A compositional modeling language

A Composi t i onal Model i ng Language Dani el Bobr ow* , Br i an Fal kenhai ner * * , AdamFar quhar #, Ri char d Fakes* , Kennet h For bus, Thomas Gr uber &, Yumi I wasaki * Xer ox Cor por at i on Pal o Al t o Resear ch Cent er 3333 Coyot e Hi l l Road Pal o Al t o, CA 94304 bobr ow@par c . xer ox . com * * Xer ox Wi l son Cent er 800 Phi l i ps Rd . , M/ S 128- 51E Webst er , NY 14580 f al ken @wr c . xer ox . co m * Knowl edge Syst ems Labor at or y Gat es Bl dg . 2A, M/ C 9020 Depar t ment of Comput er Sci ence St anf or d Uni ver si t y St anf or d, CA 94305 { axf , f akes, i wasaki ) @ksl . st anf or d. ed u $Qual i t at i ve Reasoni ng Gr oup The I nst i t ut e f or t he Lear ni ng Sci ences Nor t hwest er n Uni ver si t y 1890 Mapl e Avenue Evanst on, I L 60201 f or bus @il s . nwu . ed u 8- ' Col l oquy Syst ems I nc . 5150 El Cami no Real , Sui t e D- 21 Los Al t os, CA 94022 gr uber @col l oquy . com %Uni ver si t y of Texas at Aust i n Depar t ment of Comput er Sci ence Aust i n, TX 78712 kui per s @cs . ut exas . edu Abst r act Thi s document descr i bes a composi t i onal model i ng l anguage, CML, whi ch i s a gener al decl ar at i ve model i ng l anguage f or l ogi cal l y speci f yi ng t he symbol i c and mat hemat i cal pr oper t i es of t he st r uct ur e and behavi or of physi cal syst ems . CML i s i nt ended t o f aci l i t at e model shar i ng bet ween r esear ch gr oups, many of whi ch have l ong been usi ng si mi l ar l anguages . These l anguages ar e based pr i mar i l y on t he l anguage or i gi nal l y def i ned by Qual i t at i ve Pr ocess t heor y [ For bus 1984] and i ncl ude t he l anguages used f or t he Qual i t at i ve Physi cs Compi l er ( QPC) [ Cr awf or d 1990 ; Far quhar 1993 ; Far quhar 1994] , composi t i onal model f or mul at i on [ Fal kenhai ner 1991 ] , and t he Devi ce Model i ng Envi r onment ( DME) [ Low and I wasaki 1993] . CML i s an at t empt t o synt hesi ze and pr ovi de a cl ean r edesi gn of t hese l anguages . 1 . I nt r oduct i on Composi t i onal model i ng i s an ef f ect i ve par adi gm f or f or mul at i ng a behavi or model of physi cal syst em by composi ng descr i pt i ons of symbol i c and mat hemat i cal pr oper t i es of i ndi vi dual syst em component s . Thi s paper descr i bes Composi t i onal Model i ng Language ( CML) , whi ch i s a gener al decl ar at i ve model i ng l anguage f or r epr esent i ng physi cal knowl edge r equi r ed f or composi t i onal model i ng . CML i s i nt ended t o f aci l i t at e model shar i ng bet ween r esear ch gr oups, many of whi ch has l ong been usi ng 12 0 , Benj ami n Kui per s% QR- 96 si mi l ar l anguages . These l anguages ar e based pr i mar i l y on t he l anguage or i gi nal l y def i ned by Qual i t at i ve Pr ocess Theor y [ For bus 1984] and i ncl ude t he l anguages used f or t he Qual i t at i ve Physi cs Compi l er [ Far quhar 1994] , composi t i onal model f or mul at i on [ Fal kenhai ner 1991] , and t he Devi ce Model i ng Envi r onment [ Low and I wasaki 1993] . CML i s an at t empt t o synt hesi ze and pr ovi de a cl ean r edesi gn of t hese l anguages . The speci f i cat i on of CML has been f or mul at ed by r esear cher s i nvol ved i n t hose pr oj ect s . CML was desi gned wi t h ef f i ci ency, expr essi veness and ease of use i n mi nd . The l anguage i s r est r i ct ed enough t o al l ow ef f i ci ent i mpl ement at i on of pr ocedur es t o pr edi ct behavi or . The synt ax i s si mpl e and r eadabl e so t hat a per son f ami l i ar wi t h t he domai n wi l l be abl e t o r ead and easi l y under st and an expr essi on of knowl edge of t he domai n i n t he l anguage . The l anguage suppor t s l umped par amet er or di nar y di f f er ent i al equat i ons t hat ar e common i n engi neer i ng model i ng. Fi nal l y, t he l anguage suppor t s a var i et y of di f f er ent appr oaches t o r epr esent i ng physi cal phenomena ; i t al l ows t he def i ni t i on and use of domai n t heor i es t hat use component s, pr ocess, bond gr aphs, ki nemat i c pai r s, et c . , and al so suppor t s bot h r el at i onal and obj ect - or i ent ed speci f i cat i on st yl es . CML speci f i es a set of t op- l evel f or ms f or def i ni ng model s and an ont ol ogy of pr i mi t i ve f unct i ons, r el at i ons, and const ant s . CML i s i nt ended t o be an open, evol vi ng l anguage, of whi ch t hi s document descr i bes t he base l anguage . Var i ous ext ensi ons wi l l undoubt edl y be def i ned di f f er ent as t hey nat ur al l y ar i se i n t he cour se of i t s use by peopl e . An i mpor t ant goal i n desi gni ng t he base l anguage r easonabl y possi bl e . i s t o suppor t as much shar i ng as i s shar i ng t he cont ent of CML knowl edge f aci l i t at e Al so, t o f i l l y t r ansl at abl e t o t he knowl edge C M L i s bases, ( KI F) [ Geneser et h and Fi kes 1992] , f or m at i nt er change convent i ons est abl i shed by KI F have adopt ed we and wher ever possi bl e. 1. 