŸ1
– 1 • p
 s
' ( a 0 H)
' ï ) 1 e †  ‚f Q R) i4
1 ˜ „ s s 4
Syntactically: successful, as p a .
‘ r
PDL
nŸ1
– 1 • e '¬ „ s
Semantically: contraction is unsuccessful!
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Incompleteness
Example
, p a , a
‘ r
ï ð' • ) 0' e †  gf 4 – ) 0' „ s 4
Unique model: W R p p p
r r
1 ' Es Rh)
Q ) Rmi) ih4
Q ) j 1 4 Q R) i41 s pR4
4 k
p a p a .
‘ r r r
nŸ1
– 1 • p
 s
' ( a 0 H)
' ï ) 1 e †  ‚f Q R) i4
1 ˜ „ s s 4
Syntactically: successful, as p a .
‘ r
PDL
nŸ1
– 1 • e '¬ „ s
Semantically: contraction is unsuccessful!
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Completeness: Modularity
Theorem ˜
If and satisfy Postulate PS*, then iff
‘ r ˜ ˜ ‘ r
nŸ1
– 1 • s ¥ nŸ1
– 1 • I s P Q'
W R , for every W R such that W R .
r r r ‘
1 I s P Q' 1 s 1 s ' ‚ • ‚ –
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Outlook: Semantics of Revision
Levi identity
Revise by glued e { toggle  gf amounts to
Contract by glued toggle
h
1 ¢ (¨ ¦ uqi
¥ p
Expand by glued toggle
h
2 ¦ p qi
Problem: we can contract by domain laws only
glued glued toggletoggle
h w
¢ (¨ ¦ Suqi
R ¥ p ¢ ¶ u€x
¥ y
not defined
¡ w ’ “
glued toggle
¤ ¤ 2 3x
What is the negation of
U VT X HW
an effect law?
an executability law?
Ivan José Varzinczak What is a Good Domain Description?

Decomposing Theories
Introduction
Logical Modularity
Main Results
Exploiting Modularity
Concluding Remarks
Theory Change
Outlook: Semantics of Revision
Levi identity
Revise by glued e { toggle  gf amounts to
Contract by glued toggle
h
1 ¢ (¨ ¦ uqi
¥ p
Expand by glued toggle
h
2 ¦ p qi
Problem: we can contract by domain laws only
glued glued toggletoggle
h w
¢ (¨ ¦ Suqi
R ¥ p ¢ ¶ u€x
¥ y
not defined
¡ w ’ “
glued toggle
¤ ¤ 2 3x
What is the negation of
U VT X HW
an effect law?
an executability law?
Ivan José Varzinczak What is a Good Domain Description?

Introduction
Main Results
Concluding Remarks
Related Work
Modularity
[Pirri & Reiter 1999]: deterministic actions without
ramifications in Situation Calculus
[Amir 2000]: object-oriented concepts in Situation Calculus
[Zhang et al. 2002]: EPDL approach/normal form
[Lang et al. 2003]: computational complexity
[Kakas et al. 2005]: elaboration tolerance, concurrent
actions
[Ghilardi, Lutz & Wolter, KR’06]: uniform interpolation and
conservative extensions in ` a%
Y
Ivan José Varzinczak What is a Good Domain Description?

Introduction
Main Results
Concluding Remarks
Related Work
Theory change
[Li& Pereira 1996]: motivations
[Liberatore 2000]: meta-results
[Eiter et al. 2005/06]: update in action languages
Ivan José Varzinczak What is a Good Domain Description?

Introduction
Main Results
Concluding Remarks
Summary
Claim
Consistency is not enough to evaluate a domain
description
The dynamic part of an action theory should not influence
the non-dynamic one (otherwise: problems)
Contribution
Fine-grained postulates of modularity
Algorithms to check/give hints on modularity
Satisfaction of modularity
More efficient reasoning
Important for updating theories [Herzig et al. ECAI’06]
Our results apply to every approach allowing for , ,
‘
• –
and —
Ivan José Varzinczak What is a Good Domain Description?

