(original) (raw)

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0.02352 setrgbcolor 1076 160 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 710 543 a Fn([Read)c(Ch.)38 b(10])-2 647 y([Recommended)27 b(exercises)k(10.1,) d(10.2,)h(10.5,)g(10.7,)f(10.8])40 805 y Fm(\017)21 b Fn(Sequen)n(tial)31 b(co)n(v)n(ering)e(algorithms)40 950 y Fm(\017)21 b Fn(F)n(OIL)40 1095 y Fm(\017)g Fn(Induction)30 b(as)e(in)n(v)n(erse)i(of)f(deduction)40 1240 y Fm(\017)21 b Fn(Inductiv)n(e)30 b(Logic)g(Programm)o(ing)0 2748 y Fl(229)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fk(Machine)h(L)n(e)n(arning)p Fl(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e (Hill,)j(1997)p eop %%Page: 230 2 230 1 bop 25 160 a Fo(Learning)35 b(Disjunctiv)m(e)g(Sets)g(of)f(Rules) 1618 160 y 0.8666 0.03137 0.02352 setrgbcolor 1618 160 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 64 x Fn(Metho)r(d)29 b(1:)39 b(Learn)28 b(decision)j(tree,)e(con)n(v)n (ert)g(to)g(rules)0 742 y(Metho)r(d)g(2:)39 b(Sequen)n(tial)31 b(co)n(v)n(ering)e(algorithm:)16 887 y(1.)21 b Fj(L)l(e)l(arn)30 b(one)h(rule)e Fn(with)h(high)f(accuracy)-7 b(,)29 b(an)n(y)g(co)n(v)n (erage)16 1032 y(2.)21 b(Remo)n(v)n(e)28 b(p)r(ositiv)n(e)j(examples)f (co)n(v)n(ered)e(b)n(y)h(this)h(rule)16 1177 y(3.)21 b(Rep)r(eat)0 2748 y Fl(230)334 b(lecture)17 b(slides)f(for)f(textb)q (o)q(ok)g Fk(Machine)h(L)n(e)n(arning)p Fl(,)c(T.)j(Mitc)o(hell,)h (McGra)o(w)e(Hill,)j(1997)p eop %%Page: 231 3 231 2 bop 25 160 a Fo(Sequen)m(tial)36 b(Co)m(v)m(ering)f(Algorithm) 1454 160 y 0.8666 0.03137 0.02352 setrgbcolor 1454 160 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 63 x Fi(Sequential-)0 641 y(co)n(vering)p Fn(\()p Fh(T)12 b(ar)r(g)s(et)p 692 641 26 2 v 32 w(attr)r(ibute;)j(Attr)r(ibutes;)g(E) 5 b(xampl)r(es;)14 b(T)e(hr)r(eshol)r(d)p Fn(\))40 799 y Fm(\017)21 b Fh(Lear)r(ned)p 431 799 V 31 w(r)r(ul)r(es)j Fm( )g(fg)40 944 y(\017)d Fh(R)q(ul)r(e)i Fm( )29 b Fi(learn-one-)104 1048 y(r)n(ule)p Fn(\()p Fh(T)12 b(ar)r(g)s(et)p 600 1048 V 33 w(attr)r(ibute;)j(Attr)r(ibutes;)f(E)5 b(xampl)r(es)p Fn(\))40 1193 y Fm(\017)21 b Fn(while)31 b Fi(perf)n(ormance)p Fn(\()p Fh(R)q(ul)r(e;)14 b(E)5 b(xampl)r(es)p Fn(\))104 1297 y Fh(>)24 b(T)12 b(hr)r(eshol)r(d)p Fn(,)27 b(do)125 1442 y Fg({)21 b Fh(Lear)r(ned)p 522 1442 V 31 w(r)r(ul)r(es)j Fm( )g Fh(Lear)r(ned)p 1207 1442 V 31 w(r)r(ul)r(es)c Fn(+)f Fh(R)q(ul)r(e)125 1567 y Fg({)i Fh(E)5 b(xampl)r(es)24 b Fm( )g Fh(E)5 b(xampl)r(es)29 b Fm(\000)f(f)p Fn(examples)195 1670 y(correctly)j(classi\014ed)g(b)n(y)d Fh(R)q(ul)r(e)p Fm(g)125 1795 y Fg({)21 b Fh(R)q(ul)r(e)j Fm( )29 b Fi(learn-one-)195 1899 y(r)n(ule)p Fn(\()p Fh(T)12 b(ar)r(g)s(et)p 691 1899 V 33 w(attr)r(ibute;)j(Attr)r(ibutes;)g(E)5 b(xampl)r(es)p Fn(\))40 2044 y Fm(\017)21 b Fh(Lear)r(ned)p 431 2044 V 31 w(r)r(ul)r(es)j Fm( )29 b Fn(sort)g Fh(Lear)r(ned)p 1294 2044 V 31 w(r)r(ul)r(es)g Fn(accord)g(to)104 2148 y Fi(perf)n(ormance)f Fn(o)n(v)n(er)g Fh(E)5 b(xampl)r(es)40 2293 y Fm(\017)21 b Fn(return)28 b Fh(Lear)r(ned)p 694 2293 V 31 w(r)r(ul)r(es)0 2748 y Fl(231)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fk(Machine)h(L)n(e)n(arning)p Fl(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e(Hill,)j(1997)p eop %%Page: 232 4 232 3 bop 25 170 a Fo(Learn-One-Rule)780 170 y 0.8666 0.03137 0.02352 setrgbcolor 780 170 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 0 478 a 33154007 19229320 5130977 17366384 26575831 29864919 startTexFig 0 478 a %%BeginDocument: ./bookps/learn-one-rule.ps %AI5_FileFormat 2.0 %AI3_ColorUsage: Black&White %AI3_TemplateBox: 306 396 306 396 %AI3_TileBox: 31 31 583 761 %AI3_DocumentPreview: Macintosh_ColorPic %AI5_ArtSize: 612 792 %AI5_RulerUnits: 2 %AI5_ArtFlags: 1 0 0 1 0 0 1 1 0 %AI5_TargetResolution: 800 %AI5_NumLayers: 1 %AI5_OpenToView: 6 504 2 1018 725 18 0 1 3 40 %AI5_OpenViewLayers: 7 userdict /Adobe_level2_AI5 23 dict dup begin put /packedarray where not { userdict begin /packedarray { array astore readonly } bind def /setpacking /pop load def /currentpacking false def end 0 } if pop userdict /defaultpacking currentpacking put true setpacking /initialize { Adobe_level2_AI5 begin } bind def /terminate { currentdict Adobe_level2_AI5 eq { end } if } bind def mark /setcustomcolor where not { /findcmykcustomcolor { 5 packedarray } bind def /setcustomcolor { exch aload pop pop 4 { 4 index mul 4 1 roll } repeat 5 -1 roll pop setcmykcolor } def } if /gt38? mark {version cvr cvx exec} stopped {cleartomark true} {38 gt exch pop} ifelse def userdict /deviceDPI 72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt put userdict /level2? systemdict /languagelevel known dup { pop systemdict /languagelevel get 2 ge } if put /level2ScreenFreq { begin 60 HalftoneType 1 eq { pop Frequency } if HalftoneType 2 eq { pop GrayFrequency } if HalftoneType 5 eq { pop Default level2ScreenFreq } if end } bind def userdict /currentScreenFreq level2? {currenthalftone level2ScreenFreq} {currentscreen pop pop} ifelse put level2? not { /setcmykcolor where not { /setcmykcolor { exch .11 mul add exch .59 mul add exch .3 mul add 1 exch sub setgray } def } if /currentcmykcolor where not { /currentcmykcolor { 0 0 0 1 currentgray sub } def } if /setoverprint where not { /setoverprint /pop load def } if /selectfont where not { /selectfont { exch findfont exch dup type /arraytype eq { makefont } { scalefont } ifelse setfont } bind def } if /cshow where not { /cshow { [ 0 0 5 -1 roll aload pop ] cvx bind forall } bind def } if } if cleartomark /anyColor? { add add add 0 ne } bind def /testColor { gsave setcmykcolor currentcmykcolor grestore } bind def /testCMYKColorThrough { testColor anyColor? } bind def userdict /composite? level2? { gsave 1 1 1 1 setcmykcolor currentcmykcolor grestore add add add 4 eq } { 1 0 0 0 testCMYKColorThrough 0 1 0 0 testCMYKColorThrough 0 0 1 0 testCMYKColorThrough 0 0 0 1 testCMYKColorThrough and and and } ifelse put composite? not { userdict begin gsave /cyan? 1 0 0 0 testCMYKColorThrough def /magenta? 0 1 0 0 testCMYKColorThrough def /yellow? 0 0 1 0 testCMYKColorThrough def /black? 0 0 0 1 testCMYKColorThrough def grestore /isCMYKSep? cyan? magenta? yellow? black? or or or def /customColor? isCMYKSep? not def end } if end defaultpacking setpacking currentpacking true setpacking userdict /Adobe_typography_AI5 54 dict dup begin put /initialize { begin begin Adobe_typography_AI5 begin Adobe_typography_AI5 { dup xcheck { bind } if pop pop } forall end end end Adobe_typography_AI5 begin } def /terminate { currentdict Adobe_typography_AI5 eq { end } if } def /modifyEncoding { /_tempEncode exch ddef /_pntr 0 ddef { counttomark -1 roll dup type dup /marktype eq { pop pop exit } { /nametype eq { _tempEncode /_pntr dup load dup 3 1 roll 1 add ddef 3 -1 roll put } { /_pntr exch ddef } ifelse } ifelse } loop _tempEncode } def /TE { StandardEncoding 256 array copy modifyEncoding /_nativeEncoding exch def } def % /TZ { dup type /arraytype eq { /_wv exch def } { /_wv 0 def } ifelse /_useNativeEncoding exch def pop pop findfont _wv type /arraytype eq { _wv makeblendedfont } if dup length 2 add dict begin mark exch { 1 index /FID ne { def } if cleartomark mark } forall pop /FontName exch def counttomark 0 eq { 1 _useNativeEncoding eq { /Encoding _nativeEncoding def } if cleartomark } { /Encoding load 256 array copy modifyEncoding /Encoding exch def } ifelse FontName currentdict end definefont pop } def /tr { _ax _ay 3 2 roll } def /trj { _cx _cy _sp _ax _ay 6 5 roll } def /a0 { /Tx { dup currentpoint 3 2 roll tr _psf newpath moveto tr _ctm _pss } ddef /Tj { dup currentpoint 3 2 roll trj _pjsf newpath moveto trj _ctm _pjss } ddef } def /a1 { /Tx { dup currentpoint 4 2 roll gsave dup currentpoint 3 2 roll tr _psf newpath moveto tr _ctm _pss grestore 3 1 roll moveto tr sp } ddef /Tj { dup currentpoint 4 2 roll gsave dup currentpoint 3 2 roll trj _pjsf newpath moveto trj _ctm _pjss grestore 3 1 roll moveto tr jsp } ddef } def /e0 { /Tx { tr _psf } ddef /Tj { trj _pjsf } ddef } def /e1 { /Tx { dup currentpoint 4 2 roll gsave tr _psf grestore 3 1 roll moveto tr sp } ddef /Tj { dup currentpoint 4 2 roll gsave trj _pjsf grestore 3 1 roll moveto tr jsp } ddef } def /i0 { /Tx { tr sp } ddef /Tj { trj jsp } ddef } def /i1 { W N } def /o0 { /Tx { tr sw rmoveto } ddef /Tj { trj swj rmoveto } ddef } def /r0 { /Tx { tr _ctm _pss } ddef /Tj { trj _ctm _pjss } ddef } def /r1 { /Tx { dup currentpoint 4 2 roll currentpoint gsave newpath moveto tr _ctm _pss grestore 3 1 roll moveto tr sp } ddef /Tj { dup currentpoint 4 2 roll currentpoint gsave newpath moveto trj _ctm _pjss grestore 3 1 roll moveto tr jsp } ddef } def /To { pop _ctm currentmatrix pop } def /TO { iTe _ctm setmatrix newpath } def /Tp { pop _tm astore pop _ctm setmatrix _tDict begin /W { } def /h { } def } def /TP { end iTm 0 0 moveto } def /Tr { _render 3 le { currentpoint newpath moveto } if dup 8 eq { pop 0 } { dup 9 eq { pop 1 } if } ifelse dup /_render exch ddef _renderStart exch get load exec } def /iTm { _ctm setmatrix _tm concat 0 _rise translate _hs 1 scale } def /Tm { _tm astore pop iTm 0 0 moveto } def /Td { _mtx translate _tm _tm concatmatrix pop iTm 0 0 moveto } def /iTe { _render -1 eq { } { _renderEnd _render get dup null ne { load exec } { pop } ifelse } ifelse /_render -1 ddef } def /Ta { pop } def /Tf { dup 1000 div /_fScl exch ddef % selectfont } def /Tl { pop 0 exch _leading astore pop } def /Tt { pop } def /TW { 3 npop } def /Tw { /_cx exch ddef } def /TC { 3 npop } def /Tc { /_ax exch ddef } def /Ts { /_rise exch ddef currentpoint iTm moveto } def /Ti { 3 npop } def /Tz { 100 div /_hs exch ddef iTm } def /TA { pop } def /Tq { pop } def /Th { pop pop pop pop pop } def /TX { pop } def /Tk { exch pop _fScl mul neg 0 rmoveto } def /TK { 2 npop } def /T* { _leading aload pop neg Td } def /T*- { _leading aload pop Td } def /T- { _ax neg 0 rmoveto _hyphen Tx } def /T+ { } def /TR { _ctm currentmatrix pop _tm astore pop iTm 0 0 moveto } def /TS { currentfont 3 1 roll /_Symbol_ _fScl 1000 mul selectfont 0 eq { Tx } { Tj } ifelse setfont } def /Xb { pop pop } def /Tb /Xb load def /Xe { pop pop pop pop } def /Te /Xe load def /XB { } def /TB /XB load def currentdict readonly pop end setpacking userdict /Adobe_ColorImage_AI6 known not { userdict /Adobe_ColorImage_AI6 17 dict put } if userdict /Adobe_ColorImage_AI6 get begin /initialize { Adobe_ColorImage_AI6 begin Adobe_ColorImage_AI6 { dup type /arraytype eq { dup xcheck { bind } if } if pop pop } forall } def /terminate { end } def currentdict /Adobe_ColorImage_AI6_Vars known not { /Adobe_ColorImage_AI6_Vars 14 dict def } if Adobe_ColorImage_AI6_Vars begin /channelcount 0 def /sourcecount 0 def /sourcearray 4 array def /plateindex -1 def /XIMask 0 def /XIBinary 0 def /XIChannelCount 0 def /XIBitsPerPixel 0 def /XIImageHeight 0 def /XIImageWidth 0 def /XIImageMatrix null def /XIBuffer null def /XIDataProc null def end /WalkRGBString null def /WalkCMYKString null def /StuffRGBIntoGrayString null def /RGBToGrayImageProc null def /StuffCMYKIntoGrayString null def /CMYKToGrayImageProc null def /ColorImageCompositeEmulator null def /SeparateCMYKImageProc null def /FourEqual null def /TestPlateIndex null def currentdict /_colorimage known not { /colorimage where { /colorimage get /_colorimage exch def } { /_colorimage null def } ifelse } if /_currenttransfer systemdict /currenttransfer get def /colorimage null def /XI null def /WalkRGBString { 0 3 index dup length 1 sub 0 3 3 -1 roll { 3 getinterval { } forall 5 index exec 3 index } for 5 { pop } repeat } def /WalkCMYKString { 0 3 index dup length 1 sub 0 4 3 -1 roll { 4 getinterval { } forall 6 index exec 3 index } for 5 { pop } repeat } def /StuffRGBIntoGrayString { .11 mul exch .59 mul add exch .3 mul add cvi 3 copy put pop 1 add } def /RGBToGrayImageProc { Adobe_ColorImage_AI6_Vars begin sourcearray 0 get exec dup length 3 idiv string dup 3 1 roll /StuffRGBIntoGrayString load exch WalkRGBString end } def /StuffCMYKIntoGrayString { exch .11 mul add exch .59 mul add exch .3 mul add dup 255 gt { pop 255 } if 255 exch sub cvi 3 copy put pop 1 add } def /CMYKToGrayImageProc { Adobe_ColorImage_AI6_Vars begin sourcearray 0 get exec dup length 4 idiv string dup 3 1 roll /StuffCMYKIntoGrayString load exch WalkCMYKString end } def /ColorImageCompositeEmulator { pop true eq { Adobe_ColorImage_AI6_Vars /sourcecount get 5 add { pop } repeat } { Adobe_ColorImage_AI6_Vars /channelcount get 1 ne { Adobe_ColorImage_AI6_Vars begin sourcearray 0 3 -1 roll put channelcount 3 eq { /RGBToGrayImageProc } { /CMYKToGrayImageProc } ifelse load end } if image } ifelse } def /SeparateCMYKImageProc { Adobe_ColorImage_AI6_Vars begin sourcecount 0 ne { sourcearray plateindex get exec } { sourcearray 0 get exec dup length 4 idiv string 0 2 index plateindex 4 2 index length 1 sub { get 255 exch sub 3 copy put pop 1 add 2 index } for pop pop exch pop } ifelse end } def /FourEqual { 4 index ne { pop pop pop false } { 4 index ne { pop pop false } { 4 index ne { pop false } { 4 index eq } ifelse } ifelse } ifelse } def /TestPlateIndex { Adobe_ColorImage_AI6_Vars begin /plateindex -1 def /setcmykcolor where { pop gsave 1 0 0 0 setcmykcolor systemdict /currentgray get exec 1 exch sub 0 1 0 0 setcmykcolor systemdict /currentgray get exec 1 exch sub 0 0 1 0 setcmykcolor systemdict /currentgray get exec 1 exch sub 0 0 0 1 setcmykcolor systemdict /currentgray get exec 1 exch sub grestore 1 0 0 0 FourEqual { /plateindex 0 def } { 0 1 0 0 FourEqual { /plateindex 1 def } { 0 0 1 0 FourEqual { /plateindex 2 def } { 0 0 0 1 FourEqual { /plateindex 3 def } { 0 0 0 0 FourEqual { /plateindex 5 def } if } ifelse } ifelse } ifelse } ifelse pop pop pop pop } if plateindex end } def /colorimage { Adobe_ColorImage_AI6_Vars begin /channelcount 1 index def /sourcecount 2 index 1 eq { channelcount 1 sub } { 0 } ifelse def 4 sourcecount add index dup 8 eq exch 1 eq or not end { /_colorimage load null ne { _colorimage } { Adobe_ColorImage_AI6_Vars /sourcecount get 7 add { pop } repeat } ifelse } { dup 3 eq TestPlateIndex dup -1 eq exch 5 eq or or { /_colorimage load null eq { ColorImageCompositeEmulator } { dup 1 eq { pop pop image } { Adobe_ColorImage_AI6_Vars /plateindex get 5 eq { gsave 0 _currenttransfer exec 1 _currenttransfer exec eq { 0 _currenttransfer exec 0.5 lt } { 0 _currenttransfer exec 1 _currenttransfer exec gt } ifelse { { pop 0 } } { { pop 1 } } ifelse systemdict /settransfer get exec } if _colorimage Adobe_ColorImage_AI6_Vars /plateindex get 5 eq { grestore } if } ifelse } ifelse } { dup 1 eq { pop pop image } { pop pop Adobe_ColorImage_AI6_Vars begin sourcecount -1 0 { exch sourcearray 3 1 roll put } for /SeparateCMYKImageProc load end systemdict /image get exec } ifelse } ifelse } ifelse } def /XI { Adobe_ColorImage_AI6_Vars begin gsave /XIMask exch 0 ne def /XIBinary exch 0 ne def pop pop /XIChannelCount exch def /XIBitsPerPixel exch def /XIImageHeight exch def /XIImageWidth exch def pop pop pop pop /XIImageMatrix exch def XIBitsPerPixel 1 eq { XIImageWidth 8 div ceiling cvi } { XIImageWidth XIChannelCount mul } ifelse /XIBuffer exch string def XIBinary { /XIDataProc { currentfile XIBuffer readstring pop } def currentfile 128 string readline pop pop } { /XIDataProc { currentfile XIBuffer readhexstring pop } def } ifelse 0 0 moveto XIImageMatrix concat XIImageWidth XIImageHeight scale XIMask { XIImageWidth XIImageHeight false [ XIImageWidth 0 0 XIImageHeight neg 0 0 ] /XIDataProc load /_lp /null ddef _fc /_lp /imagemask ddef imagemask } { XIImageWidth XIImageHeight XIBitsPerPixel [ XIImageWidth 0 0 XIImageHeight neg 0 0 ] /XIDataProc load XIChannelCount 1 eq { gsave 0 setgray image grestore } { false XIChannelCount colorimage } ifelse } ifelse grestore end } def end currentpacking true setpacking userdict /Adobe_Illustrator_AI5_vars 81 dict dup begin put /_eo false def /_lp /none def /_pf { } def /_ps { } def /_psf { } def /_pss { } def /_pjsf { } def /_pjss { } def /_pola 0 def /_doClip 0 def /cf currentflat def /_tm