An approach to fuzzy temporal reasoning in medicine

Ma th w are&Sof tC om puti ng 3( 19 94)26 5-27 6 An Ap p roac htoF uzz yT em poral Reas oni nginM edicine R.Mar  n a ,S.Barro b ,F .P alacios c ,R.Ruiz a ,F.M art   n a a Dep t. deI nform  ati caySi stem as.U niv.deMurc ia. E30071Espinardo.Murci a,Spai n. b De pt.deEl ectr onic aeCom putac i on.U niv.deSan tiago. E15706San tiago.Spai n. c H ospi ta lG ene ralUniv ersi tarid' Elx. E03202Elx.Al ic an te,Spain. e-mail: a r o [email protected], b senen@gaes .us c.es Ab stract Inthisw orkw eproposeanapproac hf orthea pplicationofaf uzzytemporalco nstrain tmodeltointelligen tpatientmonitoringtasks.A fteranalyzing therequiremen tsofthedomain,w edescribetheapproac ht hatw asf ollo w ed inorderto represen ttemporalinformationandsolv equeriesontempo ral re lations.Theseprocessesrequi rethecooperationofat emp oralspecialist withthedomainreasoni ng mec hanisms.Theint egrati on solut ionpresented herec or respondstoast ageoft heim pl emen tationofFRESH,atool forthe de v elopmentofin tellig entm on it oringsystemsfordy nami ce n vironments. Keyw ords: T empo ralR easoning,ExpertSystems, In telligen tMonitoring ,I n tensiveCoronaryCare. 1In troduc ti on Ag enera lstra tegyf orthepracti ca lappl icatio noftem poralreasoningt ec hni ques require s a n expli ci tdi stinct i on b et wee n do mai nrea soni ng ta sks a nd tem po ra lrea - soni ng tasks . The form er are s ol ved b ym eans of the c o nv en tional arc hitec ture of an exp e rt s y s tem (ES) basedondom ain kno wledge , whe re a s the la t ter are i mplem en ted b ym eans of a tempor al sp ecialist [1 4], a s yste m based on som e form al tem p oralco ns train tm o del that repr esen ts and m anages the inf orm ati on re g arding the p o si tion o fasetofev en ts on th e timeax is. The m ai n tas ks of a te m po ral sp e cia li s t are: a) To infer ne w t emporal relations from those that are initially r epre se nted, applying sometemporal c onstraintpropagation mechanis m that r educ es im- 265 266 R .Ma r   n,S. Ba rr o, F. Palaci os,R.R ui z&F .M art n prec isionandam bigui t yin knownr el atio nsa sm uc haspos sibl e; b)T oanal yzetheg loba lconsistencyofthese to fp artia lrel atio nsi n trod uc ed; c)T oc om pu tepo ssibl etem porals ce nario s(totalorderi ngsof thee ve n ts)tha t are co m patibl ewi ththei nitiali nform ation. Thisl astta skisbasi cinpl anningproblem s,butisl essi mp orta n ti ndiag nosti c or m o ni toringdatai n terpret ati onproblem s.Inthesecase s, thedom ainESm ust de tecttem po ra lpatternso fs ym ptom sthatsupportorrejec td ieren tdiag nosti c hypotheses.Ino rdertodot hi si twi llquerythetem poral spec i ali stontheexistence of speci ctem poralrelati onsa m ongparti cul arev en ts.Thet em poralspeci al istwil l answ erthesequeriesaf terapplyi ngtheconstra in tpro pagati ona lgo ri thm stothe te m porall abel so ftheev en ts. So me well kno wntem po ra lco nstrai nt mo del saredescribedi n[ 1, 24,2 5 ,9,2] . Ea ch mo delp ro vi desapa rti cul arc om prom isesoluti onbet w eene xpress iv epo w er ande c ie ncy ,whic hm ustbecom par ed with therequirem en tsofthed om ainin whic hi tw i llbea pplied.Som ek eya spec tstobeconsideredare: a )H ow torepresen tthetem porali