timely common knowledge
play

Timely Common Knowledge Strategy Timely Characterising Asymmetric - PowerPoint PPT Presentation

Aug 14, 2022 •120 likes •1.26k views

Introduction Background Problem & Timely Common Knowledge Strategy Timely Characterising Asymmetric Distributed Coordination via Common Knowledge Vectorial Fixed Points Timely- Coordinated Response Nested- Yannai A. Gonczarowski

  1. Introduction Epistemic Consequences Background Problem & Knowledge of Precondition Strategy Timely If a protocol P guaranteeing that L starts to wash only if a Common Knowledge given event ψ holds, then whenever L starts to wash (according Timely- to P ), L knows that ψ holds. Coordinated Response Nested- • When L acts, it must know that the car has arrived. Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 4 / 21

  2. Introduction Epistemic Consequences Background Problem & Knowledge of Precondition Strategy Timely If a protocol P guaranteeing that L starts to wash only if a Common Knowledge given event ψ holds, then whenever L starts to wash (according Timely- to P ), L knows that ψ holds. Coordinated Response Nested- • When L acts, it must know that the car has arrived. Knowledge Formulation • It must also know that between 7 time units earlier and 3 Summary time units later, R knows that the car has already arrived. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 4 / 21

  3. Introduction Epistemic Consequences Background Problem & Knowledge of Precondition Strategy Timely If a protocol P guaranteeing that L starts to wash only if a Common Knowledge given event ψ holds, then whenever L starts to wash (according Timely- to P ), L knows that ψ holds. Coordinated Response Nested- • When L acts, it must know that the car has arrived. Knowledge Formulation • It must also know that between 7 time units earlier and 3 Summary time units later, R knows that the car has already arrived. • It must also know that between 7 time units earlier and 3 time units later, R knows that between 3 time units earlier and 7 time units later, L knows that the car has already arrived. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 4 / 21

  4. Introduction Epistemic Consequences Background Problem & Knowledge of Precondition Strategy Timely If a protocol P guaranteeing that L starts to wash only if a Common Knowledge given event ψ holds, then whenever L starts to wash (according Timely- to P ), L knows that ψ holds. Coordinated Response Nested- • When L acts, it must know that the car has arrived. Knowledge Formulation • It must also know that between 7 time units earlier and 3 Summary time units later, R knows that the car has already arrived. • It must also know that between 7 time units earlier and 3 time units later, R knows that between 3 time units earlier and 7 time units later, L knows that the car has already arrived. • etc. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 4 / 21

  5. Introduction Epistemic Consequences Background Problem & Knowledge of Precondition Strategy Timely If a protocol P guaranteeing that L starts to wash only if a Common Knowledge given event ψ holds, then whenever L starts to wash (according Timely- to P ), L knows that ψ holds. Coordinated Response Nested- • When L acts, it must know that the car has arrived. Knowledge Formulation • It must also know that between 7 time units earlier and 3 Summary time units later, R knows that the car has already arrived. • It must also know that between 7 time units earlier and 3 time units later, R knows that between 3 time units earlier and 7 time units later, L knows that the car has already arrived. • etc. • Codependence ⇒ infinitely many epistemic requirements. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 4 / 21

  6. Introduction Review: Knowledge Gain and Coordination Background Problem & Strategy Many forms of coordination have a necessary and sufficient Timely Common characterising epistemic state. Knowledge Timely- Coordinated Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 5 / 21

  7. Introduction Review: Knowledge Gain and Coordination Background Problem & Strategy Many forms of coordination have a necessary and sufficient Timely Common characterising epistemic state. Knowledge Timely- Coordinated Response Nested- Halpern and Moses (1990): Common knowledge is Knowledge Formulation necessary and sufficient for simultaneous actions. Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 5 / 21

  8. Introduction Review: Knowledge Gain and Coordination Background Problem & Strategy Many forms of coordination have a necessary and sufficient Timely Common characterising epistemic state. Knowledge Timely- Coordinated Response Nested- Halpern and Moses (1990): Common knowledge is Knowledge Formulation necessary and sufficient for simultaneous actions. Summary • Necessary: A simultaneous action implies common knowledge of the action. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 5 / 21

  9. Introduction Review: Knowledge Gain and Coordination Background Problem & Strategy Many forms of coordination have a necessary and sufficient Timely Common characterising epistemic state. Knowledge Timely- Coordinated Response Nested- Halpern and Moses (1990): Common knowledge is Knowledge Formulation necessary and sufficient for simultaneous actions. Summary • Necessary: A simultaneous action implies common knowledge of the action. • Sufficient: Common knowledge of any fact arises simultaneously among all agents, and thus can be used to coordinate a simultaneous action. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 5 / 21

  10. Introduction Review: Knowledge Gain and Coordination Background Problem & Strategy Many forms of coordination have a necessary and sufficient Timely Common characterising epistemic state. Knowledge Timely- Coordinated Response Nested- Ben-Zvi and Moses (2010): Nested knowledge is necessary Knowledge Formulation and sufficient for linear ordering of actions. Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 5 / 21

  11. Introduction Review: Knowledge Gain and Coordination Background Problem & Strategy Many forms of coordination have a necessary and sufficient Timely Common characterising epistemic state. Knowledge Timely- Coordinated Response Nested- Ben-Zvi and Moses (2010): Nested knowledge is necessary Knowledge Formulation and sufficient for linear ordering of actions. Summary • Necessary: act 2 ⇒ K 2 (previously act 1 ), act 3 ⇒ K 3 K 2 (previously act 1 ), etc. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 5 / 21

  12. Introduction Review: Knowledge Gain and Coordination Background Problem & Strategy Many forms of coordination have a necessary and sufficient Timely Common characterising epistemic state. Knowledge Timely- Coordinated Response Nested- Ben-Zvi and Moses (2010): Nested knowledge is necessary Knowledge Formulation and sufficient for linear ordering of actions. Summary • Necessary: act 2 ⇒ K 2 (previously act 1 ), act 3 ⇒ K 3 K 2 (previously act 1 ), etc. • Sufficient: Nested knowledge of any fact arises linearly, and thus can be used to coordinate linearly-ordered actions. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 5 / 21

