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O =OsPROBLEM STATEMENTCoherent fusion of information for situation assessment and COA evaluation under uncertainty. Friendly language for inputting new information and answering mission-related queries.& " $ &What does it (new evidence) mean? It means that you can no longer expect to accomplish task A in two hours, unless you ensure that B does not happen. How come it took me six hours? It was probably due to the heavy rains. Thus, it would have been better to use unit-201, instead of unit-200. #QdZuAdZAdZQdZoAdZ#bo*op[qx{|/F  ` f̙f` ff̙f` 999MMM>?" dd@,?nKd@  d n<@ d`n2 p?" dd@   @@``@n?" dd@  @@``PR    @ ` ` p>> j(    s *_  "    X Click to edit Master title style!!    c $aM1"%< DOU)/?R _ tUU @     G ; V `Q   # W W ,$0N E l  `Q  Z  s *E  kN   h    lfB   6D>  hfB   6D>  hfB   6D>  hfB   6D>  hN  l    l`  l C  lfB  6D  h   BCDE@F D7kxk](V@EX3q @      l   BCVDEFV @` k   BCXDE F*(8PXXX@`T  ~B B NZD>:W 1LxB  HD>K G ~B  NZD>KM BExB  HD>KK   Bh+f)  Wu&     B\0 Yx(u)=yF (      BPk R WZ&     B,rd   WW&     B 3 OX=x   `  0El2  <Ԕ  o8 o K 2Z ~B #B NZD>  xB $ HD>  ~B % NZD>  xB & HD>  ' B48\  Wu&    ( BK YY(    ) B j= o  WZ&    * B|hD,   WW&    + B@q + MX   ` , 0 ]~B . NZD>+ "  4 Tt?" H  WProbability of Counterfactuals:   5 T?"   nFunctional Bayes Net  6 s *A ??x d` 7 c $A ??, d  H  0޽h ? f̙f    p D (    s *D ~ TYPES OF QUERIES <00   B  N D1?"hh7  N?"i;,$D 0 w# Inference to four types of claims:$$! 2$  $    Ndf?">8p$D 0<4___PPT9 #Effects of potential interventions,"$! 2$  $   @`  NHf?" 8r t$D 0@8___PPT9 )Claims about attribution (responsibility)"*! 2*  *   @`   Nx?" 8% t$D 0@8___PPT9 (Claims about direct and indirect effects")! 2)  )   @`   N?" 8 t$D 0@8___PPT9 Claims about explanations"! 2     @`H  0޽h ? f̙fi     (    s *X ,$D 0  THE OVERRIDING THEME <00     0' , @`  c $A ??=x d  c $A ??px dH  0޽h ? f̙f  M(    s *   ]OUTLINE,B  N D1?"  Tl)?"___PPT9 hReview: Causal analysis in COA evaluation Progress report: Model Correctness  J. Pearl Causal Effects  J. Tian Identifications in Linear Systems  C. Brito Actual Causation and Explanations  M. Hopkins Qualitative Planning Under Uncertainty  B. Bonet >01-10/1031+       $  $    )$$ $$P['\ @`H  0޽h ? f̙f" "w",,!(    s *% Z,$D 0 kCORRECTNESS and CORROBORATION$   B  N D1?",$D 0H  T<?"7  ZData D corroborates structure S if S is (i) falsifiable and (ii) compatible with D. [  . ,U8Xx  Z,4Ԕ?"X!  6Falsifiability: P*(S) P*6  T؇?""  jTypes of constraints: 1. conditional independencies 2. inequalities (for restricted domains) 3. functionalkk2  T Ԕ?" B @ N DԔ?"B  @ N DԔ?"B  @ N DԔ?"kB  @ N DԔ?"0IB  @ N DԔ?"cgB  @ N DԔ?"=B @ N DԔ?"B @ N DԔ?"B @ N DԔ?"