nf orm ati oncon ten tofthedom ainfactsin terms oftheelem en tsofthetem pora lconstra in tm odel ; b)Ho wtosolv ethetem poralqueri estheESw il lpresen tduringthereasoning processonthedom ain. Inpreviousw orks[3 ,1 5,1 6,1 7,4 ]w ehav epresen tedaF uzzyT em po ra lC onstrai n tNe tw orkm odel(FTCN).Inthispa pe rw eproposeaso lutio nfo ri ts a pplicationtoin tell igen tm oni toringt asksi nm edi ca ldom a ins.Then extsectio ncon tai ns adisc ussi onaboutthedom ainr eq ui rem en ts.Insecti on3w ew illi n troducesom e bas ic conceptsoftheFTCNmo del. Final ly ,w ewil ldescrib et he approac hfol lo w ed for in teg ra ti ngatem poralspe ci al istbasedontheFTCNm ode lw ithadom ai nES. The de scri pti onwil lconcen tr ateo ntheproblem sofreprese nt ingtem po ralinfo rm ati onandtheansw er ingo fq ueries. 2R equi rem en tsoftheCl i nic alD om ai n Weli mito ur ana lysis to a task in a particular dom ain: the ev al uation of t he indivi du a lrisko f patien ts in ter ned in ICCUs (In te nsiv eCo ro nary Care Uni ts ) wi th a diagno sti c of acute m yoca rd ial i nfarct i on. This ob j ecti veisappro ac h ed from the de tec ti on of early p o sti nf arc ti on re sidual isc he m ia, o nc e the acute phase of the infa r ction has b e en o ver com e. Thi sisthem os t i mp ortan tfac tor f or t he de ter m ination of th e short ter m risk o fr einfa rctio n and the se cond m ost im p ort a ntfa c tor, after t he ev al uation of the v en tr icul ar function, f or the d ete rm inati on of m edium and long term survival. Its diagnostic and quantication const itut es a pr imary ob je ctivein ICCUs [21, 12,10]. AnApproac htoFuzz yT em po ralR easoni nginMedicine 2 67 We wil lrstanal yzethedier en tt ypesoftem porali nformati on a ppearingin thed escripti ono fthedoma in facts.Thetem poralspecia li st wil lrepresen tthi s temp oralinfo rm atio nconten tb ya ssi gningdi eren tt yp es of te m po ra lla bel sto thef actssto redinthesyst em database.T hem ostfrequen tlyu se dparam etersin a nICCUcorrespondtoc lini ca lo bserv atio ns(sym pt om sa nd si gns),an teceden ts, treatm en tanda nalysi sr es ul ts,whereasm o ni toringp aram eters(hem odynam icand ECGv aria bles)correspo nd to only13%ofthetotal[11] .T hisv ari et yofdata t ypesnecessi tatestheu se of dieren tt ypesoftem por al label s. Ing enera l,cli nicalantec eden tsaredatedinanappro xi ma tef ashi ona ndwith alev eloftem poralg ra nulari t ytha ti shi gherthanother data ,l ea dingtotem porali m precisio n(e. g. \m oderatekidneyi nsu cie ncyd ia gnosedali ttl eo v eray ea r a go").Bothinthea n te ce den tsandduringthem o nitoringsta ge,w eha v etorepresen tsubjecti v esym ptom sdenedb ym eansoftem porall abel swithrespecttosom e referencepo in t(e. g.\palpi tatio nssi nceaboutv em o n thsb ef orein ternm en t" ,\a littlepai nafterthela stm eal"). Thedataf ro mana lysesandc li nicalexplo ra tion ha v eabsoluteandprec is et em porallabels.Theparame tersthataredi rectl yextractedf romthem onitor edsignal salsoha v eabso lute a ndpreci sel abel s,generate d f ro mthei ndi ceso fthe sam pl es,whic harerelati v et ot hebeginni ngofm onitori ng . Fi nall y ,som esi gnale pi sodesarebetterdescribed by m ea nso fi n terv a lsofim pre cise durati on,wheretheim