  13. Introduction Reminder: The Runs and Systems Model Background Based upon Fagin et al. (1995) Problem & Strategy Timely Common Knowledge Timely- Coordinated Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 6 / 21

  14. Introduction Reminder: The Runs and Systems Model Background Based upon Fagin et al. (1995) Problem & Strategy Timely Common Knowledge Timely- • Agents: I . Coordinated Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 6 / 21

  15. Introduction Reminder: The Runs and Systems Model Background Based upon Fagin et al. (1995) Problem & Strategy Timely Common Knowledge Timely- • Agents: I . Coordinated Response Nested- • Time: T = N ∪ { 0 } . (For ease of presentation.) Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 6 / 21

  16. Introduction Reminder: The Runs and Systems Model Background Based upon Fagin et al. (1995) Problem & Strategy Timely Common Knowledge Timely- • Agents: I . Coordinated Response Nested- • Time: T = N ∪ { 0 } . (For ease of presentation.) Knowledge Formulation • Runs: R . Each run is a function from time to: Summary • A state of the environment — and — • A state for each agent. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 6 / 21

  17. Introduction Reminder: The Runs and Systems Model Background Based upon Fagin et al. (1995) Problem & Strategy Timely Common Knowledge Timely- • Agents: I . Coordinated Response Nested- • Time: T = N ∪ { 0 } . (For ease of presentation.) Knowledge Formulation • Runs: R . Each run is a function from time to: Summary • A state of the environment — and — • A state for each agent. • A protocol governs the agents’ behaviour. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 6 / 21

  18. Introduction Set-Theoretic Reasoning Background Problem & Strategy Timely Common Knowledge Timely- Coordinated Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 7 / 21

  19. Introduction Set-Theoretic Reasoning Background Problem & Strategy • A point ( r , t ) ∈ Ω R � R × T defines a snapshot of the Timely system. Common Knowledge Timely- Coordinated Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 7 / 21

  20. Introduction Set-Theoretic Reasoning Background Problem & Strategy • A point ( r , t ) ∈ Ω R � R × T defines a snapshot of the Timely system. Common Knowledge • An event is associated with the set of points Timely- ψ ∈ F R � 2 Ω R at which it holds. Coordinated Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 7 / 21

  21. Introduction Set-Theoretic Reasoning Background Problem & Strategy • A point ( r , t ) ∈ Ω R � R × T defines a snapshot of the Timely system. Common Knowledge • An event is associated with the set of points Timely- ψ ∈ F R � 2 Ω R at which it holds. Coordinated Response • ψ ⊆ φ means “ ψ validly implies φ ”. Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 7 / 21

  22. Introduction Set-Theoretic Reasoning Background Problem & Strategy • A point ( r , t ) ∈ Ω R � R × T defines a snapshot of the Timely system. Common Knowledge • An event is associated with the set of points Timely- ψ ∈ F R � 2 Ω R at which it holds. Coordinated Response • ψ ⊆ φ means “ ψ validly implies φ ”. Nested- Knowledge Formulation Summary For any event ψ , Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 7 / 21

  23. Introduction Set-Theoretic Reasoning Background Problem & Strategy • A point ( r , t ) ∈ Ω R � R × T defines a snapshot of the Timely system. Common Knowledge • An event is associated with the set of points Timely- ψ ∈ F R � 2 Ω R at which it holds. Coordinated Response • ψ ⊆ φ means “ ψ validly implies φ ”. Nested- Knowledge Formulation Summary For any event ψ , ◯ d ψ � � � ( r , t ) | ( r , t + d ) ∈ ψ Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 7 / 21

  24. Introduction Set-Theoretic Reasoning Background Problem & Strategy • A point ( r , t ) ∈ Ω R � R × T defines a snapshot of the Timely system. Common Knowledge • An event is associated with the set of points Timely- ψ ∈ F R � 2 Ω R at which it holds. Coordinated Response • ψ ⊆ φ means “ ψ validly implies φ ”. Nested- Knowledge Formulation Summary For any event ψ , ◯ d ψ � � � ( r , t ) | ( r , t + d ) ∈ ψ ( r , t ) | ∃ t ′ ≤ t + d : ( r , t ′ ) ∈ ψ ◯ ≤ d ψ � � � Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 7 / 21

  25. Introduction Set-Theoretic Reasoning Background Problem & Strategy • A point ( r , t ) ∈ Ω R � R × T defines a snapshot of the Timely system. Common Knowledge • An event is associated with the set of points Timely- ψ ∈ F R � 2 Ω R at which it holds. Coordinated Response • ψ ⊆ φ means “ ψ validly implies φ ”. Nested- Knowledge Formulation Summary For any event ψ , ◯ d ψ � � � ( r , t ) | ( r , t + d ) ∈ ψ ( r , t ) | ∃ t ′ ≤ t + d : ( r , t ′ ) ∈ ψ ◯ ≤ d ψ � � � K j ψ � � � ( r , t ) | [( r , t )] j ⊆ ψ [( r , t )] j is the event “the local state of j is r j ( t )”. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 7 / 21

  26. Introduction Epistemic Fixed-Point Analysis Background Problem & Strategy Timely Common Knowledge Timely- Coordinated Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 8 / 21

  27. Introduction Epistemic Fixed-Point Analysis Background Problem & Strategy Timely Halpern and Moses (1990) Common Knowledge Timely- Coordinated Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 8 / 21

  28. Introduction Epistemic Fixed-Point Analysis Background Problem & Strategy Timely Halpern and Moses (1990) Common Knowledge • Common knowledge of ψ is the greatest fixed point of Timely- Coordinated x �→ E I ( ψ ∩ x ). Response • In the lattice F R . Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 8 / 21

  29. Introduction Epistemic Fixed-Point Analysis Background Problem & Strategy Timely Halpern and Moses (1990) Common Knowledge • Common knowledge of ψ is the greatest fixed point of Timely- Coordinated x �→ E I ( ψ ∩ x ). Response • In the lattice F R . Nested- Knowledge Formulation • A few variants: Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 8 / 21