1. Pat t er ns of Use A t ypi cal i mpl ement at i on suppor t i ng CML mi ght be used as f ol l ows : To pr edi ct t he behavi or of a physi cal syst em i n some domai n, knowl edge about t he physi cs of t he domai n i s capt ur ed i n a gener al pur pose domai n t heor y t hat descr i bes cl asses of r el evant obj ect s, phenomena and syst ems . The domai n t heor y of chemi cal pr ocessi ng pl ant s, f or exampl e, mi ght i ncl ude physi cal phenomena such as mass and heat f l ows, boi l i ng, evapor at i on, and condensat i on ; i t woul d al so i ncl ude chemi cal r eact i ons, t he ef f ect s of cat al yst s, and model s of component s such as r eact i on vessel s, pumps, cont r ol l er s, and f i l t er s . A domai n t heor y i n CML consi st s of a set of quant i f i ed def i ni t i ons, cal l ed model f r agment s, each of whi ch descr i bes some par t i al pi ece of t he domai n' s physi cs, such as pr ocesses ( e . g . , l i qui d f l ows) , devi ces ( e . g . , t r ansi st or s) , and obj ect s ( e . g . , cont ai ner s) . Each def i ni t i on appl i es whenever t her e exi st s a set of par t i ci pant s f or whom t he st at ed condi t i ons ar e sat i sf i ed . A speci f i c syst em or si t uat i on bei ng model ed i s cal l ed a scenar i o . A model of t he scenar i o consi st s of f r agment s t hat l ogi cal l y f ol l ow f r om t he domai n t heor y and t he scenar i o def i ni t i on . For exampl e, consi der t he si t uat i on depi ct ed i n Fi gur e 1 . A scenar i o r epr esent i ng t hi s si t uat i on woul d st at e t hat t her e i s a can cont ai ni ng some wat er pl aced over a gas heat er . I n addi t i on, t he scenar i o may al so st at e whet her or not t he gas heat er i s i ni t i al l y on, t he i ni t i al t emper at ur e and vol ume of t he wat er and so on . I n or der t o r eason about t hi s si t uat i on, t he domai n t heor y must cont ai n t he def i ni t i ons of a can, cont ai ned wat er , a gas heat er , as wel l as t he def i ni t i ons of r el evant physi cal pr ocesses such as heat f l ow and evapor at i on . The def i ni t i ons of t hese obj ect s and pr ocesses must speci f y t hei r numer i c and non- numer i c at t r i but es, such as wat er - l evel and f ame- l i t - p . The t ypes of val ues such at t r i but es t ake, f or exampl e " a numer i c, t i medependent quant i t y whose di mensi on i s l engt h" must al so be speci f i ed i n t he domai n t heor y . Once t he domai n t heor y has been const r uct ed, i t can be used t o model many di f f er ent physi cal devi ces under a var i et y of di f f er ent condi t i ons . The user speci f i es a scenar i o t hat def i nes an i ni t i al conf i gur at i on of t he devi ce, t he i ni t i al val ues of some of t he par amet er s t hat ar e r el evant t o model i ng i t , and per haps condi t i ons t hat f ur t her 1 KI F pr ovi des a st andar d encodi ng and semant i cs f or a f i r st or der l ogi c wi t h set t heor y and some mi nor ext ensi ons such as a r est r i ct ed quot e and t he abi l i t y t o r ef er t o r el at i ons di r ect l y . char act er i ze t he syst em. The CML i mpl ement at i on woul d aut omat i cal l y i dent i f y model f r agment s t hat ar e appl i cabl e i n t he scenar i o . These model f r agment s woul d be composed i nt o a si ngl e model t hat compr i ses bot h a symbol i c descr i pt i on as wel l as a set of gover ni ng equat i ons . The equat i ons may be sol ved or si mul at ed t o pr oduce a behavi or al descr i pt i on . Because t he condi t i ons under whi ch t he model f r agment s hol d ar e expl i ci t i n t he domai n t heor y, t he syst em woul d be abl e t o const r uct aut omat i cal l y addi t i onal model s t hat descr i be t he devi ce as i t moves i nt o new oper at i ng r egi ons . Fi gur e 1 : An exampl e si t uat i on wi t h a can of wat er and a heat er 1. 