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ainty t Uncer 13 Chapter 1 13 Chapter
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Outline y Uncertaint ♦ y Probabilit ♦ Semantics and Syntax ♦ Inference ♦ Rule es’ y Ba and endence Indep ♦ 2 13 Chapter
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yt Uncertain flight re efo b minutes t rt o airp r fo leave =t A action Let A Will time? on there me get t Problems: etc.) plans, drivers’ other state, (road y observabilit rtial pa 1) rts) o rep traffic CBS (K rs senso noisy 2) etc.) tire, (flat outcomes action in y uncertaint 3) traffic redicting p and delling mo of y complexit immense 4) either roach app logical purely a Hence time” on there me get will 25 A“ d: o falseho risks 1) making: decision r fo eak wo to re a that conclusions to leads 2) r o ridge b the on accident no there’s if time on there me get will 25 A“ etc.” etc intact remain tires my and rain esn’t do it and time on there me get to said eb reasonably might 1440 A( ). . . rt o airp the in overnight y sta to have I’d but 3 13 Chapter
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yt uncertain handling for ds Metho logic: nonmonotonic r o Default tire flat a have not es do r ca my Assume evidence yb contradicted unless rks ow 25 A Assume contradiction? handle to w Ho reasonable? re a assumptions What Issues: : rs facto fudge with Rules ime nT tO por AtAir 3. 0 7→25 A ass etGr W99 . 0 7→ er l ink pr S ain R7. 0 7→ ass etGr W ?? ain R causes er l ink pr S e.g., combination, with Problems Issues: y Probabilit evidence, available the Given 04 . 0 y robabilit p with time on there me get will 25 A gambling of ry theo (1565) rdamo Ca C.), (9th a ry Mahaviraca e.g., y uncertaint NOT truth of degree handles logic uzzy F( )2. 0 degree to true is ass etGr W 4 13 Chapter
('yinu ou'ogy snieas quawj!equa leo 01 snogojeuy) gI0=('w'e g 'squap!ooe pauode ou d :aouapIna Mau yhIm agueyp suolsodoud jo san!l!qeqod (suoneniis jejiwis jo aouauadxe ised woy paujeal aq ny8iw inq) uoneniis quajno ayn u!Kouapuan onsil!qeqoud,,e jo swiejo qou ae asay 900=(squap!ooe pauoda ou s)d a8pajmouy jo anens uMo s auo o1 suolisodoud azeja san!l!qeqoud :Kuqeqoud ueisakeg o annafqns 1 'suollpuoo jelul 'spej quenajal go ypel :aouejou 'suoneoy!enb 'suondaoxa aneJewnua on anj!e]:ssauize] Jos1p393ZI.rewwns suo1μosse o14sμqeqo1d Au!l!qeqoId
y Probabilit of effects summarize assertions Probabilistic etc. qualifications, exceptions, enumerate to failure : laziness etc. conditions, initial facts, relevant of lack : rance igno y: robabilit p esian y Ba r o Subjective wledge kno of state wn o one’s to ositions rop p relate Probabilities 06 . 0 =) accidents rted o rep no | 25 A( P e.g., situation current the in tendency” robabilistic “p a of claims not re a These situations) r simila of erience exp past from rned lea eb might (but evidence: new with change ositions rop p of Probabilities 15 . 0 =) a.m. 5 , accidents rted o rep no | 25 A( P e.g., truth.) not , α =| B K status entailment logical to (Analogous 5 13 Chapter
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yt uncertain under decisions Making wing: follo the elieve bI ose Supp 04 . 0 =). . . | time on there me gets 25 A( P 70 . 0 =). . . | time on there me gets 90 A( P 95 . 0 =). . . | time on there me gets 120 A( P 9999 . 0 =). . . | time on there me gets 1440 A( P ose? cho to action Which etc. cuisine, rt o airp vs. flight missing r fo references p my on ends Dep references p infer and resent rep to used is ry theo y Utilit ry theo y robabilit p + ry theo y utilit = ry theo Decision 6 13 Chapter