pr ecisioni nthedura ti oncom es f ro mthei m precisio ninthe criteri afromw hic hthebegi nningandtheend oftheepisodesareestabli sh ed(e.g . \ highSTl ev elthro ughoutthepa st30seconds" ).Consequen tly ,thetem poralspecia li stm ustperm ittherepresen tatio nofti me poin tsandin terv alswhosete m po ra l positi onwi llbei den tiedb ym eansoftem poral labelswhi chm a ybeabsoluteo r relati v e,bothprec iseandim precise. Letusno wconsidert hepro bl emofreasoninga bo ut thedom ai n.An yph ys- i opathologi ca lprocesscanbedescri bedasatem poralev ol utionof ad ynam icsystem ,t he humanbody ,whoseobserv ab le re sultisagi v ensequenceo fc li nicalm a nif estation s. Ing enera lthereisnoo ne -to- onem a ppingbet w eendiagnost i ccateg ories a ndo bse rv abl eev en tsequences.Thes am ep athol ogicalepi sodem anifes tsitsel fin di eren tp atie n tsthroughdi eren ts eq uenc esofev en ts.Theym a yd ier in the tem po ralarrangem en tofthe ev en ts andintheti m eel apsed be tw ee nthem .Exper ts desc ribetem poralp attern so fs ym ptom si nwhic ht he si gnicant i nform a tion i stherelati v earrangem en to ftheev entsandtheexistenceoftem poraldi stancesbe - twe en sym ptom st hat a r e in agre em en twi th the causal re l atio n s of the unde rlying ph ysi olo gical process. Wewi ll c onsider an e xa mple from o ur dom ai n. Early p ostinfarction re si du a l isc hem ia is dia gnose d when unequi vo cal c he st angi na (pai n) episo des a r e de tec ted, o r whe n t here are r ec urre n t acute c hanges i ntheel e ctr o cardio gram (E CG ). These criter i a are appl ied in the tim e peri od f rom the se cond da ytothe ten th da yofev olution, conditi onal o n the patien t b eing a sym ptom ati ca nd st able from the p o in t ofv iew of i sc he m ia m onitoring f oll owing the stabil izatio nof the acute s tag eofthe infarct ion [20]. Ches t angina may app e ar with or without e vide ntchanges of the ECG (early p ostinfar ctionangor). In add ition, there may b e re curr entchanges in 268 R .Ma r   n,S. Ba rr o, F. Palaci os,R.R ui z&F .M art n th eS Tand/o rTw a v esegm entso ft he ECGthatareno tacco mpanie db ya ngina (E arl ypo sti nf arcti onsilen ti sc hem i a).Si len tischem ia ep is odesa rem oref requent th an thosepresen tingangi na,a nd consequen tl ythei rdiagnosisandq uan tication must bel argel ybasedonele ctricalm onito ri ng,thegreate st problemo fwhi chi s theelim ina ti onoffal se po sitiv es[8 ].F al sepositiv es ma ybereducedb yco rrelatingthei nform ationde rive df romtheel ectri ca lm onitor ingwi ththatcom ingfrom hem odynam i cm onito ri ng,w hi c h,inadditio n,pro vi de si nf orm ati ononthepathogenesisofthetra nsi ent is chem i aepi sode.Oneofthec haracteristicpatternsisthe presenceofaleftand/or righ tv en tri cul ari m pa irm en t, be ginni ngshortlybeforet he onseto ftheelectroca rd iographi ccha nges,f oll o w ed by ar apidreco v eryandoften b yo v ershoo ti ng.Thei ni tia lc hangesarecha ra ct er iz edb yareductioni nv en tr ic - ularsystoli cpressurea ndasi m ul taneo usincrease in end-di asto li candpul m ona ry pressure[22 ].Thedeni tiv ei n terpretati onoftheinf orm ati onderi v edfromthe el ec tri ca landhem odyna m icm onitoringofthi st ypeofpa ti en ti scom pletedwi th