  30. Introduction Epistemic Fixed-Point Analysis Background Problem & Strategy Timely Halpern and Moses (1990) Common Knowledge • Common knowledge of ψ is the greatest fixed point of Timely- Coordinated x �→ E I ( ψ ∩ x ). Response • In the lattice F R . Nested- Knowledge Formulation • A few variants: Summary • Define Eventual Common Knowledge of ψ as the greatest fixed point of x �→ ∩ j ∈ I ◇ K j ( ψ ∩ x ). • Necessary and sufficient for eventual coordination. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 8 / 21

  31. Introduction Epistemic Fixed-Point Analysis Background Problem & Strategy Timely Halpern and Moses (1990) Common Knowledge • Common knowledge of ψ is the greatest fixed point of Timely- Coordinated x �→ E I ( ψ ∩ x ). Response • In the lattice F R . Nested- Knowledge Formulation • A few variants: Summary • Define Eventual Common Knowledge of ψ as the greatest fixed point of x �→ ∩ j ∈ I ◇ K j ( ψ ∩ x ). • Necessary and sufficient for eventual coordination. • Define ε -Common Knowledge of ψ as the greatest fixed point of x �→ E ε I ( ψ ∩ x ). • Necessary and sufficient for up-to- ε coordination. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 8 / 21

  32. Introduction Reasoning about Coordination Background Problem & Strategy Timely Common Knowledge Timely- Coordinated Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 9 / 21

  33. Introduction Reasoning about Coordination Background Problem & Strategy Timely Fagin et al. (1995) Common Knowledge Timely- An I -ensemble, where I ⊆ I is a set of agents, is an I -tuple of Coordinated e = ( e j ) j ∈ I ∈ F RI , in which for every agent j ∈ I , the Response events ¯ Nested- event e j is a j -local event. Knowledge Formulation • An event is j -local if it is known to j whenever it occurs. Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 9 / 21

  34. Introduction Reasoning about Coordination Background Problem & Strategy Timely Fagin et al. (1995) Common Knowledge Timely- An I -ensemble, where I ⊆ I is a set of agents, is an I -tuple of Coordinated e = ( e j ) j ∈ I ∈ F RI , in which for every agent j ∈ I , the Response events ¯ Nested- event e j is a j -local event. Knowledge Formulation • An event is j -local if it is known to j whenever it occurs. Summary Central example: the tuple ¯ e = { “ j is starting to clean right now” } j ∈ I is an ensemble. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 9 / 21

  35. Introduction Can these be Generalized to deal with Arbitrary Background Timely Constraints? Problem & Strategy Timely Common Knowledge Timely- Coordinated Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 10 / 21

  36. Introduction Can these be Generalized to deal with Arbitrary Background Timely Constraints? Problem & Strategy Definition (Timely Coordination) Timely Common Knowledge Timely- Coordinated Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 10 / 21

  37. Introduction Can these be Generalized to deal with Arbitrary Background Timely Constraints? Problem & Strategy Definition (Timely Coordination) Timely Common Knowledge 1 A timely-coordination spec is a pair ( I , δ ), where I ⊆ I is a Timely- set of agents and δ : I 2 → Z ∪ {∞} . Coordinated Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 10 / 21

  38. Introduction Can these be Generalized to deal with Arbitrary Background Timely Constraints? Problem & Strategy Definition (Timely Coordination) Timely Common Knowledge 1 A timely-coordination spec is a pair ( I , δ ), where I ⊆ I is a Timely- set of agents and δ : I 2 → Z ∪ {∞} . Coordinated Response Nested- Knowledge Formulation Summary δ ( r , l ) = − 7 δ ( l , r ) = 3 δ ( d , r ) = 6 δ ( r , d ) = 11 δ ( l , d ) = − 9 δ ( d , l ) = − 4 Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 10 / 21

  39. Introduction Can these be Generalized to deal with Arbitrary Background Timely Constraints? Problem & Strategy Definition (Timely Coordination) Timely Common Knowledge 1 A timely-coordination spec is a pair ( I , δ ), where I ⊆ I is a Timely- set of agents and δ : I 2 → Z ∪ {∞} . Coordinated Response 2 Given a timely-coordination spec ( I , δ ) and a system Nested- Knowledge e ∈ F RI is R ⊆ R , we say that an I -ensemble ¯ Formulation δ -coordinated (in R ) if for every ( j , k ) ∈ I 2 and for every Summary ( r , t ) ∈ e j , there exists t ′ ≤ t + δ ( j , k ) s.t. ( r , t ′ ) ∈ e k . δ ( r , l ) = − 7 δ ( l , r ) = 3 δ ( d , r ) = 6 δ ( r , d ) = 11 δ ( l , d ) = − 9 δ ( d , l ) = − 4 Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 10 / 21

  40. Introduction Can these be Generalized to deal with Arbitrary Background Timely Constraints? Problem & Strategy Definition (Timely Coordination) Timely Common Knowledge 1 A timely-coordination spec is a pair ( I , δ ), where I ⊆ I is a Timely- set of agents and δ : I 2 → Z ∪ {∞} . Coordinated Response 2 Given a timely-coordination spec ( I , δ ) and a system Nested- Knowledge e ∈ F RI is R ⊆ R , we say that an I -ensemble ¯ Formulation δ -coordinated (in R ) if for every ( j , k ) ∈ I 2 and for every Summary ( r , t ) ∈ e j , there exists t ′ ≤ t + δ ( j , k ) s.t. ( r , t ′ ) ∈ e k . δ ( r , l ) = − 7 δ ( l , r ) = 3 δ ( d , r ) = 6 δ ( r , d ) = 11 δ ( l , d ) = − 9 δ ( d , l ) = − 4 Captures Car-Wash, Simultaneous/Ordered Coordination, etc. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 10 / 21

  41. Introduction Main Analysis Difficulties Background Problem & Strategy Timely Common Knowledge Timely- Coordinated Response • Actions are not necessarily ordered. Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 11 / 21

