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?

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?

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?

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?

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?

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?

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?

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?

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?

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