ac linicalev a luati ono fthec ase, theresponsetothetreatment a ndthebeha vio r ofthedeterm i natio no fc ar di acenzy m es.Ingener al ,t he i den ti cati onofatem po - ra lpatternrequiresc he c kingtheexistenceofi m prec isetem poralrel atio nsbet ween thef acts,relati onsb et w eenin terv al sasw el lasre latio nsbet w eenti m epoin tsa nd rela ti onsbet w eentim ep oi n tsa ndin terv als. 3R eprese n tat i onofF uz zyT em poralR e l ati ons De ni ti on1 A fuzzyt em po ra lconstra in tnet w ork (FTCN ) N = < X ; L > isa p ai rmadeupofanites etof n +1 t emp or alvariable s X = f X 0 ;X 1 ;:::;X n g and aniteset of fuzzybinaryc onstr aintsb et we enthem L = f L i j =i;j  n g . Eac hv ariable X i represe ntsa nu nkno wnti m epo in t.Eac hb inaryco nstrain t L i j i saf uzzyd urati onthatisdenedb ym eanso fa possi bili t ydistribution  ij o v ertheuniv er seofi n tegerdurati ons, andd escribesthepossi bl evalues fo rthe tim ee lapsedbet w eenti m epoin ts X i a nd X j .Gi venapreci sein tegerdurat ion m ,  ij ( m )repr esen tsthepo ssibi lit yo ft he tim eela psedfrom X i to X j bei ng preci sely m unitso ft im e.So m eparti cu lart yp es of fuzzydurati onsa re : i) The univ ers al cons trai nt L U ,who se possi bil it ydi stri buti on satises  U ( m )= 1 ;m 2I . ii ) The p o si ti veco ns trai nt L P ,g iven b y  P ( m )=0 ;m  0. iii) The n egati veco nstrai nt L N ,giv en b y  N ( m )=0 ;m  0. iv) Then ull c onstrain t L n ul l ,gi venb y  null (0) = 1. v) The b e fore c onstraint L bef o r e , a p ositive cons traintgiven by  bef or e ( m )= 1 ;m> 0. AnApproac htoFuzz yT em po ralR easoni nginMedicine 2 69 vi)T heaf terconstrai n t L aft e r ,a negati v econstra in tgiv en by  aft e r ( m )= 1 ;m< 0. Inwha tf ol lo ws we will a ssum ethatev erycons trai nt L ij thatha snotbee ne xpli ci tly esta bli sh ed is au ni v ersalconstra in t. We will al soa ssum etha ttheconstr ain t L ji i s thesym m et ri cc onstrai n tto L ij ,giv enb y  ji ( m )=  ij ( 0 m ) ;m 2I .Ob vi ously , L after and L be fore aresym m et ricf uzzydurati ons.Am o rede ta iled fo rm ali za tion o ftheFTCNmo de lc a nbef oundin[4 ,3,1 5,16 ,1 7] .W ewi llconcen tratehereo n thepro blemo ft he represen tati onintheFTCN mo delo ftem poralen titi es (tim e poi n tsandin terv al s)a ndoftem poralrelationsbet w eenthem . D en i ti on2 A n ev en t e j i satr iad e j =( a j ;v j ;t j ) ,inw hich a j issomevar iable f r omthedomai n, v j isthepr e ci seori mpr e ci seval uet akenbythisv ariable,and t j i satemp or alentity. Anev en tco rres po ndstotheoccurrenceo fs om ed om ai nfa cti nagi v entime poi n t,where thef actisg iv enb ytheassi gnment ofav a luetoav ariable .S om e examplesofdo m ai nv ariabl esare :\ determ ina ti onofki dneyfunction" ,\c hangein v en tricula rsystoli cpressure" , ::: .Ex am pl esofv al uesa re: \norm al" ,\sustai ned i ncrease", ::: .Thetem poralen tit y t j wi llb eati m epoi n t p i o ratim ein terv al i j . D en i tion3 A tim epoi n t p j isap air p j =( X j ;L j ) ,wher e X j isatempo r al var iable and L j isasetof temp or alc onstr ai nt s L j = f L jy ;L jz ;::: g . Constrain ts L jy ;L jz ;::: establi shtherelati v eposi tionofth eti m epoin t p j withr especttootherreferencet im epo in