  42. Introduction Main Analysis Difficulties Background Problem & Strategy Timely Common Knowledge Timely- Coordinated Response • Actions are not necessarily ordered. Nested- • Dependencies may be circular. Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 11 / 21

  43. Introduction Main Analysis Difficulties Background Problem & Strategy Timely Common Knowledge Timely- Coordinated Response • Actions are not necessarily ordered. Nested- • Dependencies may be circular. Knowledge Formulation • Infinitely many epistemic consequences. Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 11 / 21

  44. Introduction Main Analysis Difficulties Background Problem & Strategy Timely Common Knowledge Timely- Coordinated Response • Actions are not necessarily ordered. Nested- • Dependencies may be circular. Knowledge Formulation • Infinitely many epistemic consequences. Summary • δ is not necessarily symmetric w.r.t. the agents in I . Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 11 / 21

  45. Introduction Symmetric Forms of Coordination are Easier Background Problem & Strategy In the simultaneous / up-to- ε / eventual coordination Timely scenarios, the constraints are symmetric (invariant under Common Knowledge permutations on I ): Timely- Coordinated Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 12 / 21

  46. Introduction Symmetric Forms of Coordination are Easier Background Problem & Strategy In the simultaneous / up-to- ε / eventual coordination Timely scenarios, the constraints are symmetric (invariant under Common Knowledge permutations on I ): Timely- Coordinated • All agents have to know that within a certain (global) Response temporal constraint all agents will act. Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 12 / 21

  47. Introduction Symmetric Forms of Coordination are Easier Background Problem & Strategy In the simultaneous / up-to- ε / eventual coordination Timely scenarios, the constraints are symmetric (invariant under Common Knowledge permutations on I ): Timely- Coordinated • All agents have to know that within a certain (global) Response temporal constraint all agents will act. Nested- Knowledge • All agents have to know that within a certain (global) Formulation temporal constraint all agents will have to know that Summary within these temporal constraints all agents will act. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 12 / 21

  48. Introduction Symmetric Forms of Coordination are Easier Background Problem & Strategy In the simultaneous / up-to- ε / eventual coordination Timely scenarios, the constraints are symmetric (invariant under Common Knowledge permutations on I ): Timely- Coordinated • All agents have to know that within a certain (global) Response temporal constraint all agents will act. Nested- Knowledge • All agents have to know that within a certain (global) Formulation temporal constraint all agents will have to know that Summary within these temporal constraints all agents will act. • etc. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 12 / 21

  49. Introduction Symmetric Forms of Coordination are Easier Background Problem & Strategy In the simultaneous / up-to- ε / eventual coordination Timely scenarios, the constraints are symmetric (invariant under Common Knowledge permutations on I ): Timely- Coordinated • All agents have to know that within a certain (global) Response temporal constraint all agents will act. Nested- Knowledge • All agents have to know that within a certain (global) Formulation temporal constraint all agents will have to know that Summary within these temporal constraints all agents will act. • etc. • Solutions are greatest fixed point of functions of the form x �→ E ∗ ( ψ ∩ x ), for some “triggering” ψ , and for E ∗ along the lines of “within a certain temporal constraint, everyone will know that . . . ”. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 12 / 21

  50. Introduction δ -Coordination is Generally Asymmetric Background Problem & Strategy Timely Common Knowledge For general δ , such a fixed point is elusive: Timely- Coordinated Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 13 / 21

  51. Introduction δ -Coordination is Generally Asymmetric Background Problem & Strategy Timely Common Knowledge For general δ , such a fixed point is elusive: Timely- Coordinated Response • In the car-wash scenario, Nested- start l ⇒ K l : within -7 to 3: start r . Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 13 / 21

  52. Introduction δ -Coordination is Generally Asymmetric Background Problem & Strategy Timely Common Knowledge For general δ , such a fixed point is elusive: Timely- Coordinated Response • In the car-wash scenario, Nested- start l ⇒ K l : within -7 to 3: start r . Knowledge Formulation Summary • Similarly yet asymmetrically, start d ⇒ K d : within -11 to -6: start r . Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 13 / 21

  53. Introduction δ -Coordination is Generally Asymmetric Background Problem & Strategy Timely Common Knowledge For general δ , such a fixed point is elusive: Timely- Coordinated Response • In the car-wash scenario, Nested- start l ⇒ K l : within -7 to 3: start r . Knowledge Formulation Summary • Similarly yet asymmetrically, start d ⇒ K d : within -11 to -6: start r . • What should E ∗ encompass? − 7 to 3 or − 11 to − 6? Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 13 / 21

  54. Introduction Searching for a Suitable Fixed Point Background Let ψ c be the event “the car c is in the car-wash facility”. Problem & Strategy Timely Common Knowledge Timely- Coordinated � � Response x �→ K ? ψ c ∩ “in ? to ? time units: x ” Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 14 / 21

  55. Introduction Searching for a Suitable Fixed Point Background Let ψ c be the event “the car c is in the car-wash facility”. Problem & Strategy Timely Common Knowledge Timely- Coordinated � � ψ c ∩ “in − 3 to 7 time units: start l ” ∩ Response start r �→ K r “in 6 to 11 time units: start d ” Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 14 / 21

  56. Introduction Searching for a Suitable Fixed Point Background Let ψ c be the event “the car c is in the car-wash facility”. Problem & Strategy Timely � � Common ψ c ∩ “in − 7 to 3 time units : start r ” ∩ Knowledge start l �→ K l “in 4 to 9 time units: start d ” Timely- Coordinated � � ψ c ∩ “in − 3 to 7 time units: start l ” ∩ Response start r �→ K r “in 6 to 11 time units: start d ” Nested- Knowledge � � ψ c ∩ “in − 9 to − 4 time units: start l ” ∩ Formulation start d �→ K d “in − 11 to − 6 time units: start r ” Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 14 / 21