Introduction
Main Results
Concluding Remarks
Summary
Claim
Consistency is not enough to evaluate a domain
description
The dynamic part of an action theory should not influence
the non-dynamic one (otherwise: problems)
Contribution
Fine-grained postulates of modularity
Algorithms to check/give hints on modularity
Satisfaction of modularity
More efficient reasoning
Important for updating theories [Herzig et al. ECAI’06]
Our results apply to every approach allowing for , ,
‘
• –
and —
Ivan José Varzinczak What is a Good Domain Description?

Introduction
Main Results
Concluding Remarks
Summary
Contribution (cont.)
Semantics of action theory contraction
Domain-independent
Does not require extra information (preferences/epistemic
entrenchment relation/. . . )
Fully automatic
Completeness result: highlights importance of modularity
Ivan José Varzinczak What is a Good Domain Description?

Introduction
Main Results
Concluding Remarks
Summary
Modularity is also fruitful. . .
for theories in general [Herzig & Varzinczak AiML’04]
in the Situation Calculus [Herzig & Varzinczak IJCAI’05]
in Description Logics [Herzig & Varzinczak JELIA’06]
(See next slide)
Future work
Fine tune contraction of effect laws
Contract by any formulas (not just laws)
Postulates about effect laws? about causation?
Ivan José Varzinczak What is a Good Domain Description?

Introduction
Main Results
Concluding Remarks
Summary
Modularity is also fruitful. . .
for theories in general [Herzig & Varzinczak AiML’04]
in the Situation Calculus [Herzig & Varzinczak IJCAI’05]
in Description Logics [Herzig & Varzinczak JELIA’06]
(See next slide)
Future work
Fine tune contraction of effect laws
Contract by any formulas (not just laws)
Postulates about effect laws? about causation?
Ivan José Varzinczak What is a Good Domain Description?

Introduction
Main Results
Concluding Remarks
Outlook: Modularity in Description Logics
Example
Suppose a passport control system in an airport
Such a system is composed of many software components
One of them an ontology (knowledge base) about
passengers
All passengers must be controlled
Ivan José Varzinczak What is a Good Domain Description?

Introduction
Main Results
Concluding Remarks
Outlook: Modularity in Description Logics
Example (Ontology)
A passenger has a passport
European citizens have European passports
Foreigners have non-European passports
Someone with double citizenship is a foreigner and a
European
Ivan José Varzinczak What is a Good Domain Description?

Introduction
Main Results
Concluding Remarks
Outlook: Modularity in Description Logics
Example (The ontology in DL)
Terminology:
Passenger passport c db y ¡
EUcitizen passport EU
b ¡
Foreigner passport EU
b ¨ ¡
2Citizen Foreigner EUcitizen
b e
Assertions:
EU POLAND
¢ ¥
EUcitizen JAN ¢ ¥
passport JAN POLAND
¢ ¤ ¥
Ivan José Varzinczak What is a Good Domain Description?

Introduction
Main Results
Concluding Remarks
Outlook: Modularity in Description Logics
Nevertheless
Passenger passport 2Citizen passport EU EU
fg gu x
g Ð gv
q rp s » Æ å gp  s â Êt Å
EUcitizen passport EU
h
2Citizen passport
å gp s » x
Foreigner passport EU
g g äs
gi g Æ å gp
å Bp âs »
2Citizen Foreigner EUcitizen
w
2Citizen Passenger
p t x
Æ â ´p
Someone with double citizenship is not a passenger
Hence. . .
!
if we have 2Citizen BINLADEN , j k
this individual is not obliged to be controlled!
Ivan José Varzinczak What is a Good Domain Description?