z/T=9/1+9/I+9/L=()d+()d+(T)d=(匝>Io1p)d:3 (m)divem=(V)d 7 Jo asqns Aue s!quana uy 9/T=(9)d=(9)d=()d=(8)d=(亿)d=(I)d83 I=(m)d"区 I>(m)d>0 1's 7m Kana Joj (m)d quawuBisse ue yilm aeds aldwes e s!japow Aullqeqod o aeds Auqeqoud y quana olwone/puom ajqissod/quiod aldwes e s!m aip e jo sllo ajqissod g a aeds ajdwes ay1-7 ias e yim uigag sorseq Ku!l!qeqoId
basics y Probabilit space sample —the Ω set a with Begin die. a of rolls ossible p 6 e.g., event atomic / rld ow ossible p/ oint p sample a is Ω ∈ ω space sample a is del mo y robabilit p r o space y robabilit p A s.t. Ω ∈ ω every r fo ) ω( P assignment an with 1 ≤) ω( P ≤0 1 =) ω( Pω Σ . 6/1 = (6) P = (5) P = (4) P = (3) P = (2) P = (1) P e.g., Ω of subset any is A event An ) ω( P} A∈ω{ Σ =) A( P 2/1 =6/1 +6/1 +6/1 = (3) P + (2) P + (1) P = 4) < roll die ( P E.g., 7 13 Chapter
8 EI adeyD z/1=9/1+9/1+9/T=(9)d+()d+(t)d=(an.4=ppO)d83 (m)d=(xi=(=X)d :X'A'Kue joy uolinq!asip qeqoud e saonpu!d 3n.4=()ppO83 sueajoog jo sjea ay8a 'aue awos on squiod ajdwes woyy uonouny e s!ajqeuen wopue y solqeriea wopuey
ariables v Random the e.g., range, some to oints p sample from function a is riable va random A oleans Bo r o reals . ue tr = (1) dd O e.g., : X r.v. any r fo distribution y robabilit p a induces P x =) ω( X: ω{ Σ =)i x = X( P }i ) ω( P 2/1 =6/1 +6/1 +6/1 = (5) P + (3) P + (1) P =) ue tr = dd O( P e.g., 8 13 Chapter
(9VD)dI+(9-VD)d+(9VDL)d=(9∧D)d← (9VD)∧(9VD)∧(9VoL)≡(9∧D)83 an s!1!yplyM u!squana olwole jo uonounfsip uollsodold q-VD0‘3s2Df=a3n4=/:83 epow o jeuo!!sodod =quod aldwes 'sa]qeuen ueajoog y!M sajqeuen ayn jo sague ayn jo nonpod ueisaue)ayn s!aoeds ajdwes ay "a'!'sa qeuen wopuel jo nas e go sanjen ayn Kq paugap ae squod aldwes ay 'suone!dde Iu!uaO an.!g=(m)g pue an.!n=(m)aayM squiod =gVD quana asof=(m)y auaym squiod ajdwes jo 1as DL quana an.1g=(m)y aaym squiod aldwes jo nas D quana :g pue K sajqeuen wopuel ueajoog uanl an s!uonisodoud ayl ajaym (squlod aldwes jo as)quana ay se uonsodod e o yu!yL suorqsodoId
ositions Prop oints) p sample of (set event the as osition rop p a of Think true is osition rop p the where : B and A riables va random olean Bo Given ue tr =) ω( A where oints p sample of set =a event se al f =) ω( A where oints p sample of set =a¬ event ue tr =) ω( B and ue tr =) ω( A where oints p =b ∧a event defined re a oints p sample the applications, AI in Often the i.e., riables, va random of set a of values the yb riables va the of ranges the of duct ro p rtesian Ca the is space sample del mo logic ositional rop p = oint p sample riables, va olean Bo With . b ¬ ∧ar o, se al f = B, ue tr = A e.g., true is it which in events atomic of disjunction = osition Prop )b ∧a( ∨)b ¬ ∧a( ∨)b ∧a¬( ≡)b ∨a( e.g., )b ∧a( P +)b ¬ ∧a( P +)b ∧a¬( P =)b ∨a( P ⇒ 9 13 Chapter
OI I odeo 'awooino jo ssalpuea Kauow aso]on se os naq on paouoj aq ueo swoixe asay aejoIA ey san!l!qeqod o1 3u!poooe siaq oym qua3e ue :(IE6I)au!ap anJL (9VD)d-(9)d+(D)d=(9∧D)d83 s31lμqeqo1d panejal aney isnw squana paneja Klleiol ulejao 1eyn Kjdw!suolluyap ay 乙K4 l!qeqo.Id∂sn AuM
y? probabilit use y Wh related have must events related logically certain that imply definitions The robabilities p )b ∧a( P −)b( P +) a( P =)b ∨a( P E.g., >A B True B A violate that robabilities p to rding acco ets b who agent an (1931): Finetti de outcome. of rdless rega money lose to as so et b to rced fo eb can axioms these 10 13 Chapter