tscorrespondingtot he tem poralv ari- a bles X y ;X z ;:: : F orexam pl e,ani nstan ta neo us ev en t e 1 ,whichiskno wntoha v e occur edin1 990,appro xim atel y1 5d a ysbefo rethei nstan ta neo us ev en t e 2 ,will hav ea te m po ra ll abel t 1 a ss oc iatedtoitg iv enb yav ari able X 1 and as et oft w o tem po ralconstrai n ts L 1 = f L 10 ;L 12 g ; L 1 0 isa co ns train twithrespecttothet im e o ri gi n,expressedb ythei mpreci seabsolutedate(\the year1990 "),andinwhi ch thei m preci si oni sasso ci ated wi ththeuseofl o wtemp or al gran ula ri t y; L 12 i san i m precisetem poralconst rain t(\a ppro xim atel y15d ay sb ef ore" )wi threspectto the te m po ra lv a ri abl e X 2 associ atedwi ththet im ep oint at whi chthereferen ce ev ent e 2 occurred. Den iti on 4 A tim ei nte rv al i j is a tr iad i j =( p j a ;p j b ;L j a j b ) ,i nw hich p j a an d p j b cor resp on d to the i ni tial and n al t ime p oi nt s of the interval r esp ectively, an d L j a j b is a p osit ive c onstr ai nt betw een the temp or al variabl es c orr esp on ding to t hese time p oints, w hi ch r epr esents t h e dur ati on of the interval. Thes e de ni tions perm it a direc t repr es en tati on of the tem po ral p ositi on of the ev ents i n t he ne t work .Ho wev er , w eare i nte res ted i nha vi ng a m o r e gene ral w ay of e xpre ssing this t hatisclose r to t he u ser . For the user, the temporal entitie s are dene d by e stablishing temporal relations between them,which ar e expr ess ed by 270 R .Ma r   n,S. Ba rr o, F. Palaci os,R.R ui z&F .M art n meansofling uistictem poral labe ls.W eha v edenedthes yn tacticandsem an ti c ru le sofa temp or alent ityr ep resentationlanguage whic ht rans l atesl ingui sti ctempo ra lla bel si n tofuzzyconst rain ts[ 4].Thel anguageperm itse xpressi onsofthe type \poi n t p 2 oc cu rs appr oxi mat ely 10 minu tesa f terp oint p 1 and afewminutes b efor einterval i 3 " ,wheretheexpressions in ita licscorrespondtoli ng uistictem pora ll abel s.Thel ingui st ic label scanbestatedinan absoluteorrel ativ efa shi on. Relati v ela belsestabli sh tem poralrel ati onsbetw ee nt im epoi n ts,bet w eenin te rv al s andbet w eentim epoi n tsa nd in terv al s.Absol utel abel se stabli shtem po ra lrelations withrespecttothetim eo ri gin(adateo nthecal endar). Therearethreet ypesoft em po ra lrel ationsbet w eenti me po in ts,whi chare expressedb ym eanso fl ingui sti clabels f d g -before , f d g -after,and f d g -equal ,i n whic h d isaf uzzyduratio n(e. g.\a ppro xim atel y10m in utes",\afewm i n utes", ::: ).Observ ethateac htemp oralrel ationcanberepresen tedasaFTCNtha t only con tai nsthetem poralvariablesandconstrai n tsi nther ela ti on.TheFTCN as so ciatedwi theac htem poralr el ationdependsonthel ingui st i clabel l b ym eans ofwhi chtherel atio ni se xp ressed.F orm al ly ,the te mp or a lrel atio nsbet w eent im e po in tsaredenedasfollo w s: De ni ti on5 Atemp oralr elati on R b etwe entwoti mep oints p i and p j ,est ablishe dbyme ansoft helinguisticlab el l ,isaFTCN N R = < X R ; L R > givenby X R = f X 0 g[f X i ;X j g and L R = f L i j g ,w her ethep ossibil itydistr ibution  ij c or r esp ondingto L i j i s:  ij = 8 < :  d ; f or l = f d g - b efor e ;  - d ; f