  57. Introduction Searching for a Suitable Fixed Point Background Let ψ c be the event “the car c is in the car-wash facility”. Problem & Strategy Timely � � Common ψ c ∩ “in − 7 to 3 time units : start r ” ∩ Knowledge start l �→ K l “in 4 to 9 time units: start d ” Timely- Coordinated � � ψ c ∩ “in − 3 to 7 time units: start l ” ∩ Response start r �→ K r “in 6 to 11 time units: start d ” Nested- Knowledge � � ψ c ∩ “in − 9 to − 4 time units: start l ” ∩ Formulation start d �→ K d “in − 11 to − 6 time units: start r ” Summary A vectorial E ∗ ! Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 14 / 21

  58. Introduction Searching for a Suitable Fixed Point Background Let ψ c be the event “the car c is in the car-wash facility”. Problem & Strategy Timely � � Common ψ c ∩ “in − 7 to 3 time units : start r ” ∩ Knowledge start l �→ K l “in 4 to 9 time units: start d ” Timely- Coordinated � � ψ c ∩ “in − 3 to 7 time units: start l ” ∩ Response start r �→ K r “in 6 to 11 time units: start d ” Nested- Knowledge � � ψ c ∩ “in − 9 to − 4 time units: start l ” ∩ Formulation start d �→ K d “in − 11 to − 6 time units: start r ” Summary A vectorial E ∗ ! Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 14 / 21

  59. Introduction Searching for a Suitable Fixed Point Background Let ψ c be the event “the car c is in the car-wash facility”. Problem & Strategy Timely � � Common ψ c ∩ “in − 7 to 3 time units : start r ” ∩ Knowledge start l �→ K l “in 4 to 9 time units: start d ” Timely- Coordinated � � ψ c ∩ “in − 3 to 7 time units: start l ” ∩ Response start r �→ K r “in 6 to 11 time units: start d ” Nested- Knowledge � � ψ c ∩ “in − 9 to − 4 time units: start l ” ∩ Formulation start d �→ K d “in − 11 to − 6 time units: start r ” Summary A vectorial E ∗ !   � � � ◯ ≤ δ ( j , k ) x k ( x j ) j ∈ I �→  K j ψ ∩  k ∈ I \{ j } j ∈ I Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 14 / 21

  60. Introduction Timely Common Knowledge Background Problem & Strategy Definition (Timely Common Knowledge) Timely Common Knowledge Timely- Coordinated Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 15 / 21

  61. Introduction Timely Common Knowledge Background We work in the lattice F RI . Problem & Strategy Definition (Timely Common Knowledge) Timely Common Knowledge Let R ⊆ R and let ( I , δ ) be a timely-coordination spec. For Timely- each ψ ∈ F R , we define δ -common knowledge of ψ by I , Coordinated Response denoted by C δ I ψ , to be the greatest fixed point of the function Nested- Knowledge Formulation Summary f δ F RI F RI ψ : →   � � � ◯ ≤ δ ( i , j ) x j ( x i ) i ∈ I �→  K i ψ ∩  j ∈ I \{ i } i ∈ I Note Lemma C δ C δ I ψ is a tuple. I ψ is well-defined. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 15 / 21

  62. Introduction Timely Common Knowledge Properties Background Problem & Strategy Timely Common Knowledge Timely- Coordinated Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 16 / 21

  63. Introduction Timely Common Knowledge Properties Background Problem & Strategy Timely Many Desirable Properties — E.g. Induction Rule Common Knowledge ξ ∈ F RI satisfying ¯ Every ¯ ψ (¯ ξ ) also satisfies ¯ ξ ≤ f δ ξ ≤ C δ I ψ . Timely- Coordinated • Recall that ≤ means “coordinate-wise validly implies”. Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 16 / 21

  64. Introduction Timely Common Knowledge Properties Background Problem & Strategy Timely Many Desirable Properties — E.g. Induction Rule Common Knowledge ξ ∈ F RI satisfying ¯ Every ¯ ψ (¯ ξ ) also satisfies ¯ ξ ≤ f δ ξ ≤ C δ I ψ . Timely- Coordinated • Recall that ≤ means “coordinate-wise validly implies”. Response Nested- Knowledge Theorem Formulation Summary C δ I ψ is the largest δ -coordinated ensemble s.t. ( C δ I ) j ⊆ ψ for every agent j ∈ I. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 16 / 21

  65. Introduction Timely Common Knowledge Properties Background Problem & Strategy Timely Many Desirable Properties — E.g. Induction Rule Common Knowledge ξ ∈ F RI satisfying ¯ Every ¯ ψ (¯ ξ ) also satisfies ¯ ξ ≤ f δ ξ ≤ C δ I ψ . Timely- Coordinated • Recall that ≤ means “coordinate-wise validly implies”. Response Nested- Knowledge Theorem Formulation Summary C δ I ψ is the largest δ -coordinated ensemble s.t. ( C δ I ) j ⊆ ψ for every agent j ∈ I. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 16 / 21

  66. Introduction Timely Common Knowledge Properties Background Problem & Strategy Timely Many Desirable Properties — E.g. Induction Rule Common Knowledge ξ ∈ F RI satisfying ¯ Every ¯ ψ (¯ ξ ) also satisfies ¯ ξ ≤ f δ ξ ≤ C δ I ψ . Timely- Coordinated • Recall that ≤ means “coordinate-wise validly implies”. Response Nested- Knowledge Theorem Formulation Summary C δ I ψ is the largest δ -coordinated ensemble s.t. ( C δ I ) j ⊆ ψ for every agent j ∈ I. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 16 / 21

  67. Introduction Timely Common Knowledge Properties Background Problem & Strategy Timely Many Desirable Properties — E.g. Induction Rule Common Knowledge ξ ∈ F RI satisfying ¯ Every ¯ ψ (¯ ξ ) also satisfies ¯ ξ ≤ f δ ξ ≤ C δ I ψ . Timely- Coordinated • Recall that ≤ means “coordinate-wise validly implies”. Response Nested- Knowledge Theorem Formulation Summary C δ I ψ is the largest δ -coordinated ensemble s.t. ( C δ I ) j ⊆ ψ for every agent j ∈ I. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 16 / 21