*B @ N DԔ?"]Z!B @ N DԔ?"SB @ N DԔ?"xB @ N DԔ?"(%B @ N DԔ?":VB @ N DԔ?"kB  N DԔ?"B @ N DԔ?"&   S 0e0e    BC\DE(F > 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| iS[Jc&P.6V\ @   S" @  fZ GHGIԔ?" Y  T,?"  ZConstraints implied by S&  TD ?"y   DP*&  T$"?"F aP*(S)@~2  H ?"P  TԞ?"YPy FD (Data)"     ` GSHDZISԔ?"\0 ! T?"i ;e.g.,F t " <s ~T   ) ## tB $ T DԔ?"&B % T DԔ?"3B & T DԔ?"R ' T'?" ) 3w ( Th?" ) 3x ) T?"  ) 3y * TL:?"J  ) 3zb + 3 r G_ HI`SԔ?" H , c $A ?? Tx dH  0޽h ??` + f̙f     H1 (  H  H s *tQ?,$D 0 1FROM CORROBORATING MODELS TO CORROBORATING CLAIMS22$ 2  B H N D1?"hh,$D 0< H TD?"F JA corroborated structure can imply identifiable yet uncorroborated claims..KJ8Xx H T?" F/@ ;e.g.,B H T DԔ?"#[# H T<~?"ev 5x H T?"e 5yB  H T DԔ?"#[#  H T`,?"ev 5x  H T?"e 5y  H T?"lP9 5ab H 3 r G_ H;ITԔ?" 3,$D 0H H 0޽h ? H f̙f7     LO (  L  L s * Q?,$D 0 1FROM CORROBORATING MODELS TO CORROBORATING CLAIMS22$ 2  B L N D1?"hh,$D 0< L T?"F JA corroborated structure can imply identifiable yet uncorroborated claims..KJ8Xx L TH?" F/@ ;e.g., L T?"ev 5x L T#?"e 5y  L T$'?"ev 5x  L T*?"e 5y   L T(.?"2/y,$D 0 Ca = 0"b L 3 r G_ H;ITԔ?" 3,$D 0H L 0޽h ? L f̙f jb%0(  0  0 s *LQ?,$D 0 1FROM CORROBORATING MODELS TO CORROBORATING CLAIMS22$ 2  B 0 N D1?"hh,$D 0< 0 T?"F JA corroborated structure can imply identifiable yet uncorroborated claims..KJ8Xx 0 T?" F/@ ;e.g.,B 0 T DԔ?"#[#  0 T̃?"ev 5x  0 TP?"e 5y  0 T,l?"e ,$0 5zB 0 T DԔ?"#[# 0 TQ?"ev 5x 0 T?"e 5y 0 T̏?"lP9 5al !e<  $0e!< ,$D0t  e9 "0 e9,$D0 0 T?" q9 5aB 0 T DԔ?"r ## 0 TL?" e  5x 0 T?"e 5y 0 T4?" e 5zB 0 T DԔ?"((  0 T?"9 5b/ #0 Ht?"!<  3Some claims can be more corroborated than others. 042 2b %0 3 r G_ H;ITԔ?"* S,$D 0H 0 0޽h ? %0 f̙f ~P(  P  P s *Q?,$D 0 1FROM CORROBORATING MODELS TO CORROBORATING CLAIMS22$ 2  B P N D1?"hh,$D 0< P T?"F JA corroborated structure can imply identifiable yet uncorroborated claims..KJ8Xx P T?" F/@ ;e.g.,B P T DԔ?"#[# P T{?"ev 5x P Thz?"e 5y  P T%?"e ,$0 5zB  P T DԔ?"#[#  P T(?"ev 5x  P T%?"e 5y  P Tt?"lP9 5az !e<  P e!< ,$D0  e9 P  e9,$D0 P T?" q9 5aB P T DԔ?"r ## P T|?" e  5x P T?"e 5y P T ?" e 5zB P T DԔ?"(( P TÈ?"9 5b/ P Hƈ?"!<  3Some claims can be more corroborated than others. 042 2b P 3 r G_ H;ITԔ?"Js,$D 0H P 0޽h ? P f̙f pd(  d  d s *Q?,$D 0 1FROM CORROBORATING MODELS TO CORROBORATING CLAIMS22$ 2  B d N D1?"hh,$D 0< d T?"F JA corroborated structure can imply identifiable yet uncorroborated claims..KJ8Xx d T?" F/@ ;e.g.,B d T DԔ?"#[# d T?"ev 5x d T| ?"e 5y  d TX?"e ,$0 5zB  d T DԔ?"#[#  d Tx?"ev 5x  d TX?"e 5y  d T?"lP9 5ab d@ 3 rZ GyHI@Ԕ?"" o,$D 0z !e<  d e!< ,$D0  e9 d  e9,$D0 d TĜ?" q9 5aB d T DԔ?"r ## d Tl?" e  5x d TP!?"e 5y d T #?" e 5zB d T DԔ?"