or l = f d g - af ter ;  d 0 ; f or l = f d g - e qual ; d is ap osit ivefuzzydur ationwhose p ossi bili tydistr ibut ion is  d , d 0 isanullfuzzy dur ationwhosep ossibi litydistribu t ionis  d 0 ,an d  - d i st he sy mm et ricdistr ibut ion to  d . In thes am ew a y ,w edenethefollowingt ypesoftem poralrel atio ns bet w een ti me po in tsa ndti m ein terv al s, andb et w eentim ein terv alsandt im ep oin ts: De ni ti on 6 Atemp or alr el ation R betweenatimep oint p i and at imei nt er val i j , establ ished byme ansofthe li nguisti clab el l ,i saFTCN N R = < X R ; L R > given by X R = f X 0 g[f X i ;X j a ;X j b g and L R = f L ij a ;L ij b ;L j a j b g ,w her ethep ossi bi lit y di stri bu t ion s  ij a and  ij b cor resp on di ng to L ij a and L ij b ,r esp ectively ar e:  ij a =  d ;  ij b =  be fo re ; for l = f d g -b efor e ;  ij a =  d 0 ;  ij b =  be for e ; for l = f d 0 g -b eginning ;  ij a =  d x ;  ij b =  - d y ; for l = f d x ;d y g -b elongs ;  ij a =  af t er ;  ij b =  d 0 ; for l = f d 0 g -end ;  ij a =  af t er ;  ij b =  - d ; for l = f d g -after ; the possibility distribution  j a j b correspo nding to L j a j b is  bef o r e , d , d x an d d y are positive fuzzy durations, and d 0 is a nu l l fuzzy duration. AnApproac htoFuzz yT em po ralR easoni nginMedicine 2 71 Den i ti on7 Thetemp or alrelati on sb etw e eni nt ervalsandt imep ointsar ethe in ver seofthepr eviousone sa nd ar egi venby: i j f d g -b efor e p i , p i f d g -after i j ; i j f d 0 g - end p i , p i f d g -end i j ; i j f d x ;d y g -c ontains p i , p i f d x ;d y g -b el ongs i j ; i j f d 0 g - b e ginn ing p i , p i f d 0 g -b e gi nn ing i j ; i j f d g -after p i , p i f d g -b efore i j : W ewil lo mitt hedeni tiono fthethi rtee nt em po ra lrel ati onsbet ween in terv a ls, whi ch aredenedinthesa m ew a yas theo nesabo v e.Asaconcl usion, an ynondi sjunc tiv etem po ra lrela ti oncan be ling uisticall yrepresented andtransla tedin to aFTCN N R = < X R ; L R > whi chconstitutesi tsin terna lreprese n tatio n.Inorder toi ncorporatearelati on R toapre-ex isti ngFTCN N = < X ; L > ,anewFTCN i sobtai ned N 0 = < X 0 ; L 0 > ,gi v enb y N 0 = N[N R ,wheretheFTCNunion o peratorisgi venb y: X 0 = X [ X R ; L 0 = f L 0 ij =L 0 ij = L ij \ L R ij ;L ij 2 L;L R i j 2 L R g : 4Q ue ryonF uzz yT e m poralRe l at ionsinFRESH FR ESH(F uzzyT em po ra lRea so ningExpe rtSystemShell )isatoolfo rt hedev el- o pm en to fin tell igen tm oni to ri ngsys tem si ndynam i cen vironm en ts tha to urgroup i sdev elopi ng.A tthi sstage,w eha v ea pproac hedtheco nstructi ono fa nexpert systemfo rthecli nicaldomain w eha v edescribedabo v e.Thew orkinthiso perati onaldo m ai nwi llbeusedin ordertotestthev ali dit yofo ur a pproa chpriortothe constructiono fthegeneral to ol. FRESHincl udesatem poralspecial ist basedontheFTCNm odel ,tha tm an ages theproc es so frepresen tingthetem po rali nform ationco n ten tofth ee ven tsina tem porald atab l ac kbo ard.Curren tly ,e vent i nputcom esfromtheuser .D i eren t t yp es o frea soni ngagen tsha ve been im pl em en tedandtheyw illb ei n tegratedin FRE SH's ar c hitecture.Thosec ur rently a v ai labl earea gentsb ased on algo ri thm i c sig nalprocessingtec hniques,ag en