matrix def /_renderStart [ /e0 /r0 /a0 /o0 /e1 /r1 /a1 /i0 ] def /_renderEnd [ null null null null /i1 /i1 /i1 /i1 ] def /_render -1 def /_rise 0 def /_ax 0 def /_ay 0 def /_cx 0 def /_cy 0 def /_leading [ 0 0 ] def /_ctm matrix def /_mtx matrix def /_sp 16#020 def /_hyphen (-) def /_fScl 0 def /_cnt 0 def /_hs 1 def /_nativeEncoding 0 def /_useNativeEncoding 0 def /_tempEncode 0 def /_pntr 0 def /_tDict 2 dict def /_wv 0 def /Tx { } def /Tj { } def /CRender { } def /_AI3_savepage { } def /_gf null def /_cf 4 array def /_if null def /_of false def /_fc { } def /_gs null def /_cs 4 array def /_is null def /_os false def /_sc { } def /_pd 1 dict def /_ed 15 dict def /_pm matrix def /_fm null def /_fd null def /_fdd null def /_sm null def /_sd null def /_sdd null def /_i null def /discardSave null def /buffer 256 string def /beginString null def /endString null def /endStringLength null def /layerCnt 1 def /layerCount 1 def /perCent (%) 0 get def /perCentSeen? false def /newBuff null def /newBuffButFirst null def /newBuffLast null def /clipForward? false def end userdict /Adobe_Illustrator_AI5 known not { userdict /Adobe_Illustrator_AI5 91 dict put } if userdict /Adobe_Illustrator_AI5 get begin /initialize { Adobe_Illustrator_AI5 dup begin Adobe_Illustrator_AI5_vars begin discardDict { bind pop pop } forall dup /nc get begin { dup xcheck 1 index type /operatortype ne and { bind } if pop pop } forall end newpath } def /terminate { end end } def /_ null def /ddef { Adobe_Illustrator_AI5_vars 3 1 roll put } def /xput { dup load dup length exch maxlength eq { dup dup load dup length 2 mul dict copy def } if load begin def end } def /npop { { pop } repeat } def /sw { dup length exch stringwidth exch 5 -1 roll 3 index mul add 4 1 roll 3 1 roll mul add } def /swj { dup 4 1 roll dup length exch stringwidth exch 5 -1 roll 3 index mul add 4 1 roll 3 1 roll mul add 6 2 roll /_cnt 0 ddef { 1 index eq { /_cnt _cnt 1 add ddef } if } forall pop exch _cnt mul exch _cnt mul 2 index add 4 1 roll 2 index add 4 1 roll pop pop } def /ss { 4 1 roll { 2 npop (0) exch 2 copy 0 exch put pop gsave false charpath currentpoint 4 index setmatrix stroke grestore moveto 2 copy rmoveto } exch cshow 3 npop } def /jss { 4 1 roll { 2 npop (0) exch 2 copy 0 exch put gsave _sp eq { exch 6 index 6 index 6 index 5 -1 roll widthshow currentpoint } { false charpath currentpoint 4 index setmatrix stroke } ifelse grestore moveto 2 copy rmoveto } exch cshow 6 npop } def /sp { { 2 npop (0) exch 2 copy 0 exch put pop false charpath 2 copy rmoveto } exch cshow 2 npop } def /jsp { { 2 npop (0) exch 2 copy 0 exch put _sp eq { exch 5 index 5 index 5 index 5 -1 roll widthshow } { false charpath } ifelse 2 copy rmoveto } exch cshow 5 npop } def /pl { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform } def /setstrokeadjust where { pop true setstrokeadjust /c { curveto } def /C /c load def /v { currentpoint 6 2 roll curveto } def /V /v load def /y { 2 copy curveto } def /Y /y load def /l { lineto } def /L /l load def /m { moveto } def } { /c { pl curveto } def /C /c load def /v { currentpoint 6 2 roll pl curveto } def /V /v load def /y { pl 2 copy curveto } def /Y /y load def /l { pl lineto } def /L /l load def /m { pl moveto } def } ifelse /d { setdash } def /cf { } def /i { dup 0 eq { pop cf } if setflat } def /j { setlinejoin } def /J { setlinecap } def /M { setmiterlimit } def /w { setlinewidth } def /XR { 0 ne /_eo exch ddef } def /H { } def /h { closepath } def /N { _pola 0 eq { _doClip 1 eq { _eo {eoclip} {clip} ifelse /_doClip 0 ddef } if newpath } { /CRender { N } ddef } ifelse } def /n { N } def /F { _pola 0 eq { _doClip 1 eq { gsave _pf grestore _eo {eoclip} {clip} ifelse newpath /_lp /none ddef _fc /_doClip 0 ddef } { _pf } ifelse } { /CRender { F } ddef } ifelse } def /f { closepath F } def /S { _pola 0 eq { _doClip 1 eq { gsave _ps grestore _eo {eoclip} {clip} ifelse newpath /_lp /none ddef _sc /_doClip 0 ddef } { _ps } ifelse } { /CRender { S } ddef } ifelse } def /s { closepath S } def /B { _pola 0 eq { _doClip 1 eq gsave F grestore { gsave S grestore _eo {eoclip} {clip} ifelse newpath /_lp /none ddef _sc /_doClip 0 ddef } { S } ifelse } { /CRender { B } ddef } ifelse } def /b { closepath B } def /W { /_doClip 1 ddef } def /* { count 0 ne { dup type /stringtype eq { pop } if } if newpath } def /u { } def /U { } def /q { _pola 0 eq { gsave } if } def /Q { _pola 0 eq { grestore } if } def /*u { _pola 1 add /_pola exch ddef } def /*U { _pola 1 sub /_pola exch ddef _pola 0 eq { CRender } if } def /D { pop } def /*w { } def /*W { } def /` { /_i save ddef clipForward? { nulldevice } if 6 1 roll 4 npop concat pop userdict begin /showpage { } def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash /setstrokeadjust where {pop false setstrokeadjust} if newpath 0 setgray false setoverprint } def /~ { end _i restore } def /O { 0 ne /_of exch ddef /_lp /none ddef } def /R { 0 ne /_os exch ddef /_lp /none ddef } def /g { /_gf exch ddef /_fc { _lp /fill ne { _of setoverprint _gf setgray /_lp /fill ddef } if } ddef /_pf { _fc _eo {eofill} {fill} ifelse } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /G { /_gs exch ddef /_sc { _lp /stroke ne { _os setoverprint _gs setgray /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /k { _cf astore pop /_fc { _lp /fill ne { _of setoverprint _cf aload pop setcmykcolor /_lp /fill ddef } if } ddef /_pf { _fc _eo {eofill} {fill} ifelse } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /K { _cs astore pop /_sc { _lp /stroke ne { _os setoverprint _cs aload pop setcmykcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /x { /_gf exch ddef findcmykcustomcolor /_if exch ddef /_fc { _lp /fill ne { _of setoverprint _if _gf 1 exch sub setcustomcolor /_lp /fill ddef } if } ddef /_pf { _fc _eo {eofill} {fill} ifelse } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /X { /_gs exch ddef findcmykcustomcolor /_is exch ddef /_sc { _lp /stroke ne { _os setoverprint _is _gs 1 exch sub setcustomcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /A { pop } def /annotatepage { userdict /annotatepage 2 copy known {get exec} {pop pop} ifelse } def /XT { pop pop } def /discard { save /discardSave exch store discardDict begin /endString exch store gt38? { 2 add } if load stopped pop end discardSave restore } bind def userdict /discardDict 7 dict dup begin put /pre38Initialize { /endStringLength endString length store /newBuff buffer 0 endStringLength getinterval store /newBuffButFirst newBuff 1 endStringLength 1 sub getinterval store /newBuffLast newBuff endStringLength 1 sub 1 getinterval store } def /shiftBuffer { newBuff 0 newBuffButFirst putinterval newBuffLast 0 currentfile read not { stop } if put } def 0 { pre38Initialize mark currentfile newBuff readstring exch pop { { newBuff endString eq { cleartomark stop } if shiftBuffer } loop } { stop } ifelse } def 1 { pre38Initialize /beginString exch store mark currentfile newBuff readstring exch pop { { newBuff beginString eq { /layerCount dup load 1 add store } { newBuff endString eq { /layerCount dup load 1 sub store layerCount 0 eq { cleartomark stop } if } if } ifelse shiftBuffer } loop } if } def 2 { mark { currentfile buffer readline not { stop } if endString eq { cleartomark stop } if } loop } def 3 { /beginString exch store /layerCnt 1 store mark { currentfile buffer readline not { stop } if dup beginString eq { pop /layerCnt dup load 1 add store } { endString eq { layerCnt 1 eq { cleartomark stop } { /layerCnt dup load 1 sub store } ifelse } if } ifelse } loop } def end userdict /clipRenderOff 15 dict dup begin put { /n /N /s /S /f /F /b /B } { { _doClip 1 eq { /_doClip 0 ddef _eo {eoclip} {clip} ifelse } if newpath } def } forall /Tr /pop load def /Bb {} def /BB /pop load def /Bg {12 npop} def /Bm {6 npop} def /Bc /Bm load def /Bh {4 npop} def end /Lb { 4 npop 6 1 roll pop 4 1 roll pop pop pop 0 eq { 0 eq { (%AI5_BeginLayer) 1 (%AI5_EndLayer--) discard } { /clipForward? true def /Tx /pop load def /Tj /pop