  68. Introduction Timely Common Knowledge Properties Background Problem & Strategy Timely Many Desirable Properties — E.g. Induction Rule Common Knowledge ξ ∈ F RI satisfying ¯ Every ¯ ψ (¯ ξ ) also satisfies ¯ ξ ≤ f δ ξ ≤ C δ I ψ . Timely- Coordinated • Recall that ≤ means “coordinate-wise validly implies”. Response Nested- Knowledge Theorem Formulation Summary C δ I ψ is the largest δ -coordinated ensemble s.t. ( C δ I ) j ⊆ ψ for every agent j ∈ I. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 16 / 21

  69. Introduction Timely Common Knowledge Properties Background Problem & Strategy Timely Many Desirable Properties — E.g. Induction Rule Common Knowledge ξ ∈ F RI satisfying ¯ Every ¯ ψ (¯ ξ ) also satisfies ¯ ξ ≤ f δ ξ ≤ C δ I ψ . Timely- Coordinated • Recall that ≤ means “coordinate-wise validly implies”. Response Nested- Knowledge Theorem Formulation Summary C δ I ψ is the largest δ -coordinated ensemble s.t. ( C δ I ) j ⊆ ψ for every agent j ∈ I. Observation The ensemble in which the j’th event is “ ( C δ I ) j holds for the first time” is δ -coordinated. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 16 / 21

  70. Introduction Applying Timely Common Knowledge Background Problem & Strategy Timely Common Knowledge Timely- Coordinated Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 17 / 21

  71. Introduction Applying Timely Common Knowledge Background ( ψ c is the event “the car c is in the car-wash facility”.) Problem & Strategy Timely Common Knowledge Timely- Coordinated Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 17 / 21

  72. Introduction Applying Timely Common Knowledge Background ( ψ c is the event “the car c is in the car-wash facility”.) Problem & Strategy Observation Timely Common Every protocol solving the car-wash problem corresponds to a Knowledge Timely- δ -coordinated ensemble ¯ e s.t. e j ⊆ ψ c for every agent j ∈ I. Coordinated Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 17 / 21

  73. Introduction Applying Timely Common Knowledge Background ( ψ c is the event “the car c is in the car-wash facility”.) Problem & Strategy Observation Timely Common Every protocol solving the car-wash problem corresponds to a Knowledge Timely- δ -coordinated ensemble ¯ e s.t. e j ⊆ ψ c for every agent j ∈ I. Coordinated Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 17 / 21

  74. Introduction Applying Timely Common Knowledge Background ( ψ c is the event “the car c is in the car-wash facility”.) Problem & Strategy Observation Timely Common Every protocol solving the car-wash problem corresponds to a Knowledge Timely- δ -coordinated ensemble ¯ e s.t. e j ⊆ ψ c for every agent j ∈ I. Coordinated Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 17 / 21

  75. Introduction Applying Timely Common Knowledge Background ( ψ c is the event “the car c is in the car-wash facility”.) Problem & Strategy Observation Timely Common Every protocol solving the car-wash problem corresponds to a Knowledge Timely- δ -coordinated ensemble ¯ e s.t. e j ⊆ ψ c for every agent j ∈ I. Coordinated Response Nested- Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 17 / 21

  76. Introduction Applying Timely Common Knowledge Background ( ψ c is the event “the car c is in the car-wash facility”.) Problem & Strategy Observation Timely Common Every protocol solving the car-wash problem corresponds to a Knowledge Timely- δ -coordinated ensemble ¯ e s.t. e j ⊆ ψ c for every agent j ∈ I. Coordinated Response Nested- Corollary (Necessary and Sufficient for Solving Car-Wash) Knowledge Formulation Summary Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 17 / 21

  77. Introduction Applying Timely Common Knowledge Background ( ψ c is the event “the car c is in the car-wash facility”.) Problem & Strategy Observation Timely Common Every protocol solving the car-wash problem corresponds to a Knowledge Timely- δ -coordinated ensemble ¯ e s.t. e j ⊆ ψ c for every agent j ∈ I. Coordinated Response Nested- Corollary (Necessary and Sufficient for Solving Car-Wash) Knowledge Formulation Summary • The protocol in which each robot j starts washing/drying at the first instant at which ( C δ I ψ c ) j holds (during each run) is an optimal solution for the car-wash problem. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 17 / 21

  78. Introduction Applying Timely Common Knowledge Background ( ψ c is the event “the car c is in the car-wash facility”.) Problem & Strategy Observation Timely Common Every protocol solving the car-wash problem corresponds to a Knowledge Timely- δ -coordinated ensemble ¯ e s.t. e j ⊆ ψ c for every agent j ∈ I. Coordinated Response Nested- Corollary (Necessary and Sufficient for Solving Car-Wash) Knowledge Formulation Summary • The protocol in which each robot j starts washing/drying at the first instant at which ( C δ I ψ c ) j holds (during each run) is an optimal solution for the car-wash problem. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 17 / 21

  79. Introduction Applying Timely Common Knowledge Background ( ψ c is the event “the car c is in the car-wash facility”.) Problem & Strategy Observation Timely Common Every protocol solving the car-wash problem corresponds to a Knowledge Timely- δ -coordinated ensemble ¯ e s.t. e j ⊆ ψ c for every agent j ∈ I. Coordinated Response Nested- Corollary (Necessary and Sufficient for Solving Car-Wash) Knowledge Formulation Summary • The protocol in which each robot j starts washing/drying at the first instant at which ( C δ I ψ c ) j holds (during each run) is an optimal solution for the car-wash problem. Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 17 / 21

  80. Introduction Applying Timely Common Knowledge Background ( ψ c is the event “the car c is in the car-wash facility”.) Problem & Strategy Observation Timely Common Every protocol solving the car-wash problem corresponds to a Knowledge Timely- δ -coordinated ensemble ¯ e s.t. e j ⊆ ψ c for every agent j ∈ I. Coordinated Response Nested- Corollary (Necessary and Sufficient for Solving Car-Wash) Knowledge Formulation Summary • The protocol in which each robot j starts washing/drying at the first instant at which ( C δ I ψ c ) j holds (during each run) is an optimal solution for the car-wash problem. • The car-wash problem is solvable in a run r iff there exists t s.t. ( r , t ) ∈ ( C δ I ψ c ) j for some/all j . Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 17 / 21