(( d T&?"9 5b/ d H?"!<  3Some claims can be more corroborated than others. 042 2T d <v޽h @ ? d f̙f tlX(  X  X s *,͈Q?,$D 0 1FROM CORROBORATING MODELS TO CORROBORATING CLAIMS22$ 2  B X N D1?"hh,$D 0< X Tш?"F JA corroborated structure can imply identifiable yet uncorroborated claims..KJ8Xx X T8܈?" F/@ ;e.g.,B X T DԔ?"#[# X T߈?"ev 5x X T@?"e 5y  X T?"e ,$0 5zB  X T DԔ?"#[#  X T?"ev 5x  X T?"e 5y  X T4Ո?"lP9 5a\ X T ?" ",$D 0 Definition: An identifiable claim C is corroborated by data if some minimal set of assumptions in S sufficient for identifying C is corroborated by the data.   0  X T?"f",$D 0 @Graphical criterion: minimal substructure = maximal supergraph>A, 6 b X@ 3 rZ GyHI@Ԕ?"" o,$D 0z !e<  X e!< ,$D0  e9 X  e9,$D0 X T?" q9 5aB X T DԔ?"r ## X TP0?" e  5x X TD?"e 5y X T3?" e 5zB X T DԔ?"(( X T@?"9 5b/ X H?"!<  3Some claims can be more corroborated than others. 042 2H X 0޽h ? X f̙f .((  (B ( N D1?"hh,$D 0< ( T C?"F JA corroborated structure can imply identifiable yet uncorroborated claims..KJ8Xx ( T\?" F/@ ;e.g., ( TK?" q9 5aB ( T DԔ?"#[# ( T<`?"ev 5x  ( T?"e 5y  ( T~?"e  5zB  ( T DԔ?"#[#  ( TԀ?"ev 5x  ( T?"e 5y ( TX?"e  5z ( T?"lP9 5a ( T?"9 5bB ( T DԔ?"#r # ( T8?"e  5x ( T?"e 5y ( T?"e  5zB ( T DԔ?"((b ( 3 r G_ H;ITԔ?"" K,$D 0  ( s * Q?,$D 0 1FROM CORROBORATING MODELS TO CORROBORATING CLAIMS22$ 2  - ,( N$?"!<  3Some claims can be more corroborated than others. 042 2\ -( T)?" ",$D 0 Definition: An identifiable claim C is corroborated by data if some minimal set of assumptions in S sufficient for identifying C is corroborated by the data.   0 p .( T4?"f",$D 0 @Graphical criterion: minimal substructure = maximal supergraph,A@ 6 H ( 0޽h ? ( f̙f @;(  @ @ s *  ]OUTLINE,B @ N D1?" @ Tx?"___PPT9 VReview: Causal analysis in COA evaluation Progress report: Model Correctness  J. Pearl Causal Effects  J. Tian Identifications in Linear Systems  C. Brito Actual Causation and Explanations  M. Hopkins Qualitative Planning Under Uncertainty  B. Bonet >01-10/1031+777777777777      $  $    )$$ $$P['\ @`H @ 0޽h ? f̙f0  ?( } X  C D3     c $DQD @   ; The subject of my lecture this evening is CAUSALITY. It is not an easy topic to speak about, but it is a fun topic to speak about. It is not easy because, like religion, sex and intelligence, causality was meant to be practiced, not analyzed. And it is fun, because, like religion, sex and intelligence, emotions run high, examples are plenty, there are plenty of interesting people to talk to, and above all, an exhilarating experience of watching our private thoughts magnified under the microscope of formal analysis.   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