load def currentdict end clipRenderOff begin begin } ifelse } { 0 eq { save /discardSave exch store } if } ifelse } bind def /LB { discardSave dup null ne { restore } { pop clipForward? { currentdict end end begin /clipForward? false ddef } if } ifelse } bind def /Pb { pop pop 0 (%AI5_EndPalette) discard } bind def /Np { 0 (%AI5_End_NonPrinting--) discard } bind def /Ln /pop load def /Ap /pop load def /Ar { 72 exch div 0 dtransform dup mul exch dup mul add sqrt dup 1 lt { pop 1 } if setflat } def /Mb { q } def /Md { } def /MB { Q } def /nc 3 dict def nc begin /setgray { pop } bind def /setcmykcolor { 4 npop } bind def /setcustomcolor { 2 npop } bind def currentdict readonly pop end end setpacking Adobe_level2_AI5 /initialize get exec Adobe_Illustrator_AI5_vars Adobe_Illustrator_AI5 Adobe_typography_AI5 /initialize get exec Adobe_ColorImage_AI6 /initialize get exec Adobe_Illustrator_AI5 /initialize get exec [ 39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe 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showpage Adobe_Illustrator_AI5 /terminate get exec Adobe_ColorImage_AI6 /terminate get exec Adobe_typography_AI5 /terminate get exec Adobe_level2_AI5 /terminate get exec %%EndDocument endTexFig 0 2748 a Fl(232)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fk(Machine)h(L)n(e)n(arning)p Fl(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e (Hill,)j(1997)p eop %%Page: 233 5 233 4 bop 0 142 a Fi(Learn-One-R)m(ule)40 283 y Fm(\017)21 b Fh(P)12 b(os)24 b Fm( )29 b Fn(p)r(ositiv)n(e)i Fh(E)5 b(xampl)r(es)40 424 y Fm(\017)21 b Fh(N)9 b(eg)27 b Fm( )i Fn(negativ)n(e)i Fh(E)5 b(xampl)r(es)40 565 y Fm(\017)21 b Fn(while)31 b Fh(P)12 b(os)p Fn(,)29 b(do)170 706 y Fj(L)l(e)l(arn)h(a)h Fh(N)9 b(ew)r(R)q(ul)r(e)125 826 y Fg({)21 b Fh(N)9 b(ew)r(R)q(ul)r(e)24 b Fm( )29 b Fn(most)f(general)i (rule)f(p)r(ossible)125 947 y Fg({)21 b Fh(N)9 b(ew)r(R)q(ul)r(eN)g(eg) 28 b Fm( )c Fh(N)9 b(eg)125 1067 y Fg({)21 b Fn(while)31 b Fh(N)9 b(ew)r(R)q(ul)r(eN)g(eg)s Fn(,)30 b(do)247 1188 y Fj(A)l(dd)h(a)g(new)g(liter)l(al)f(to)g(sp)l(e)l(cialize)g Fh(N)9 b(ew)r(R)q(ul)r(e)185 1300 y Fn(1.)21 b Fh(C)6 b(andidate)p 679 1300 26 2 v 31 w(l)r(iter)r(al)r(s)23 b Fm( )29 b Fn(generate)h(candidates)185 1412 y(2.)21 b Fh(B)t(est)p 458 1412 V 32 w(l)r(iter)r(al)k Fm( )f Fn(argmax)1141 1431 y Ff(L)p Fe(2)p Ff(C)t(andidate)p 1507 1431 V 29 w(l)q(iter)r(al)q(s)273 1515 y Fh(P)12 b(er)r(f)d(or)r(mance)p Fn(\()p Fh(S)c(pecial)r(iz)t(eR)q(ul)r(e)p Fn(\()p Fh(N)k(ew)r(R)q(ul)r(e;)16 b(L)p Fn(\)\))185 1627 y(3.)21 b(add)28 b Fh(B)t(est)p 625 1627 V 32 w(l)r(iter)r(al)i Fn(to)g Fh(N)9 b(ew)r(R)q(ul)r(e)29 b Fn(preconditions)185 1740 y(4.)21 b Fh(N)9 b(ew)r(R)q(ul)r(eN)g(eg)28 b Fm( )h Fn(subset)g(of)g Fh(N)9 b(ew)r(R)q(ul)r(eN)g(eg)273 1843 y Fn(that)29 b(satis\014es)h Fh(N)9 b(ew)r(R)q(ul)r(e)29 b Fn(preconditions)125 1964 y Fg({)21 b Fh(Lear)r(ned)p 522 1964 V 31 w(r)r(ul)r(es)j Fm( )g Fh(Lear)r(ned)p 1207 1964 V 31 w(r)r(ul)r(es)c Fn(+)f Fh(N)9 b(ew)r(R)q(ul)r(e)125 2084 y Fg({)21 b Fh(P)12 b(os)24 b Fm( )g Fh(P)12 b(os)29 b Fm(\000)g(f)p Fn(mem)n(b)r(ers)d(of)j Fh(P)12 b(os)29 b Fn(co)n(v)n(ered)g(b)n(y)195 2188 y Fh(N)9 b(ew)r(R)q(ul)r(e)p Fm(g)40 2329 y(\017)21 b Fn(Return)29 b Fh(Lear)r(ned)p 724 2329 V 31 w(r)r(ul)r(es)0 2748 y Fl(233)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fk(Machine)h(L)n(e)n(arning)p Fl(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e(Hill,)j(1997)p eop %%Page: 234 6 234 5 bop 25 170 a Fd(Subtleties:)56 b(Learn)40 b(One)g(Rule)1492 170 y 0.8666 0.03137 0.02352 setrgbcolor 1492 170 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 16 592 a Fn(1.)21 b(Ma)n(y)28 b(use)h Fj(b)l(e)l(am)h(se)l(ar)l(ch)16 737 y Fn(2.)21 b(Easily)30 b(generalizes)i(to)d(m)n(ulti-v)-5 b(alued)30 b(target)104 841 y(functions)16 987 y(3.)21 b(Cho)r(ose)29 b(ev)-5 b(aluation)32 b(function)e(to)f(guide)h(searc)n (h:)131 1132 y Fm(\017)21 b Fn(En)n(trop)n(y)28 b(\(i.e.,)i (information)g(gain\))131 1256 y Fm(\017)21 b Fn(Sample)28 b(accuracy:)1031 1314 y Fh(n)1083 1327 y Ff(c)p 1031 1352 80 2 v 1045 1432 a Fh(n)195 1523 y Fn(where)h Fh(n)496 1535 y Ff(c)548 1523 y Fn(=)f(correct)i(rule)f(predictions,)i Fh(n)23 b Fn(=)29 b(all)195 1626 y(predictions)131 1751 y Fm(\017)21 b Fh(m)28 b Fn(estimate:)919 1805 y Fh(n)971 1818 y Ff(c)1018 1805 y Fn(+)19 b Fh(mp)p 919 1843 304 2 v 955 1923 a(n)g Fn(+)g Fh(m)0 2748 y Fl(234)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fk(Machine)h(L)n(e)n(arning)p Fl(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e(Hill,)j(1997)p eop %%Page: 235 7 235 6 bop 25 160 a Fo(V)-9 b(arian)m(ts)36 b(of)e(Rule)h(Learning)g (Programs)1695 160 y 0.8666 0.03137 0.02352 setrgbcolor 1695 160 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 40 592 a Fm(\017)21 b Fj(Se)l(quential)28 b Fn(or)g Fj(simultane)l(ous)i Fn(co)n(v)n(ering)f(of)g(data?)40 737 y Fm(\017)21 b Fn(General)29 b Fm(!)g Fn(sp)r(eci\014c,)h(or)f(sp)r (eci\014c)h Fm(!)f Fn(general?)40 883 y Fm(\017)21 b Fn(Generate-and-test,)29 b(or)g(example-driv)n(en?)40 1028 y Fm(\017)21 b Fn(Whether)29 b(and)g(ho)n(w)f(to)h(p)r(ost-prune?) 40 1173 y Fm(\017)21 b Fn(What)29 b(statisti)q(cal)j(ev)-5 b(aluati)q(on)31 b(function?)0 2748 y Fl(235)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fk(Machine)h(L)n(e)n(arning)p Fl(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e(Hill,)j(1997)p eop %%Page: 236 8 236 7 bop 25 160 a Fo(Learning)35 b(First)h(Order)g(Rules)1291 160 y 0.8666 0.03137 0.02352 setrgbcolor 1291 160 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 64 x Fn(Wh)n(y)29 b(do)g(that?)40 696 y Fm(\017)21 b Fn(Can)29 b(learn)g(sets)g(of)g(rules)h(suc)n(h)e(as)104 874 y Fh(Ancestor)r Fn(\()p Fh(x;)15 b(y)s Fn(\))24 b Fm( )g Fh(P)12 b(ar)r(ent)p Fn(\()p Fh(x;)k(y)s Fn(\))104 978 y Fh(Ancestor)r Fn(\()p Fh(x;)f(y)s Fn(\))24 b Fm( )g Fh(P)12 b(ar)r(ent)p Fn(\()p Fh(x;)k(z)t Fn(\))k Fm(^)f Fh(Ancestor)r Fn(\()p Fh(z)t(;)c(y)s Fn(\))40 1157 y Fm(\017)21 b Fn(General)29 b(purp)r(ose)g(programming)d(language)104 1260 y Fi(Pr)n(olog)p Fn(:)38 b(programs)26 b(are)j(sets)g(of)h(suc)n (h)e(rules)0 2748 y Fl(236)334 b(lecture)17 b(slides)f(for)f(textb)q(o) q(ok)g Fk(Machine)h(L)n(e)n(arning)p Fl(,)c(T.)j(Mitc)o(hell,)h(McGra)o (w)e(Hill,)j(1997)p eop %%Page: 237 9 237 8 bop 25 155 a Fd(First)32 b(Order)h(Rule)g(for)f(Classifying)j(W) -10 b(eb)25 279 y(P)m(ages)361 279 y 0.8666 0.03137 0.02352 setrgbcolor 361 279 a 0 434 1947 2 v 0 587 a 0 0 0 setrgbcolor 0 587 a 691 656 a Fn([Slattery)j(,)31 b(1997])0 813 y(course\(A\))e Fm( )269 917 y Fn(has-w)n(ord\(A,)e (instructor\),)269 1021 y(Not)h(has-w)n(ord\(A,)g(go)r(o)r(d\),)269 1125 y(link-from\(A,)h(B\),)269 1228 y(has-w)n(ord\(B,)f(assign\),)269 1332 y(Not)g(link-from\(B,)i(C\))0 1496 y(T)-7 b(rain:)39 b(31/31,)29 b(T)-7 b(est:)38 b(31/34)0 2748 y Fl(237)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fk(Machine)h(L)n(e)n (arning)p Fl(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e(Hill,)j(1997)p eop %%Page: 238 10 238 9 bop 0 148 a Fi(F)m(OIL)p Fn(\()p Fh(T)12 b(ar)r(g)s(et)p 526 148 26 2 v 33 w(pr)r(edicate;)j(P)d(r)r(edicates;)k(E)5 b(xampl)r(es)p Fn(\))40 287 y Fm(\017)21 b Fh(P)12 b(os)24 b Fm( )29 b Fn(p)r(ositiv)n(e)i Fh(E)5 b(xampl)r(es)40 428 y Fm(\017)21 b Fh(N)9 b(eg)27 b Fm( )i Fn(negativ)n(e)i Fh(E)5 b(xampl)r(es)40 569 y Fm(\017)21 b Fn(while)31 b Fh(P)12 b(os)p Fn(,)29 b(do)170 710 y Fj(L)l(e)l(arn)h(a)h Fh(N)9 b(ew)r(R)q(ul)r(e)125 830 y Fg({)21 b Fh(N)9 b(ew)r(R)q(ul)r(e) 24 b Fm( )29 b Fn(most)f(general)i(rule)f(p)r(ossible)125 950 y Fg({)21 b Fh(N)9 b(ew)r(R)q(ul)r(eN)g(eg)28 b Fm( )c Fh(N)9 b(eg)125 1070 y Fg({)21 b Fn(while)31 b Fh(N)9 b(ew)r(R)q(ul)r(eN)g(eg)s Fn(,)30 b(do)247 1190 y Fj(A)l(dd)h(a)g(new)g (liter)l(al)f(to)g(sp)l(e)l(cialize)g Fh(N)9 b(ew)r(R)q(ul)r(e)185 1302 y Fn(1.)21 b Fh(C)6 b(andidate)p 679 1302 V 31 w(l)r(iter)r(al)r (s)23 b Fm( )29 b Fn(generate)h(candidates)185 1414 y(2.)21 b Fh(B)t(est)p 458 1414 V 32 w(l)r(iter)r(al)k Fm( )273 1518 y Fn(argmax)553 1537 y Ff(L)p