  81. Introduction Applying Timely Common Knowledge Background ( ψ c is the event “the car c is in the car-wash facility”.) Problem & Strategy Observation Timely Common Every protocol solving the car-wash problem corresponds to a Knowledge Timely- δ -coordinated ensemble ¯ e s.t. e j ⊆ ψ c for every agent j ∈ I. Coordinated Response Nested- Corollary (Necessary and Sufficient for Solving Car-Wash) Knowledge Formulation Summary • The protocol in which each robot j starts washing/drying at the first instant at which ( C δ I ψ c ) j holds (during each run) is an optimal solution for the car-wash problem. • The car-wash problem is solvable in a run r iff there exists t s.t. ( r , t ) ∈ ( C δ I ψ c ) j for some/all j . We prove this for a general class of Timely-Coordinated Response (TCR) problems that we define. (General I , δ , actions, etc.) Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 17 / 21

  82. Introduction The Iterative Definition of Common Knowledge Background Problem & Strategy Definition (Common Knowledge - Popular Definiton) Timely Common Knowledge Let R ⊆ R and let I ⊆ I . For every ψ ∈ F R , Timely- Coordinated ∞ Response � E I n ψ, C I ψ � Nested- Knowledge n =1 Formulation Summary where E I 0 ψ � ψ and E I n ψ � E I E I n − 1 ψ for every n ∈ N . Yannai A. Gonczarowski (HUJI) Timely Common Knowledge January 8, 2013 18 / 21

Recommend

Common Knowledge AND Global Games 1 This talk combines common knowledge with global games

Common Knowledge AND Global Games 1 This talk combines common knowledge with global games

Common Knowledge AND Global Games 1 This talk combines common knowledge with global games another advanced branch of game theory See Stephen Morriss work 2 Today well go back to a puzzle that arose during the Hawk-Dove lecture:

503 views • 35 slides
Common Knowledge in Email Exchanges Krzysztof R. Apt CWI, Amsterdam, the Netherlands ,

Common Knowledge in Email Exchanges Krzysztof R. Apt CWI, Amsterdam, the Netherlands ,

Common Knowledge in Email Exchanges Krzysztof R. Apt CWI, Amsterdam, the Netherlands , University of Amsterdam based on joint work with Floor Sietsma, CWI Common Knowledge in Email Exchanges p. 1/2 History: Common, Knowledge COMMON,

794 views • 41 slides
reached with positive probability under behavior strategies i i ( i map from

reached with positive probability under behavior strategies i i ( i map from

How Irrational Are Subjects in Extensive- Form Games? (Joint with Drew Fudenberg) Two views of equilibrium (1) introspective axiomatic versions of common knowledge tracing procedure (2) learning common knowledge a conclusion, not an

379 views • 27 slides
Timely Dataflow with Heterogeneous Systems eg timely + arrayfire = win? Nat McAleese

Timely Dataflow with Heterogeneous Systems eg timely + arrayfire = win? Nat McAleese

Timely Dataflow with Heterogeneous Systems eg timely + arrayfire = win? Nat McAleese Heterogenous computing Computing over a variety of hardware What is ArrayFire? Free; general-purpose; open-source (kinda) Targets parallel and

675 views • 9 slides
Me Knowledge Management Paradox Where is Knowledge ? People Processes Market Products

Me Knowledge Management Paradox Where is Knowledge ? People Processes Market Products

What the schools do to you! the others Me Knowledge Management Paradox Where is Knowledge ? People Processes Market Products Knowledge Mngmt in Corporations Common Denominators Focus on Id., Transfer & Use of Knowledge Focus

458 views • 12 slides
Night! Common Core Curriculum Define knowledge and skills students should have within their

Night! Common Core Curriculum Define knowledge and skills students should have within their

Welcome to Family Literacy Night! Common Core Curriculum Define knowledge and skills students should have within their K-12 education careers Are aligned with college and work expectations Are clear, understandable and consistent

388 views • 17 slides
A Georgia School of Excellence CHS Counselors Test Your Knowledge Common Misconceptions (Pre

A Georgia School of Excellence CHS Counselors Test Your Knowledge Common Misconceptions (Pre

A Georgia School of Excellence CHS Counselors Test Your Knowledge Common Misconceptions (Pre test) Please type exactly as you see below: http://bit.ly/2E7btdm Meet the Counseling Department Elizabeth Chilson A-Dap Curtisa Johnson

629 views • 34 slides
Forward Guidance without Common Knowledge Discussion Paul Pichler University of Vienna &

Forward Guidance without Common Knowledge Discussion Paul Pichler University of Vienna &

George-Marios Angeletos & Chen Lian Forward Guidance without Common Knowledge Discussion Paul Pichler University of Vienna & Oesterreichische Nationalbank Gerzensee, November 2017 Main contributions Dynamic Beauty Contests

424 views • 8 slides
vulnerabilities CVE, Common Vulnerabilities and Exposures CWE, Common Weakness Enumeration

vulnerabilities CVE, Common Vulnerabilities and Exposures CWE, Common Weakness Enumeration

Security & Knowledge Management a.a. 2019/20 There are a set of sources that provide updated information about security vulnerabilities CVE, Common Vulnerabilities and Exposures CWE, Common Weakness Enumeration CAPEC,

197 views • 8 slides
Timely Advice Time Occurs 599 Times In 546 Verses Time Is Important ! In The

Timely Advice Time Occurs 599 Times In 546 Verses Time Is Important ! In The

Timely Advice Time Occurs 599 Times In 546 Verses Time Is Important ! In The Year 2019 365 Days 8,760 Hours 525,600 Minutes 31,536,000 Seconds Timely Advice Yesterday is a cancelled check; tomorrow is a promissory

453 views • 18 slides
The Coinductive Formulation of Common Knowledge Colm Baston and Venanzio Capretta Functional