Introduction
Main Results
Concluding Remarks
Outlook: Modularity in Description Logics
Nevertheless
Passenger passport 2Citizen passport EU EU
fg gu x
g Ð gv
q rp s » Æ å gp  s â Êt Å
EUcitizen passport EU
h
2Citizen passport
å gp s » x
Foreigner passport EU
g g äs
gi g Æ å gp
å Bp âs »
2Citizen Foreigner EUcitizen
w
2Citizen Passenger
p t x
Æ â ´p
Someone with double citizenship is not a passenger
Hence. . .
!
if we have 2Citizen BINLADEN , j k
this individual is not obliged to be controlled!
Ivan José Varzinczak What is a Good Domain Description?

Introduction
Main Results
Concluding Remarks
Outlook: Modularity in Description Logics
Nevertheless
Passenger passport 2Citizen passport EU EU
fg gu x
g Ð gv
q rp s » Æ å gp  s â Êt Å
EUcitizen passport EU
h
2Citizen passport
å gp s » x
Foreigner passport EU
g g äs
gi g Æ å gp
å Bp âs »
2Citizen Foreigner EUcitizen
w
2Citizen Passenger
p t x
Æ â ´p
Someone with double citizenship is not a passenger
Hence. . .
!
if we have 2Citizen BINLADEN , j k
this individual is not obliged to be controlled!
Ivan José Varzinczak What is a Good Domain Description?

Introduction
Main Results
Concluding Remarks
Outlook: Modularity in Description Logics
Nevertheless
Passenger passport 2Citizen passport EU EU
fg gu x
g Ð gv
q rp s » Æ å gp  s â Êt Å
EUcitizen passport EU
h
2Citizen passport
å gp s » x
Foreigner passport EU
g g äs
gi g Æ å gp
å Bp âs »
2Citizen Foreigner EUcitizen
w
2Citizen Passenger
p t x
Æ â ´p
Someone with double citizenship is not a passenger
Hence. . .
!
if we have 2Citizen BINLADEN , j k
this individual is not obliged to be controlled!
Ivan José Varzinczak What is a Good Domain Description?

Introduction
Main Results
Concluding Remarks
Outlook: Modularity in Description Logics
Nevertheless
Passenger passport 2Citizen passport EU EU
fg gu x
g Ð gv
q rp s » Æ å gp  s â Êt Å
EUcitizen passport EU
h
2Citizen passport
å gp s » x
Foreigner passport EU
g g äs
gi g Æ å gp
å Bp âs »
2Citizen Foreigner EUcitizen
w
2Citizen Passenger
p t x
Æ â ´p
Someone with double citizenship is not a passenger
Hence. . .
!
if we have 2Citizen BINLADEN , j k
this individual is not obliged to be controlled!
Ivan José Varzinczak What is a Good Domain Description?

Introduction
Main Results
Concluding Remarks
Outlook: Modularity in Description Logics
Nevertheless
Passenger passport 2Citizen passport EU EU
fg gu x
g Ð gv
q rp s » Æ å gp  s â Êt Å
EUcitizen passport EU
h
2Citizen passport
å gp s » x
Foreigner passport EU
g g äs
gi g Æ å gp
å Bp âs »
2Citizen Foreigner EUcitizen
w
2Citizen Passenger
p t x
Æ â ´p
Someone with double citizenship is not a passenger
Hence. . .
!
if we have 2Citizen BINLADEN , j k
this individual is not obliged to be controlled!
Ivan José Varzinczak What is a Good Domain Description?

Introduction
Main Results
Concluding Remarks
Outlook: Modularity in Description Logics
Our results. . .
can be applied in DL, too
Ivan José Varzinczak What is a Good Domain Description?

Introduction
Main Results
Concluding Remarks
Thank you!
Merci beaucoup !
Danke schön!
Choukran!
¡Muchas gracias!
Muito obrigado!
Ivan José Varzinczak What is a Good Domain Description?

Can We Ask for More?
Postulate about effects
PE (No implicit effect laws):
˜ ˜
if a and a ,
‘ ‘
˜
‚ýnŸ1
— 1 – 1 • ® ' e {²c
÷ df ‚ nŸ1
— 1 – 1 • ® '¬ e †tc
 gf
then a
‘
• 1 ® ' e †tc
÷ df
Ivan José Varzinczak What is a Good Domain Description?

