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- 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 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 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 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 ' A' iff A' for every P T Deﬁnition is a consequence of the set of global axioms in all PDL-models (noted PDL ) iff for every , if , then ' ' ' . 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 ' A' iff A' for every P T Deﬁnition is a consequence of the set of global axioms in all PDL-models (noted PDL ) iff for every , if , then ' ' ' . 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 tease r tease alive s 1 walking alive 1 ' e f tease walking alive tease alive alive e f 1 Q ' e j f Q loaded shoot alive k alive tease e { Q gf 1 alive tease alive Q ' e { f Q e Q gf alive 1 loaded tease loaded 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 tease r tease alive s 1 walking alive 1 ' e f tease walking alive tease alive alive e f 1 Q ' e j f Q loaded shoot alive k alive tease e { Q gf 1 alive tease alive Q ' e { f Q e Q gf alive 1 loaded tease loaded 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 tease r tease alive s 1 walking alive 1 ' e f tease walking alive tease alive alive e f 1 ' Q e j f Q loaded shoot alive k alive tease e { Q gf 1 alive tease alive Q ' e { f Q e Q gf alive 1 loaded tease loaded 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 tease r tease alive s 1 walking alive 1 e ' f tease walking alive tease alive alive e f 1 Q ' e j f Q loaded shoot alive k alive tease e { Q gf 1 alive tease alive Q ' e { f Q e Q gf alive 1 loaded tease loaded 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 tease r tease alive s 1 walking alive 1 e ' f tease walking alive tease alive alive e f 1 Q ' e j f Q loaded shoot alive k alive tease e { Q gf 1 alive tease alive Q ' e { f Q e Q gf alive 1 loaded tease loaded 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 tease r tease alive s 1 walking alive 1 e ' f tease walking alive tease alive alive e f 1 Q ' e j f Q loaded shoot alive k alive tease e { Q gf 1 alive tease alive Q ' e { f Q e Q gf alive 1 loaded tease loaded 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 ' a 5R ' a 5R ' a 5 : the action theory of a given domain r n1 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 ' a 5R ' a 5R ' a 5 : the action theory of a given domain r n1 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 ' a 5R ' a 5R ' a 5 : the action theory of a given domain r n1 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 $dT % # a : effect laws for a a : executability laws for a a : inexecutability laws for a r a a a : domain description for a 1 n1 1 s a, a, and a ' a 5R ' a 5R ' a 5 : the action theory of a given domain r n1 1 1 s Ivan José Varzinczak What is a Good Domain Description?
- 44. Decomposing Theories Introduction Logical Modularity Main Results Exploiting Modularity Concluding Remarks Theory Change What About the Frame Problem? In our example If we had an action wait loaded wait loaded ¡ ¢¤ £ h PDL ¤ ¤ ¤ ¦ i Deﬁnition Dependence relation [Castilho et al. 99]: Fª©$§¦¥ % D C ¨ % # 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©$§¦¥ % D C ¨ % # Example shoot Q «¥ alive, tease ¥ walking, tease ¬¥ alive From wait Q «¥ ¬ loaded conclude loaded e wait loaded f Ivan José Varzinczak What is a Good Domain Description?
- 46. Decomposing Theories Introduction Logical Modularity Main Results Exploiting Modularity Concluding Remarks Theory Change What About the Frame Problem? In our example If we had an action wait loaded wait loaded ¡ ¢¤ £ h PDL ¤ ¤ ¤ ¦ i Deﬁnition Dependence relation [Castilho et al. 99]: Fª©$§¦¥ % D C ¨ % # 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 ¨ % # 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 n1 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 n1 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 n1 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 ' 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 ' 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?

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