The Coinductive Formulation of Common Knowledge Colm Baston and Venanzio Capretta Functional

The Coinductive Formulation of Common Knowledge Colm Baston and Venanzio Capretta Functional Programming Lab School of Computer Science University of Nottingham ITP, Oxford, 09/07/2018 Epistemic Modal Logic A propositional logic extended with

883 views • 75 slides
knowledge via evidence resources Kelvin Ka-Wai Tam Director of Center for EBHC Taipei Medical

knowledge via evidence resources Kelvin Ka-Wai Tam Director of Center for EBHC Taipei Medical

[Theme Group] How do I timely update my knowledge via evidence resources Kelvin Ka-Wai Tam Director of Center for EBHC Taipei Medical University-Shuang-Ho Hospital Joyce Kee-Hsin Chen Supervisor, Dept. of Nursing Executive Secretary, EB-KTC

611 views • 22 slides
Responding in a timely manner Martin Thompson - @mjpt777 Hard Real-time Soft Real-time Squidgy

Responding in a timely manner Martin Thompson - @mjpt777 Hard Real-time Soft Real-time Squidgy

Responding in a timely manner Martin Thompson - @mjpt777 Hard Real-time Soft Real-time Squidgy Real-time The Unaware 1. How to Test and Measure 2. A little bit of Theory 3. A little bit of Practice 4. Common Pitfalls 5. Useful Algorithms and

1.05k views • 92 slides
Instructional Shifts for the Common Core www.engageNY.org Instructional Shifts for the Common

Instructional Shifts for the Common Core www.engageNY.org Instructional Shifts for the Common

Instructional Shifts for the Common Core www.engageNY.org Instructional Shifts for the Common Core Six Shifts in ELA/Literacy Six Shifts in Math Balancing Informational and Focus Literary Text Coherence Building Knowledge

505 views • 5 slides
Common Knowledge: Formalizing the Social Applications 1 Today and Thursday well take a step

Common Knowledge: Formalizing the Social Applications 1 Today and Thursday well take a step

Common Knowledge: Formalizing the Social Applications 1 Today and Thursday well take a step in the direction of formalizing the social puzzles, such as omission commission. 2 First, a reminder of the set-up and the theorem 3 The set-

932 views • 59 slides
Web Mining For Knowledge Discovery Using Ontology as a Background knowledge Searching using

Web Mining For Knowledge Discovery Using Ontology as a Background knowledge Searching using

Web Mining For Knowledge Discovery Using Ontology as a Background knowledge Searching using Googles rules Google searches for all words Google ignores many common words (stop words) Google finds results anywhere in a document,

301 views • 14 slides
Uncertainty In Coordination Games Christos A. Ioannou Motivation Common Knowledge

Uncertainty In Coordination Games Christos A. Ioannou Motivation Common Knowledge

Uncertainty In Coordination Games Christos A. Ioannou Motivation Common Knowledge Coordination games emphasize that equilibrium cannot be pinned down uniquely because beliefs are indeterminate. Global Coordination games assume that

691 views • 52 slides
Common Knowledge Gaps Identified in PSA Lead Trainer Applications Produce Safety Educators

Common Knowledge Gaps Identified in PSA Lead Trainer Applications Produce Safety Educators

Common Knowledge Gaps Identified in PSA Lead Trainer Applications Produce Safety Educators Call #32 June 25, 2018 Donna Pahl, PSA The Produce Safety Alliance Team Instructions All participants are muted. There will be time for

718 views • 43 slides
Smarter Balanced Assessment Consortium Common Core State Standards Define the knowledge and

Smarter Balanced Assessment Consortium Common Core State Standards Define the knowledge and

Smarter Balanced Assessment Consortium Common Core State Standards Define the knowledge and skills students need for college and career Developed voluntarily and cooperatively by states; more than 40 states have adopted

626 views • 28 slides
Smarter Balanced Assessment Consortium Common Core State Standards Define the knowledge and

Smarter Balanced Assessment Consortium Common Core State Standards Define the knowledge and

Smarter Balanced Assessment Consortium Common Core State Standards Define the knowledge and skills students need for college and career Developed voluntarily and cooperatively by states; more than 40 states have adopted

972 views • 29 slides
Forward Guidance without Common Knowledge November 9, 2017 1/30 George-Marios Angeletos Chen

Forward Guidance without Common Knowledge November 9, 2017 1/30 George-Marios Angeletos Chen

Forward Guidance without Common Knowledge November 9, 2017 1/30 George-Marios Angeletos Chen Lian MIT and NBER, MIT Standard: RE with CK Forward Guidance: Context or Pretext? How does the economy respond to news

574 views • 42 slides
Ticket to Work Program Timely Progress Review Basics 1 Objectives Discuss Timely Progress

Ticket to Work Program Timely Progress Review Basics 1 Objectives Discuss Timely Progress

Ticket to Work Program Timely Progress Review Basics 1 Objectives Discuss Timely Progress Review (TPR) fundamentals Discuss how the Ticket to Work Program impacts Continuing Disability Reviews (CDR) Discuss TPR requirements

994 views • 29 slides
KNOWLEDGE ACQUISITION AND CONSTRUCTION Transfer of Knowledge Knowledge acquisition is the

KNOWLEDGE ACQUISITION AND CONSTRUCTION Transfer of Knowledge Knowledge acquisition is the

KNOWLEDGE ACQUISITION AND CONSTRUCTION Transfer of Knowledge Knowledge acquisition is the process of extracting knowledge from whatever source including document, manuals, case studies, etc. Knowledge elicitation is a type of the

373 views • 26 slides
KBS Knowledge-Based Systems Group The need of common-sense reasoning on top of ontologies Minh

KBS Knowledge-Based Systems Group The need of common-sense reasoning on top of ontologies Minh

Realizing Default Logic over Description Logic Knowledge Bases Minh Dao-Tran, Thomas Eiter, Thomas Krennwallner KBS Group, Institute of Information Systems, Vienna University of Technology ECSQARU 2009 July 2, 2009 KBS Knowledge-Based

871 views • 47 slides

More recommend