Fe(2)p Ff(C)t(andidate)p 919 1537 V 29 w(l)q(iter)r(al)q(s)1155 1518 y Fh(F)12 b(oil)p 1327 1518 V 32 w(Gain)p Fn(\()p Fh(L;)i(N)9 b(ew)r(R)q(ul)r(e)p Fn(\))185 1630 y(3.)21 b(add)28 b Fh(B)t(est)p 625 1630 V 32 w(l)r(iter)r(al)i Fn(to)g Fh(N)9 b(ew)r(R)q(ul)r(e)29 b Fn(preconditions)185 1742 y(4.)21 b Fh(N)9 b(ew)r(R)q(ul)r(eN)g(eg)28 b Fm( )h Fn(subset)g(of)g Fh(N)9 b(ew)r(R)q(ul)r(eN)g(eg)273 1845 y Fn(that)29 b(satis\014es)h Fh(N)9 b(ew)r(R)q(ul)r(e)29 b Fn(preconditions)125 1965 y Fg({)21 b Fh(Lear)r(ned)p 522 1965 V 31 w(r)r(ul)r(es)j Fm( )g Fh(Lear)r(ned)p 1207 1965 V 31 w(r)r(ul)r(es)c Fn(+)f Fh(N)9 b(ew)r(R)q(ul)r(e)125 2085 y Fg({)21 b Fh(P)12 b(os)24 b Fm( )g Fh(P)12 b(os)29 b Fm(\000)g(f)p Fn(mem)n(b)r(ers)d(of)j Fh(P)12 b(os)29 b Fn(co)n(v)n(ered)g(b)n(y)195 2189 y Fh(N)9 b(ew)r(R)q(ul)r(e)p Fm(g)40 2330 y(\017)21 b Fn(Return)29 b Fh(Lear)r(ned)p 724 2330 V 31 w(r)r(ul)r(es)0 2748 y Fl(238)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fk(Machine)h(L)n(e)n(arning)p Fl(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e(Hill,)j(1997)p eop %%Page: 239 11 239 10 bop 25 160 a Fo(Sp)s(ecializing)37 b(Rules)e(in)h(F)m(OIL)1275 160 y 0.8666 0.03137 0.02352 setrgbcolor 1275 160 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 69 x Fn(Learning)29 b(rule:)39 b Fh(P)12 b Fn(\()p Fh(x)715 556 y Fc(1)748 543 y Fh(;)i(x)835 556 y Fc(2)867 543 y Fh(;)h(:)f(:)g(:)g(;)h(x)1108 556 y Ff(k)1143 543 y Fn(\))24 b Fm( )g Fh(L)1369 556 y Fc(1)1415 543 y Fh(:)15 b(:)f(:)g(L)1589 556 y Ff(n)0 647 y Fn(Candidate)30 b(sp)r(eciali)q (zati)q(ons)i(add)c(new)h(literal)j(of)d(form:)40 792 y Fm(\017)21 b Fh(Q)p Fn(\()p Fh(v)247 805 y Fc(1)279 792 y Fh(;)14 b(:)h(:)f(:)g(;)g(v)512 805 y Ff(r)543 792 y Fn(\),)29 b(where)g(at)g(least)h(one)f(of)g(the)h Fh(v)1631 805 y Ff(i)1682 792 y Fn(in)f(the)104 896 y(created)g (literal)j(m)n(ust)27 b(already)j(exist)h(as)d(a)h(v)-5 b(ariable)31 b(in)104 1000 y(the)e(rule.)40 1145 y Fm(\017)21 b Fh(E)5 b(q)s(ual)r Fn(\()p Fh(x)418 1158 y Ff(j)449 1145 y Fh(;)14 b(x)536 1158 y Ff(k)571 1145 y Fn(\),)29 b(where)g Fh(x)955 1158 y Ff(j)1014 1145 y Fn(and)g Fh(x)1231 1158 y Ff(k)1295 1145 y Fn(are)g(v)-5 b(ariables)104 1249 y(already)30 b(presen)n(t)e(in)i(the)f(rule)40 1394 y Fm(\017)21 b Fn(The)29 b(negation)h(of)f(either)h(of)f(the)g(ab)r(o)n (v)n(e)g(forms)f(of)104 1498 y(literals)0 2748 y Fl(239)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fk(Machine)h(L)n(e)n (arning)p Fl(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e(Hill,)j(1997)p eop %%Page: 240 12 240 11 bop 25 170 a Fo(Information)35 b(Gain)g(in)h(F)m(OIL)1248 170 y 0.8666 0.03137 0.02352 setrgbcolor 1248 170 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 62 649 a Fh(F)12 b(oil)p 234 649 26 2 v 32 w(Gain)p Fn(\()p Fh(L;)i(R)q Fn(\))24 b Fm(\021)g Fh(t)844 530 y Fb(0)844 603 y(B)844 628 y(B)844 654 y(@)880 649 y Fn(log)991 669 y Fc(2)1137 591 y Fh(p)1180 604 y Fc(1)p 1043 629 265 2 v 1043 708 a Fh(p)1086 721 y Fc(1)1137 708 y Fn(+)19 b Fh(n)1275 721 y Fc(1)1331 649 y Fm(\000)g Fn(log)1528 669 y Fc(2)1674 591 y Fh(p)1717 604 y Fc(0)p 1579 629 V 1579 708 a Fh(p)1622 721 y Fc(0)1674 708 y Fn(+)g Fh(n)1812 721 y Fc(0)1849 530 y Fb(1)1849 603 y(C)1849 628 y(C)1849 654 y(A)0 841 y Fn(Where)40 987 y Fm(\017)i Fh(L)28 b Fn(is)i(the)f(candidate)h(literal)i(to)d(add)g(to)g(rule)g Fh(R)40 1132 y Fm(\017)21 b Fh(p)147 1145 y Fc(0)208 1132 y Fn(=)28 b(n)n(um)n(b)r(er)f(of)i(p)r(ositiv)n(e)j(bindings)d(of) g Fh(R)40 1277 y Fm(\017)21 b Fh(n)156 1290 y Fc(0)216 1277 y Fn(=)29 b(n)n(um)n(b)r(er)d(of)j(negativ)n(e)i(bindings)f(of)f Fh(R)40 1422 y Fm(\017)21 b Fh(p)147 1435 y Fc(1)208 1422 y Fn(=)28 b(n)n(um)n(b)r(er)f(of)i(p)r(ositiv)n(e)j(bindings)d(of) g Fh(R)21 b Fn(+)e Fh(L)40 1568 y Fm(\017)i Fh(n)156 1581 y Fc(1)216 1568 y Fn(=)29 b(n)n(um)n(b)r(er)d(of)j(negativ)n(e)i (bindings)f(of)f Fh(R)20 b Fn(+)f Fh(L)40 1713 y Fm(\017)i Fh(t)29 b Fn(is)g(the)g(n)n(um)n(b)r(er)e(of)i(p)r(ositiv)n(e)j (bindings)d(of)g Fh(R)h Fn(also)104 1817 y(co)n(v)n(ered)f(b)n(y)f Fh(R)20 b Fn(+)f Fh(L)0 1962 y Fn(Note)40 2107 y Fm(\017)i(\000)14 b Fn(log)296 2127 y Fc(2)402 2072 y Ff(p)432 2083 y Fa(0)p 348 2087 166 2 v 348 2137 a Ff(p)378 2149 y Fa(0)404 2137 y Fc(+)p Ff(n)486 2149 y Fa(0)547 2107 y Fn(is)29 b(optimal)h(n)n(um)n(b)r(er)c(of)j(bits)h(to)g(indicate)104 2211 y(the)f(class)h(of)f(a)g(p)r(ositiv)n(e)i(binding)f(co)n(v)n(ered) f(b)n(y)f Fh(R)0 2748 y Fl(240)334 b(lecture)17 b(slides)f(for)f(textb) q(o)q(ok)g Fk(Machine)h(L)n(e)n(arning)p Fl(,)c(T.)j(Mitc)o(hell,)h (McGra)o(w)e(Hill,)j(1997)p eop %%Page: 241 13 241 12 bop 25 170 a Fo(Induction)37 b(as)c(In)m(v)m(erted)j(Deduction) 1525 170 y 0.8666 0.03137 0.02352 setrgbcolor 1525 170 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 64 x Fn(Induction)30 b(is)f(\014nding)g Fh(h)g Fn(suc)n(h)f(that)292 709 y(\()p Fm(8h)p Fh(x)456 721 y Ff(i)479 709 y Fh(;)14 b(f)9 b Fn(\()p Fh(x)650 721 y Ff(i)674 709 y Fn(\))p Fm(i)25 b(2)f Fh(D)r Fn(\))30 b Fh(B)23 b Fm(^)d Fh(h)f Fm(^)g Fh(x)1341 721 y Ff(i)1388 709 y Fm(`)24 b Fh(f)9 b Fn(\()p Fh(x)1598 721 y Ff(i)1621 709 y Fn(\))0 862 y(where)40 1007 y Fm(\017)21 b Fh(x)153 1020 y Ff(i)204 1007 y Fn(is)30 b Fh(i)p Fn(th)f(training)h(instance)40 1153 y Fm(\017)21 b Fh(f)9 b Fn(\()p Fh(x)237 1166 y Ff(i)261 1153 y Fn(\))29 b(is)g(the)h(target)f(function)i(v)-5 b(alue)30 b(for)f Fh(x)1552 1166 y Ff(i)40 1298 y Fm(\017)21 b Fh(B)33 b Fn(is)d(other)f(bac)n(kground)f(kno)n(wledge)0 1743 y(So)h(let's)h(design)f(inductiv)n(e)i(algorithm)f(b)n(y)e(in)n(v) n(erting)0 1847 y(op)r(erators)h(for)g(automated)f(deduction!)0 2748 y Fl(241)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fk(Machine)h(L)n(e)n(arning)p Fl(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e (Hill,)j(1997)p eop %%Page: 242 14 242 13 bop 25 170 a Fo(Induction)37 b(as)c(In)m(v)m(erted)j(Deduction) 1525 170 y 0.8666 0.03137 0.02352 setrgbcolor 1525 170 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 69 x Fn(\\pairs)29 b(of)g(p)r(eople,)h Fm(h)p Fh(u;)15 b(v)s Fm(i)29 b Fn(suc)n(h)g(that)g(c)n(hild)h(of)f Fh(u)g Fn(is)h Fh(v)s Fn(,")0 800 y Fh(f)9 b Fn(\()p Fh(x)133 813 y Ff(i)157 800 y Fn(\))24 b(:)644 b Fh(C)6 b(hil)r(d)p Fn(\()p Fh(B)t(ob;)13 b(S)5 b(har)r(on)p Fn(\))118 917 y Fh(x)167 929 y Ff(i)214 917 y Fn(:)42 b Fh(M)9 b(al)r(e)p Fn(\()p Fh(B)t(ob)p Fn(\))p Fh(;)15 b(F)d(emal)r(e)p Fn(\()p Fh(S)5 b(har)r(on)p Fn(\))p Fh(;)15 b(F)d(ather)r Fn(\()p Fh(S)5 b(har)r(on;)15 b(B)t(ob)p Fn(\))121 1033 y Fh(B)28 b Fn(:)481 b Fh(P)12 b(ar)r(ent)p Fn(\()p Fh(u;)k(v)s Fn(\))25 b Fm( )f Fh(F)12 b(ather)r Fn(\()p Fh(u;)j(v)s Fn(\))0 1236 y(What)28 b(satis\014es)h(\()p Fm(8h)p Fh(x)720 1249 y Ff(i)743 1236 y Fh(;)14 b(f)9 b Fn(\()p Fh(x)914 1249 y Ff(i)938 1236 y Fn(\))p Fm(i)24 b(2)h Fh(D)r Fn(\))j Fh(B)21 b Fm(^)c Fh(h)f Fm(^)h Fh(x)1593 1249 y Ff(i)1639 1236 y Fm(`)24 b Fh(f)9 b Fn(\()p Fh(x)1849 1249 y Ff(i)1873 1236 y Fn(\)?)353 1390 y Fh(h)403 1403 y Fc(1)458 1390 y Fn(:)43 b Fh(C)6 b(hil)r(d)p Fn(\()p Fh(u;)13 b(v)s Fn(\))24 b Fm( )g Fh(F)12 b(ather)r Fn(\()p Fh(v)s(;)k(u)p Fn(\))353 1506 y Fh(h)403 1519 y Fc(2)458 1506 y Fn(:)42 b Fh(C)6 b(hil)r(d)p Fn(\()p Fh(u;)13 b(v)s Fn(\))24 b Fm( )g Fh(P)12 b(ar)r(ent)p Fn(\()p Fh(v)s(;)k(u)p Fn(\))0 2748 y Fl(242)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok) g Fk(Machine)h(L)n(e)n(arning)p Fl(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e (Hill,)j(1997)p eop %%Page: 243 15 243 14 bop 104 143 a Fn(Induction)30 b(is,)f(in)h(fact,)f(the)h(in)n(v) n(erse)f(op)r(eration)h(of)104 247 y(deduction,)g(and)e(cannot)h(b)r(e) g(conceiv)n(ed)i(to)e(exist)104 350 y(without)h(the)g(corresp)r(onding) f(op)r(eration,)h(so)f(that)104 454 y(the)g(question)i(of)e(relativ)n (e)i(imp)r(ortance)e(cannot)104 558 y(arise.)39 b(Who)29 b(thinks)h(of)f(asking)h(whether)f(addition)104 662 y(or)f(subtraction) i(is)g(the)f(more)f(imp)r(ortan)n(t)g(pro)r(cess)104 765 y(in)h(arithmetic?)40 b(But)29 b(at)g(the)g(same)f(time)h(m)n(uc)n (h)104 869 y(di\013erence)h(in)f(di\016cult)n(y)i(ma)n(y)d(exist)j(b)r (et)n(w)n(een)e(a)104 973 y(direct)h(and)e(in)n(v)n(erse)i(op)r (eration;)g Fh(:)14 b(:)g(:)29 b Fn(it)h(m)n(ust)d(b)r(e)104 1077 y(allo)n(w)n(ed)j(that)f(inductiv)n(e)i(in)n(v)n(estigati)q(ons)h (are)c(of)h(a)104 1181 y(far)g(higher)g(degree)g(of)g(di\016cult)n(y)i (and)d(complexit)n(y)104 1284 y(than)h(an)n(y)f(questions)j(of)e (deduction)p Fh(:)15 b(:)g(:)f(:)0 1442 y Fn(\(Jev)n(ons)30 b(1874\))0 2748 y Fl(243)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q (ok)g Fk(Machine)h(L)n(e)n(arning)p Fl(,)c(T.)j(Mitc)o(hell,)h(McGra)o (w)e(Hill,)j(1997)p eop %%Page: 244 16 244 15 bop 25 170 a Fo(Induction)37 b(as)c(In)m(v)m(erted)j(Deduction) 1525 170 y 0.8666 0.03137 0.02352 setrgbcolor 1525 170 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 64 x Fn(W)-7 b(e)29 b(ha)n(v)n(e)g(mec)n(hanical)g Fj(de)l(ductive)e Fn(op)r(erators)0 642 y Fh(F)12 b Fn(\()p Fh(A;)j(B)t Fn(\))25 b(=)f Fh(C)6 b Fn(,)28 b(where)h Fh(A)18 b Fm(^)i Fh(B)29 b Fm(`)23 b Fh(C)0 796 y Fn(need)29 b Fj(inductive)f Fn(op)r(erators)0 949 y Fh(O)r Fn(\()p Fh(B)t(;)15 b(D)r Fn(\))25 b(=)f Fh(h)29 b Fn(where)g(\()p Fm(8h)p Fh(x)923 962 y Ff(i)945 949 y Fh(;)15 b(f)9 b Fn(\()p Fh(x)1117 962 y Ff(i)1140 949 y Fn(\))p Fm(i)25 b(2)g Fh(D)r Fn(\))20 b(\()p Fh(B)t Fm(^)p Fh(h)p Fm(^)p Fh(x)1754 962 y Ff(i)1778 949 y Fn(\))25 b Fm(`)e Fh(f)9 b Fn(\()p Fh(x)2045 962 y Ff(i)2069 949 y Fn(\))0 2748 y Fl(244)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fk(Machine)h(L)n(e)n(arning)p Fl(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e(Hill,)j(1997)p eop %%Page: 245 17 245 16 bop 25 170 a Fd(Induction)41 b(as)e(In)m(v)m(erted)h(Deduction) 1760 170 y 0.8666 0.03137 0.02352 setrgbcolor 1760 170 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 63 x Fn(P)n(ositiv)n(es:)40 683 y Fm(\017)21 b Fn(Subsumes)27 b(earlier)j(idea)g(of)f(\014nding)g Fh(h)f Fn(that)i(\\\014ts")104 786 y(training)g(data)40 932 y Fm(\017)21 b Fn(Domain)28 b(theory)h Fh(B)34 b Fn(helps)29 b(de\014ne)g(meaning)f(of)h(\\\014t") 104 1035 y(the)g(data)689 1139 y Fh(B)24 b Fm(^)19 b Fh(h)g Fm(^)g Fh(x)1048 1152 y Ff(i)1095 1139 y Fm(`)24 b Fh(f)9 b Fn(\()p Fh(x)1305 1152 y Ff(i)1328 1139 y Fn(\))40 1291 y Fm(\017)21 b Fn(Suggests)29 b(algorithms)g(that)h (searc)n(h)e Fh(H)35 b Fn(guided)30 b(b)n(y)e Fh(B)0 2748 y Fl(245)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fk(Machine)h(L)n(e)n(arning)p Fl(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e (Hill,)j(1997)p eop %%Page: 246 18 246 17 bop 25 170 a Fd(Induction)41 b(as)e(In)m(v)m(erted)h(Deduction) 1760 170 y 0.8666 0.03137 0.02352 setrgbcolor 1760 170 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 63 x Fn(Negativ)n(es:)40 683 y Fm(\017)21 b Fn(Do)r(esn't)29 b(allo)n(w)i(for)d(noisy)i(data.)39 b(Consider)310 836 y(\()p Fm(8h)p Fh(x)474 849 y Ff(i)497 836 y Fh(;)14 b(f)9 b Fn(\()p Fh(x)668 849 y Ff(i)692 836 y Fn(\))p Fm(i)25 b(2)f Fh(D)r Fn(\))30 b(\()p Fh(B)24 b Fm(^)c Fh(h)f Fm(^)g Fh(x)1393 849 y Ff(i)1416 836 y Fn(\))24 b Fm(`)g Fh(f)9 b Fn(\()p Fh(x)1683 849 y Ff(i)1707 836 y Fn(\))40 1010 y Fm(\017)21 b Fn(First)29 b(order)e(logic)j(giv)n(es)f (a)f Fj(huge)g Fn(h)n(yp)r(othesis)h(space)f Fh(H)88 1156 y Fm(!)21 b Fn(o)n(v)n(er\014tting...)88 1280 y Fm(!)g Fn(in)n(tractabili)q(t)o(y)31 b(of)e(calculati)q(ng)j(all)e (acceptable)h Fh(h)p Fn('s)0 2748 y Fl(246)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fk(Machine)h(L)n(e)n(arning)p Fl(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e(Hill,)j(1997)p eop %%Page: 247 19 247 18 bop 25 170 a Fo(Deduction:)47 b(Resolution)35 b(Rule)1318 170 y 0.8666 0.03137 0.02352 setrgbcolor 1318 170 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 49 655 a Fh(P)87 b Fm(_)54 b Fh(L)25 759 y Fm(:)p Fh(L)c Fm(_)g Fh(R)p 0 791 389 2 v 49 864 a(P)87 b Fm(_)50 b Fh(R)16 1104 y Fn(1.)21 b(Giv)n(en)29 b(initial)k(clauses)d Fh(C)952 1117 y Fc(1)1012 1104 y Fn(and)e Fh(C)1241 1117 y Fc(2)1273 1104 y Fn(,)g(\014nd)h(a)f(literal)k Fh(L)104 1208 y Fn(from)27 b(clause)j Fh(C)623 1221 y Fc(1)683 1208 y Fn(suc)n(h)f(that)g Fm(:)p Fh(L)g Fn(o)r(ccurs)g(in)g(clause)h Fh(C)1891 1221 y Fc(2)16 1353 y Fn(2.)21 b(F)-7 b(orm)27 b(the)i(resolv)n(en)n(t)h Fh(C)35 b Fn(b)n(y)28 b(including)j(all)g (literals)104 1457 y(from)c Fh(C)369 1470 y Fc(1)429 1457 y Fn(and)i Fh(C)659 1470 y Fc(2)690 1457 y Fn(,)g(except)h(for)f Fh(L)f Fn(and)h Fm(:)p Fh(L)p Fn(.)38 b(More)104 1561 y(precisely)-7 b(,)31 b(the)e(set)g(of)h(literals)h(o)r(ccurring)f(in)g (the)104 1665 y(conclusion)g Fh(C)35 b Fn(is)447 1818 y Fh(C)30 b Fn(=)24 b(\()p Fh(C)725 1831 y Fc(1)776 1818 y Fm(\000)19 b(f)p Fh(L)p Fm(g)p Fn(\))g Fm([)h Fn(\()p Fh(C)1231 1831 y Fc(2)1282 1818 y Fm(\000)f(f:)p Fh(L)p Fm(g)p Fn(\))104 1972 y(where)29 b Fm([)g Fn(denotes)g(set)h(union,)f (and)f(\\)p Fm(\000)p Fn(")h(denotes)g(set)104 2076 y(di\013erence.)0 2748 y Fl(247)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fk(Machine)h(L)n(e)n(arning)p Fl(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e (Hill,)j(1997)p eop %%Page: 248 20 248 19 bop 25 160 a Fo(In)m(v)m(erting)36 b(Resolution)980 160 y 0.8666 0.03137 0.02352 setrgbcolor 980 160 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a -77 478 a 33154007 10277740 657817 36574658 39271710 48546938 startTexFig -77 478 a %%BeginDocument: ./bookps/res-rule.ps 50 dict begin /arrowHeight 8 def /arrowWidth 4 def /none null def /numGraphicParameters 17 def /stringLimit 65535 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { /patternGrayLevel idef patternGrayLevel -1 eq { /patternString idef } if false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 [FontBBox] 1 get FontMatrix end transform exch pop def /vertoffset 0 descender sub printSize sub printFont /Courier ne printFont /Courier-Bold ne and { 1 add } if def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def %I Idraw 7 Grid 8 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 0.799705 0 0 0.799705 0 0 ] concat /originalCTM matrix currentmatrix def Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t u Begin %I Line %I b 65535 1 1 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 -115 242 ] concat %I 283 502 235 606 Line End Begin %I Line %I b 65535 1 1 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 -115 242 ] concat %I 283 502 371 654 Line End End %I eop Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 505 712 ] concat %I [ (PassExam) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 589.001 712 ] concat %I [ ( Study) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 481 712 ] concat %I [ (C:) ] Text End Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t u Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 269 234 ] concat %I 283 502 235 606 Line End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 269 234 ] concat %I 283 502 371 654 Line End End %I eop Begin %I Rect %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 -110.999 245.001 ] concat %I 187 454 379 486 Rect End Begin %I Rect %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 -115 234 ] concat %I 659 654 859 686 Rect End Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 455.664 231.074 ] concat Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.00037 0 0 1.00037 -157.058 212.828 ] concat %I 287 266 298 266 Line End Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.00037 0 0 1.00037 -157.058 211.828 ] concat %I 298 267 298 263 Line End End %I eop Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 35 871 ] concat %I [ (PassExam) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 123 871 ] concat %I [ ( KnowMaterial) ] Text End Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t u Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 17 871.5 ] concat %I [ (C :) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 21.4991 862 ] concat %I [ (1) ] Text End End %I eop Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 -11.0041 390.074 ] concat Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.00037 0 0 1.00037 -157.058 