Can We Ask for More?
Example
loaded shoot alive
l
‘ e { Q gf 1
loaded alive shoot alive
ï ð' • v1 '
Q €j ‚ k e { f o
hasGun shoot hasGun shoot
r
– ) 0' „ s ‘i4
— 1 R0'
Q ) e {  gf 4
shoot Q ­¥ alive
˜
hasGun loaded shoot alive
‘
˜
‚tnŸ1
— 1 – 1 • ® ' Q y e † Q ‚f
hasGun loaded shoot
‘
˜
‚tnŸ1
— 1 – 1 • ® '¬ Q y e †  ‚f
but hasGun loaded shoot alive
‘
• 1 ® '¬ Q y e † Q gf
Ivan José Varzinczak What is a Good Domain Description?

Can We Ask for More?
Example
loaded shoot alive
l
‘ e { Q gf 1
loaded alive shoot alive
ï ð' • v1 '
Q €j ‚ k e { f o
hasGun shoot hasGun shoot
r
– ) 0' „ s ‘i4
— 1 R0'
Q ) e {  gf 4
shoot Q ­¥ alive
˜
hasGun loaded shoot alive
‘
˜
‚tnŸ1
— 1 – 1 • ® ' Q y e † Q ‚f
hasGun loaded shoot
‘
˜
‚tnŸ1
— 1 – 1 • ® '¬ Q y e †  ‚f
but hasGun loaded shoot alive
‘
• 1 ® '¬ Q y e † Q gf
Ivan José Varzinczak What is a Good Domain Description?

Can We Ask for More?
Example
loaded shoot alive
l
‘ e { Q gf 1
loaded alive shoot alive
ï ð' • v1 '
Q €j ‚ k e { f o
hasGun shoot hasGun shoot
r
– ) 0' „ s ‘i4
— 1 R0'
Q ) e {  gf 4
shoot Q ­¥ alive
˜
hasGun loaded shoot alive
‘
˜
‚tnŸ1
— 1 – 1 • ® ' Q y e † Q ‚f
hasGun loaded shoot
‘
˜
‚tnŸ1
— 1 – 1 • ® '¬ Q y e †  ‚f
but hasGun loaded shoot alive
‘
• 1 ® '¬ Q y e † Q gf
Ivan José Varzinczak What is a Good Domain Description?

Can We Ask for More?
Postulate about effects
P (No unattainable effects):
˜ ˜

if a , then a
‘ ‘
• 1 ® ' e †tc
÷ qf ‚tnŸ1
— 1 – 1 • ® '¬ e †²c
 gf
Ivan José Varzinczak What is a Good Domain Description?

Can We Ask for More?
Example
loaded shoot alive
l
‘ e { Q gf 1
loaded alive shoot alive
ï ð' • v1 '
Q €j ‚ k e { f o
hasGun shoot hasGun shoot
r
– ) 0' „ s ‘i4
— 1 R0'
Q ) e {  gf 4
shoot Q ­¥ alive
˜
• ® ' Q €j hasGun ˜
‚ loaded k e † shoot alive
Q gf
but hasGun loaded shoot
‘
‚ýnŸ1
— 1 – 1 • ® ' Q €j ‚ k e †  gf
Ivan José Varzinczak What is a Good Domain Description?

Can We Ask for More?
Example
loaded shoot alive
l
‘ e { Q gf 1
loaded alive shoot alive
ï ð' • v1 '
Q €j ‚ k e { f o
hasGun shoot hasGun shoot
r
– ) 0' „ s ‘i4
— 1 R0'
Q ) e {  gf 4
shoot Q ­¥ alive
˜
• ® ' Q €j hasGun ˜
‚ loaded k e † shoot alive
Q gf
but hasGun loaded shoot
‘
‚ýnŸ1
— 1 – 1 • ® ' Q €j ‚ k e †  gf
Ivan José Varzinczak What is a Good Domain Description?