tsb asedo nfuzzyp roductionrule sandagen ts ba sed on a l ing ui st i ctem p oral lte ri ng technique . They a r e des crib ed in de tai lin ot her pap e rs [5 ,6, 7, 19] . The e v en ts are a r ranged on the te m po ra lda ta blac kboard indi e ren t abstrac ti on lev el s, and are orga nize d in to ev en thi s tori e s, eac ho ne associ ated wi th a cli nical param e ter . In part i cul ar, the e ven t history ge nerate d b yea ch l ing ui st i ctem p oral l t ering agen tco nta ins a seque nce o f sig na l episo des dete cte d in the sig nal o ver whi ch it op e rates . F or the de tec tio n of episo de s w e appl yim p rec i se criteri aofv alue, durati on a nd tem p oral se parati on (e.g .ECG episo des wi th hi gh ST v alue, dur a tion of m ore th a n appro xim ately 30 s ec o n ds and sep aration larger th an approximately 30 se conds). As a re sult of the impr ec ision of the criter ia, the e vents are dened over impre cise timeinte rvals. The te mporal 272 R .Ma r   n,S. Ba rr o, F. Palaci os,R.R ui z&F .M art n Fi gure1: T em poralspeci al ist spec i ali stinsertsthesetim ei nterv alsi ntheFTCN.Inorder to solv etheq ueries pr es en tedb ythereasoni nga gen ts ,thetem poralspeci al istc he c ksf ortheexistence of spec i ctem poralrelati onsb et we entheev en ts,correlating ev en tsf ro mthesi gnal andev en tscorrespondingt oo thert ypesofcl ini cal data. Therepresen tation of theev en thi sto ry H ( a )= f e 1 ;e 2 ;::: g a ssoci atedwith a cl ini calp aram et er a isoutli nedi nFigure 1. Thetem poralen tit y t j corresponding toeac heve nt e j poin tstot he no desoftheFTCN,andi tsco rres po ndenceo v erthe net w o rk is obtained by m eansofthetem po rale ntit yr epresen ta ti on la nguage,a s describedintheprevio ussectio n.T hetem po ra lspe cial istdecom posesthenet wo rk in toaset of particula r top olo gies and appli es a nal gorithm that p ropa gates th e c ons trai nt s and a nalyzes consiste ncy to each s ub-net work. Al l the alg orithm susedfo r t he diere n t particularto po logi es are e xecut ed in po lynom ial tim e. G iv en t wote mpo ra lv aria bl es X i and X j ,w ewil lcal l M ij the m ini mum c o ns train tbet wee n th em after applyi ng the propaga tion alg orithm sand  M ij the c o r res p ondi ng p ossibil it y distr i but i on. M ij is a m inim all yi mprec i se cons trai ntwhi ch r esults from com bi ning all the inf or m atio n that aec ts the tem pora ldi sta nce bet ween b othv ariables. O nce the m inimum constr a in t M ij is kno wn, the tem p oral s p e ci ali st can answ er q u eries on the temp oral re lationbetwee n X i and X j . The que ries pre sente d by t he domain r easoning mechanismshavetheformat AnApproac htoFuzz yT em po ralR easoni nginMedicine 2 73 ( Q;S ;C v ;C t ). S isasel ectio nofev en ts give nb y S = f e=type ( e ) ^ R v ( e:v alu e;vref ) ^ R t ( e:time;tref ) g ,whi c hcorrespondstothesetofev en tso fa givent ypewhose valuesandtim esv eri fycer tain co nditio ns. R v is av al ueconditi onthatco mpares thev alueoftheev en twitha refe rencev alue.Inasim i lar wa y, R t is at im e conditi onthatcom pares thet im eoftheev en twi thar efer enceti m eandisgi v enb y a n yo ftheli nguistice xpre ssionstha tcanbegenerate db ym eansofthetem