212.828 ] concat %I 287 266 298 266 Line End Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.00037 0 0 1.00037 -157.058 211.828 ] concat %I 298 267 298 263 Line End End %I eop Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-medium-r-*-140-* /Helvetica 14 SetF %I t [ 1.00037 0 0 1.00037 102.038 872.002 ] concat %I [ (V) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 195 916 ] concat %I [ (KnowMaterial ) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 309 916 ] concat %I [ ( Study) ] Text End Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t u Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 176 916 ] concat %I [ (C :) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 179.999 907 ] concat %I [ (2) ] Text End End %I eop Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 176.054 435.074 ] concat Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.00037 0 0 1.00037 -157.058 212.828 ] concat %I 287 266 298 266 Line End Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.00037 0 0 1.00037 -157.058 211.828 ] concat %I 298 267 298 263 Line End End %I eop Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-medium-r-*-140-* /Helvetica 14 SetF %I t [ 1.00037 0 0 1.00037 287.102 917.002 ] concat %I [ (V) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 419 871.253 ] concat %I [ (PassExam) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 509.001 871.253 ] concat %I [ ( KnowMaterial) ] Text End Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 375.631 390.327 ] concat Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.00037 0 0 1.00037 -157.058 212.828 ] concat %I 287 266 298 266 Line End Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.00037 0 0 1.00037 -157.058 211.828 ] concat %I 298 267 298 263 Line End End %I eop Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 385.138 -0.253376 ] concat Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 17 871.5 ] concat %I [ (C :) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 21.4991 862 ] concat %I [ (1) ] Text End End %I eop Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-medium-r-*-140-* /Helvetica 14 SetF %I t [ 1.00037 0 0 1.00037 487.172 872.255 ] concat %I [ (V) ] Text End Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 -1.00037 0 ] concat Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 577.18 911.752 ] concat %I [ (KnowMaterial ) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 693.181 911.752 ] concat %I [ ( Study) ] Text End Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 558.383 430.826 ] concat Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.00037 0 0 1.00037 -157.058 212.828 ] concat %I 287 266 298 266 Line End Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.00037 0 0 1.00037 -157.058 211.828 ] concat %I 298 267 298 263 Line End End %I eop Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 381.818 -3.75479 ] concat Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 176 916 ] concat %I [ (C :) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 179.999 907 ] concat %I [ (2) ] Text End End %I eop Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-medium-r-*-140-* /Helvetica 14 SetF %I t [ 1.00037 0 0 1.00037 667.416 912.754 ] concat %I [ (V) ] Text End End %I eop Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-medium-r-*-140-* /Helvetica 14 SetF %I t [ 1.00037 0 0 1.00037 568.195 713.002 ] concat %I [ (V) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 123.501 719.756 ] concat %I [ (PassExam) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 207.502 719.756 ] concat %I [ ( Study) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 99.501 719.756 ] concat %I [ (C:) ] Text End Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 73.0233 238.83 ] concat Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.00037 0 0 1.00037 -157.058 212.828 ] concat %I 287 266 298 266 Line End Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.00037 0 0 1.00037 -157.058 211.828 ] concat %I 298 267 298 263 Line End End %I eop Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-medium-r-*-140-* /Helvetica 14 SetF %I t [ 1.00037 0 0 1.00037 185.55 720.003 ] concat %I [ (V) ] Text End End %I eop showpage end %%EndDocument endTexFig 0 2748 a Fl(248)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fk(Machine)h(L)n(e)n(arning)p Fl(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e (Hill,)j(1997)p eop %%Page: 249 21 249 20 bop 25 160 a Fo(In)m(v)m(erted)36 b(Resolution)f(\(Prop)s (ositional\))1662 160 y 0.8666 0.03137 0.02352 setrgbcolor 1662 160 a 0 322 1947 2 v 0 475 a 0 0 0 setrgbcolor 0 475 a 6 593 a Fg(1.)22 b Fn(Giv)n(en)29 b(initial)k(clauses)d Fh(C)952 606 y Fc(1)1012 593 y Fn(and)e Fh(C)6 b Fn(,)29 b(\014nd)f(a)h(literal)j Fh(L)104 696 y Fn(that)d(o)r(ccurs)g(in)h (clause)g Fh(C)973 709 y Fc(1)1004 696 y Fn(,)f(but)g(not)g(in)g (clause)h Fh(C)6 b Fn(.)6 842 y Fg(2.)22 b Fn(F)-7 b(orm)27 b(the)i(second)g(clause)h Fh(C)1072 855 y Fc(2)1132 842 y Fn(b)n(y)f(including)i(the)104 946 y(follo)n(wing)g(literal)q(s)435 1099 y Fh(C)497 1112 y Fc(2)552 1099 y Fn(=)24 b(\()p Fh(C)h Fm(\000)19 b Fn(\()p Fh(C)944 1112 y Fc(1)996 1099 y Fm(\000)g(f)p Fh(L)p Fm(g)p Fn(\)\))g Fm([)h(f:)p Fh(L)p Fm(g)0 2748 y Fl(249)334 b(lecture)17 b(slides)f(for)f(textb)q (o)q(ok)g Fk(Machine)h(L)n(e)n(arning)p Fl(,)c(T.)j(Mitc)o(hell,)h (McGra)o(w)e(Hill,)j(1997)p eop %%Page: 250 22 250 21 bop 25 170 a Fo(First)36 b(order)f(resolution)1024 170 y 0.8666 0.03137 0.02352 setrgbcolor 1024 170 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 64 x Fn(First)30 b(order)e(resolution:)16 683 y(1.)21 b(Find)29 b(a)g(literal)j Fh(L)688 696 y Fc(1)748 683 y Fn(from)c(clause)i Fh(C)1268 696 y Fc(1)1299 683 y Fn(,)f(literal)j Fh(L)1660 696 y Fc(2)1720 683 y Fn(from)104 787 y(clause)e Fh(C)420 800 y Fc(2)451 787 y Fn(,)f(and)f(substitution)k Fh(\022)f Fn(suc)n(h)d(that)104 891 y Fh(L)163 904 y Fc(1)194 891 y Fh(\022)f Fn(=)d Fm(:)p Fh(L)468 904 y Fc(2)500 891 y Fh(\022)16 1036 y Fn(2.)d(F)-7 b(orm)27 b(the)i(resolv)n(en)n(t)h Fh(C)35 b Fn(b)n(y)28 b(including)j(all)g(literals)104 1140 y(from)c Fh(C)369 1153 y Fc(1)401 1140 y Fh(\022)k Fn(and)e Fh(C)702 1153 y Fc(2)733 1140 y Fh(\022)r Fn(,)h(except)g(for) f Fh(L)1290 1153 y Fc(1)1321 1140 y Fh(\022)j Fn(and)c Fm(:)p Fh(L)1676 1153 y Fc(2)1708 1140 y Fh(\022)r Fn(.)104 1244 y(More)g(precisely)-7 b(,)31 b(the)f(set)f(of)g(literals)j(o)r (ccurring)e(in)104 1348 y(the)f(conclusion)i Fh(C)j Fn(is)401 1501 y Fh(C)c Fn(=)24 b(\()p Fh(C)679 1514 y Fc(1)730 1501 y Fm(\000)19 b(f)p Fh(L)918 1514 y Fc(1)949 1501 y Fm(g)p Fn(\))p Fh(\022)k Fm([)c Fn(\()p Fh(C)1259 1514 y Fc(2)1311 1501 y Fm(\000)g(f)p Fh(L)1499 1514 y Fc(2)1530 1501 y Fm(g)p Fn(\))p Fh(\022)0 2748 y Fl(250)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fk(Machine)h(L)n(e)n(arning)p Fl(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e(Hill,)j(1997)p eop %%Page: 251 23 251 22 bop 25 160 a Fo(In)m(v)m(erting)36 b(First)g(order)f(resolution) 1466 160 y 0.8666 0.03137 0.02352 setrgbcolor 1466 160 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 170 628 a Fh(C)232 641 y Fc(2)287 628 y Fn(=)24 b(\()p Fh(C)h Fm(\000)19 b Fn(\()p Fh(C)679 641 y Fc(1)730 628 y Fm(\000)h(f)p Fh(L)919 641 y Fc(1)950 628 y Fm(g)p Fn(\))p Fh(\022)1066 641 y Fc(1)1099 628 y Fn(\))p Fh(\022)1174 592 y Fe(\000)p Fc(1)1172 649 y(2)1273 628 y Fm([)f(f:)p Fh(L)1508 641 y Fc(1)1540 628 y Fh(\022)1580 641 y Fc(1)1613 628 y Fh(\022)1655 592 y Fe(\000)p Fc(1)1653 649 y(2)1734 628 y Fm(g)0 2748 y Fl(251)334 b(lecture)17 b(slides)f(for)f(textb)q(o) q(ok)g Fk(Machine)h(L)n(e)n(arning)p Fl(,)c(T.)j(Mitc)o(hell,)h(McGra)o (w)e(Hill,)j(1997)p eop %%Page: 252 24 252 23 bop 25 160 a Fo(Cigol)295 160 y 0.8666 0.03137 0.02352 setrgbcolor 295 160 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a -77 478 a 33154007 14256220 1907671 26181140 33088225 39863746 startTexFig -77 478 a %%BeginDocument: ./oldbookps/res-rule2.ps 50 dict begin /arrowHeight 8 def /arrowWidth 4 