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What Is a Good Domain Description? Evaluating & Revising Action Theories in Dynamic Logic

Ivan Varzinczak, profile picture
Ivan Varzinczak

The document discusses reasoning about actions and domains using logical formulas. It describes how to represent actions, their effects, executability, and domain constraints. The goal is to enable inference tasks like prediction, explanation, and planning. The document outlines decomposing action theories into modules to avoid unwanted conclusions and exploit logical modularity when evaluating and revising theories.

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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  Ï–» 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 ƒ†RPI ‚ „ ) 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  Ï–» 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 ƒ†RPI ‚ „ ) 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  Ï–» 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 ƒ†RPI ‚ „ ) 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  Ï–» 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 ƒ†RPI ‚ „ ) 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  Ï–» 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 ƒ†RPI ‚ „ ) 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  Ï–» 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 ƒ†RPI ‚ „ ) 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  Ï–» 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 ƒ†RPI ‚ „ ) 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  Ï–» 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  Ï–» 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  Ï–» 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  Ï–» 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  Ï–» 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  Ï–» 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  Ï–» 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?

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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?
  • 13. 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?
  • 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 $dT % # a : effect laws for a ’ a : executability laws for a “ a : inexecutability laws for a ” ‘ r a a a : domain description for a • 1 – n1 — ‚1 s a, a, and a • ˜ Ž' a • 5R™ œ › š – ˜ ' a – 5R™ œ › š — ˜ Ž' a — 5ž™ œ › š : the action theory of a given domain ‘ r ‚ nŸ1 — 1 – 1 • s Ivan José Varzinczak What is a Good Domain Description?
  • 44. Decomposing Theories Introduction Logical Modularity Main Results Exploiting Modularity Concluding Remarks Theory Change What About the Frame Problem? In our example If we had an action wait loaded wait loaded ¡ ’ “ ¢¤ £” h PDL ¤ ¤ ¤ ¦ i Definition Dependence relation [Castilho et al. 99]: Fª©•$§¦¥ % 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?
  • 45. 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©•$§¦¥ % D C ¨ % # ˆ Example shoot Q «¥ alive, tease ¥ walking, tease ¬¥ alive From wait Q «¥ ¬ loaded conclude loaded e †… wait loaded f Ivan José Varzinczak What is a Good Domain Description?
  • 46. Decomposing Theories Introduction Logical Modularity Main Results Exploiting Modularity Concluding Remarks Theory Change What About the Frame Problem? In our example If we had an action wait loaded wait loaded ¡ ’ “ ¢¤ £” h PDL ¤ ¤ ¤ ¦ i Definition Dependence relation [Castilho et al. 99]: Fª©•$§¦¥ % 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?
  • 47. 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?
  • 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?
  • 57. 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?
  • 58. 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?
  • 59. 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?
  • 60. 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?
  • 61. 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?
  • 62. 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?
  • 63. 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?
  • 64. 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?
  • 65. 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?
  • 66. 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?
  • 67. 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?
  • 68. 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?
  • 69. 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?
  • 70. 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?
  • 71. 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?
  • 72. 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?
  • 73. 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?
  • 74. 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  Ï–» 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 ƒ†RPI ‚ „ ) 4  Ž' ¬ '¬ alive ‘ imp ) 0' 4 Ivan José Varzinczak What is a Good Domain Description?
  • 75. 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  Ï–» 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 ƒ†RPI ‚ „ ) 4  Ž' ¬ '¬ alive ‘ imp ) 0' 4 Ivan José Varzinczak What is a Good Domain Description?
  • 76. 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  Ï–» 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 ƒ†RPI ‚ „ ) 4  Ž' ¬ '¬ alive ‘ imp ) 0' 4 Ivan José Varzinczak What is a Good Domain Description?
  • 77. 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  Ï–» 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 ƒ†RPI ‚ „ ) 4  Ž' ¬ '¬ alive ‘ imp ) 0' 4 Ivan José Varzinczak What is a Good Domain Description?
  • 78. 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  Ï–» 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 ƒ†RPI ‚ „ ) 4  Ž' ¬ '¬ alive ‘ imp ) 0' 4 Ivan José Varzinczak What is a Good Domain Description?
  • 79. 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  Ï–» 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 ƒ†RPI ‚ „ ) 4  Ž' ¬ '¬ alive ‘ imp ) 0' 4 Ivan José Varzinczak What is a Good Domain Description?
  • 80. 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  Ï–» 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 ƒ†RPI ‚ „ ) 4  Ž' ¬ '¬ alive ‘ imp ) 0' 4 Ivan José Varzinczak What is a Good Domain Description?
  • 81. 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?
  • 82. 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?
  • 83. 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?
  • 84. 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?
  • 85. 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?
  • 86. 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?
  • 87. 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?
  • 88. 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?
  • 89. 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?
  • 90. 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?
  • 91. 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?
  • 92. 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?
  • 93. 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?
  • 94. 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?
  • 95. 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?
  • 96. 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?
  • 97. 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?
  • 98. 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?
  • 99. 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?
  • 100. 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?
  • 101. 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?
  • 102. 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  Ï–» 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?
  • 103. 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  Ï–» 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?
  • 104. 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  Ï–» 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?
  • 105. 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  Ï–» 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?
  • 106. 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  Ï–» 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?
  • 107. 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  Ï–» 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?
  • 108. 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  Ï–» 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?
  • 109. 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?
  • 110. 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?
  • 111. 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?
  • 112. 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?
  • 113. 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?
  • 114. 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?
  • 115. 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?
  • 116. 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?
  • 117. 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?
  • 118. 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?
  • 119. 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?
  • 120. 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?
  • 121. 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?
  • 122. 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?
  • 123. 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?
  • 124. 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?
  • 125. 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?
  • 126. 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?
  • 127. 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?
  • 128. 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?
  • 129. 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?
  • 130. 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?
  • 131. 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?
  • 132. 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?
  • 133. 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?
  • 134. 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?
  • 135. 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?
  • 136. 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?
  • 137. 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?
  • 138. 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?
  • 139. 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?
  • 140. 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?
  • 141. 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?
  • 142. 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?
  • 143. 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?
  • 144. 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?
  • 145. 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?
  • 146. 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?
  • 147. 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?
  • 148. 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?
  • 149. 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?
  • 150. 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?
  • 151. 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?
  • 152. 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?
  • 153. 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?
  • 154. 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?
  • 155. 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?
  • 156. 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?
  • 157. 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?
  • 158. 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?
  • 159. 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?
  • 160. 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?
  • 161. 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?
  • 162. 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?
  • 163. 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?
  • 164. 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?
  • 165. 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?
  • 166. 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?
  • 167. 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?
  • 168. 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?
  • 169. 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?
  • 170. 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?
  • 171. 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?
  • 172. 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?
  • 173. 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?
  • 174. 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?
  • 175. 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?
  • 176. 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?
  • 177. 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?
  • 178. 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?
  • 179. 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?
  • 180. 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?
  • 181. 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?
  • 182. 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?
  • 183. 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?