po ra l en tit yrepresen tationl anguagedescri bedintheprev ious secti on.Byi tself, S i s a nunq ua n tiedform ul aw it ha freev ari able. Q isanagg re gati onoperato rthat i sappli edtotheev en tso ft he sel ectio nsetandcanbea quan tier( 9 ; 8 ),oran o perator(m axim um ,m i ni mum, a v erag e,rst,last,m axim al i n terv a l, ::: ). Q i s a ppl iedtothev al ue or ti m eo feac honeoftheev entso fs et S . C v and C t a rev al ue a ndtim econditi ons,r es pectiv el y ,si m i la rtothos ei ncludedinset S .Thi ssyn tax perm itsquestionsofthet yp e:Ha v ea llev en tsofv en tricularsy stol icpressurewith valuehig herthan100m m Hgand whic hoccurredduringthei nt ervalofthela st is chem i aepisodeoccurredle ss thanappro xi m ately3m i n utes be fo rethebegi nning o fthel astSTc ha nge ?T he expressi onbet w eenbracke ts is thatwhic hcorrespo nds totheselecti onset.F or eac honeoftheev en tssel ec te dw em ustcheckthetim e conditi on C t .Intheexam pl e, C t correspondstoatem po ralrel atio nwiththetim e i n terv a la ssoci atedw iththereferenceev en t\la st ST c hang e". Thequerypa rserdecom po sestheseexpressi onsi n toquestio nstothedatabl ac kboa rdonthev alueoftheev en tsandquestio ns tothetem poralspecia li ston the relati v etem poralpositio noftheev en ts.Inp a rti cul ar,thetem poralspec ial isto nly receiv esthesequenceo fqueriesonthetim econdi tions C t = R t ( t 1 ;t 2 )where t 1 i sthetem poralen tit yassociatedwi thso m espe ci cev en to fthesel ectionse tand t 2 isthetem poralen tit yassocia tedwi ththerefere nceev en t. R t ca nbea n ytem - poralrel ationbe tw eentim epoi n ts,bet w eentime poi n tsandi n terv a lsorbet ween i n terva ls.Thetem poralspeci ali stg en eratesaquerynet w ork N R thati sc om pared wi tht he mini m umFTCN N storedi nthe blac kb oard.Thecom pari sonp rocess i s reduced to com paringthei ndivi dualc onst rain tso fnet w ork N witht he respectiv e constra in ts ofnet w ork N R .F orexample ,aqueryo narel ation R t bet w een tw o i n terva ls is de com po sedb ythetem por al sp ec ia li stin tofourel ementaryq uerieson the co nstrai n tso ftheiniti al and nalv aria bleso fthein terv al s. Ane lementaryqueryhasthef ormat: X i D ij X j ?In orde rt osolv eitw ehav et o c hecki fbet w eenthei nst a n tscorrespon di ngtonodes X i and X j adurati on co m - pa ti ble wi th D ij has elapse d. By m e ans o f the sam etem poral en tity re pre se n ta tion languag eusedf or the i ntr o duction of inf orm ati on, w e obtai n the p oss i bil ity distributi on  D ij as so ciated wi th the durationw e are a ski ng f or. On the other hand, the real dur a tion e l aps ed b et wee n the no des is kno wn; i t corre spo nds to the m inim um constr a in t M ij and is re pre sen ted b y the p oss i bil it y distribution  M ij .Constrain t M ij will ha ve been o bta ined b ythep ropa gatio nal gori thm s from the input inform ati on piec es. F orm al ly ,w ewan ttoc heck to what e xten tth econ te n t of the prop ositi on \ the tem p oral di sta nce b e t ween X i and X j is D ij "i sco mpatibl e with the r efere nce prop osition \the te mp oral distance between X i and X j is M ij ". The temp oral sp e cialist obtains a p ossibilityme asure and meas ure of nec ess ity,respec-