def /none null def /numGraphicParameters 17 def /stringLimit 65535 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { /patternGrayLevel idef patternGrayLevel -1 eq { /patternString idef } if false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 [FontBBox] 1 get FontMatrix end transform exch pop def /vertoffset 0 descender sub printSize sub printFont /Courier ne printFont /Courier-Bold ne and { 1 add } if def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def %I Idraw 7 Grid 8 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 0.799705 0 0 0.799705 0 0 ] concat /originalCTM matrix currentmatrix def Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 -53.5 -44.9999 ] concat %I 177 654 265 566 Line End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 -53.5 -44.9999 ] concat %I 265 566 353 654 Line End Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 60.5 75 ] concat %I 177 654 265 566 Line End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 60.5 75 ] concat %I 265 566 353 654 Line End Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 2.00072 334.123 ] concat Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-140-* /Times-Italic 14 SetF %I t [ 1 0 0 1 133 415.874 ] concat %I [ (Father Tom, Bob ) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 174.064 415.876 ] concat %I [ (\( ) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 232.086 415.876 ] concat %I [ (\)) ] Text End End %I eop Begin %I Rect %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1.07309 0 0 1 -135.391 244.997 ] concat %I 409 489 709 510 Rect End Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t u Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-120-* /Times-Italic 12 SetF %I t [ 1 0 0 1 522.969 748.497 ] concat %I [ ( ) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-medium-r-*-140-* /Helvetica 14 SetF %I t [ 1.00037 0 0 1.00037 520.024 749.499 ] concat %I [ (V) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-14-*-*-*-*-*-*-* /elvetica 14 SetF %I t [ 1 0 0 1 413.351 749.497 ] concat %I [ ( ) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-14-*-*-*-*-*-*-* /elvetica 14 SetF %I t [ 1 0 0 1 509.351 749.497 ] concat %I [ ( ) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-140-* /Times-Italic 14 SetF %I t [ 1 0 0 1 433.351 749.997 ] concat %I [ ( Father x,z) ] Text End Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 403.496 267.571 ] concat Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.00037 0 0 1.00037 -157.058 212.828 ] concat %I 287 266 298 266 Line End Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.00037 0 0 1.00037 -157.058 211.828 ] concat %I 298 267 298 263 Line End End %I eop Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-140-* /Times-Italic 14 SetF %I t [ 1 0 0 1 537.355 749.997 ] concat %I [ ( Father z,y) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-medium-r-*-140-* /Helvetica 14 SetF %I t [ 1.00037 0 0 1.00037 415.982 749.499 ] concat %I [ (V) ] Text End Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 302.455 267.571 ] concat Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.00037 0 0 1.00037 -157.058 212.828 ] concat %I 287 266 298 266 Line End Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.00037 0 0 1.00037 -157.058 211.828 ] concat %I 298 267 298 263 Line End End %I eop Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 -5.64769 320.852 ] concat Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-140-* /Times-Italic 14 SetF %I t [ 1 0 0 1 317.998 429.145 ] concat %I [ (GrandChild y,x ) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 386.142 429.147 ] concat %I [ (\( ) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 409.151 429.147 ] concat %I [ (\)) ] Text End End %I eop Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 486.534 749.999 ] concat %I [ (\( ) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 508.542 749.999 ] concat %I [ (\)) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 587.571 749.999 ] concat %I [ (\() ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 609.579 749.999 ] concat %I [ (\)) ] Text End End %I eop Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 6.00223 248.091 ] concat Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-140-* /Times-Italic 14 SetF %I t [ 1 0 0 1 400.999 455.905 ] concat %I [ (Bob/y, Tom/z) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 475.175 455.907 ] concat %I [ (}) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 394.142 455.907 ] concat %I [ ({ ) ] Text End End %I eop Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 -9.0033 211.078 ] concat Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 278.103 359.132 ] concat %I [ ({ ) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 344.127 359.132 ] concat %I [ (}) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-140-* /Times-Italic 14 SetF %I t [ 1 0 0 1 285.002 359.13 ] concat %I [ (Shannon/x) ] Text End End %I eop Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t u Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-140-* /Times-Italic 14 SetF %I t [ 1 0 0 1 135.997 514.999 ] concat %I [ (GrandChild Bob, Shannon) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 205.076 515.001 ] concat %I [ (\() ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 288.106 515.001 ] concat %I [ (\)) ] Text End End %I eop Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t u Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-140-* /Times-Italic 14 SetF %I t [ 1 0 0 1 41.0011 630.995 ] concat %I [ (Father Shannon, Tom) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 82.0302 630.997 ] concat %I [ (\() ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 168.062 630.997 ] concat %I [ (\)) ] Text End End %I eop Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t u Begin %I Rect %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 -115.5 241.495 ] concat %I 379 373 634 395 Rect End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-medium-r-*-140-* /Helvetica 14 SetF %I t [ 1.00037 0 0 1.00037 392.523 630.496 ] concat %I [ (V) ] Text End Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 277.996 148.569 ] concat Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.00037 0 0 1.00037 -157.058 212.828 ] concat %I 287 266 298 266 Line End Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.00037 0 0 1.00037 -157.058 211.828 ] concat %I 298 267 298 263 Line End End %I eop Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-140-* /Times-Italic 14 SetF %I t [ 1 0 0 1 272.9 630.995 ] concat %I [ (GrandChild Bob,x) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-140-* /Times-Italic 14 SetF %I t [ 1 0 0 1 411.899 630.995 ] concat %I [ ( Father x,Tom) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 379.052 630.997 ] concat %I [ (\)) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 342.038 630.997 ] concat %I [ (\() ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 462.082 630.997 ] concat %I [ (\() ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 503.098 630.997 ] concat %I [ (\)) ] Text End End %I eop End %I eop showpage end %%EndDocument endTexFig 0 2748 a Fl(252)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fk(Machine)h(L)n(e)n(arning)p Fl(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e (Hill,)j(1997)p eop %%Page: 253 25 253 24 bop 25 160 a Fo(Progol)354 160 y 0.8666 0.03137 0.02352 setrgbcolor 354 160 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 64 x Fi(Pr)n(ogol)p Fn(:)37 b(Reduce)29 b(com)n(b)e(explosion)j(b)n(y)e(generating)h(the)0 642 y(most)f(sp)r(eci\014c)i(acceptable)h Fh(h)16 800 y Fn(1.)21 b(User)28 b(sp)r(eci\014es)i Fh(H)35 b Fn(b)n(y)28 b(stating)i(predicates,)g(functions,)104 903 y(and)e(forms)g(of)h (argumen)n(ts)e(allo)n(w)n(ed)j(for)f(eac)n(h)16 1049 y(2.)21 b Fi(Pr)n(ogol)28 b Fn(uses)h(sequen)n(tial)i(co)n(v)n(ering)e (algorithm.)104 1153 y(F)-7 b(or)28 b(eac)n(h)h Fm(h)p Fh(x)534 1165 y Ff(i)557 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