2. Not at i on and Synt ax The CML synt ax i s based on t he Common Li sp st andar d [ St eel e 1990] ; a sequence of char act er s i s a l egal CML expr essi on onl y i f i t i s accept abl e t o t he Common Li sp r eader wi t h st andar d set t i ngs . I n t hi s document , we wi l l adopt t he f ol l owi ng not at i onal convent i ons : Var i abl es ar e mar ked wi t h a ? pr ef i x, t o di st i ngui sh t hem f r om obj ect and r el at i on const ant s . Wher e t he synt ax al l ows f or a f i ni t e ser i es of i t ems i ndexed f r om 1 t o n, t he f i r st i t em of t he sequence i s gi ven wi t h t he subscr i pt 1 and t he r emai ni ng n1 i t ems ar e abbr evi at ed by " . . . n " . For exampl e, ( ( par t i ci pant L : t ype t 1) . . . n) i s t he not at i on f or ( ( par t i ci pant s : t ype t ype, ) . . . ( par t i ci pant n : t ype t ypezyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLK ) ) . 2. Gener al Semant i cs The goal of CML i s t o pr ovi de a common synt ax wi t h a wel l - def i ned semant i cs so t hat di f f er ent i mpl ement at i ons, wi t h di f f er ent i nt er nal r epr esent at i ons and i nf er ence pr ocedur es, wi l l be abl e t o accur at el y par se t he same domai n t heor y . The synt ax and semant i cs of CML t opl evel f or ms i s pr esent ed i n Sect i on 3 . The semant i cs of a set of CML t op - l evel f or ms i s pr ovi ded by t r ansl at i ng t hem i nt o f i r st or der l ogi c such as def i ned i n KI F, and CML i nher i t s t he l ogi c' s model - t heor et i c semant i cs . I n t hi s sect i on, we descr i be t he gener al semant i cs of r el at i ons, i ndi vi dual s and quant i t i es under l yi ng t he def i ni t i ons of t he t op- l evel f or ms . Bobr ow 13 CML suppor t s ever ywher e cont i nuous 2. 1. Quant i t i es CML i s desi gned t o model t i me- var yi ng physi cal syst ems, such as t he movement of a mechani cal devi ce or t he pr ocess of a chemi cal r eact i on . I n engi neer i ng model s, t he pr oper t i es and st at e of such syst ems ar e descr i bed by var i abl es, par amet er s, coef f i ci ent s, and const ant s . I n CML, t he t er m quant i t y encompasses t hese not i ons . A quant i t y i s ei t her a const ant or a unar y f unct i on whose ar gument i s a t i me . I n t he synt ax of CML, t i me i s l ef t as an i mpl i ci t par amet er t o t i me- dependent quant i t i es, f unct i ons, and r el at i ons . Al l non- const ant quant i t i es ar e r est r i ct ed t o have a f i ni t e number of cr i t i cal poi nt s or di scont i nuous changes over any f i ni t e i nt er val . Thi s r est r i ct i on r ul es out cer t ai n cl asses of poor l y behaved syst ems, such as osci l l at or s wi t h i nf i ni t e f r equency, t hat pose pr obl ems f or numer i c i nt egr at i on and qual i t at i ve si mul at i on t echni ques . Quant i t i es may be numer i c or non- numer i c . Nonnumer i c quant i t i es ar e si mpl y const ant s or unar y f unct i ons of t i me sat i sf yi ng t he above f i ni t e- change r equi r ement . Thei r val ues ar e unr est r i ct ed . A numer i c quant i t y i s associ at ed wi t h a si ngl e physi cal di mensi on, gi ven by t he f unct i on di mens i on. CML speci f i es a cor e set of f undament al physi cal di mensi ons : t he seven def i ned by t he Syst em I nt er nat i onal e ( mass, l engt h, t i me, char ge, t emper at ur e, amount , and l umi nosi t y) pl us a di mensi on f or di mensi onl ess number s . Real number s ar e di mensi onl ess const ant quant i t i es . CML al so pr ovi des a t op- l evel f or m t o al l ow def i ni t i on of any ot her di mensi ons . A di mensi on i s a pr oper t y t hat i s used t o di st i ngui sh i ncompat i bl e quant i t i es . Quant i t i es of t he same di mensi on can be compar ed, added, and so on . These oper at i ons ar e not def i ned f or quant i t i es of di f f er ent di mensi ons . A mat hemat i cal r el at i on hol ds on non- const ant quant i t i es i f i t hol ds on t hei r val ues at each t i me t hat t hey ar e def i ned . A numer i c t i me- dependent quant i t y i s a f unct i on of t i me whose val ues al l have t he same di mensi on . The val ue of a numer i c t i me- dependent quant i t y i s a numer i c const ant quant i t y . The magni t ude of a numer i c const ant quant i t y i s speci f i ed i n uni t s of measur e . A uni t of measur e i s i t sel f a const ant quant i t y used as a r ef er ence f or a gi ven di mensi on . For exampl e, t he met er i s a uni t of measur e f or t he l engt h di mensi on and t he second i s a uni t of measur e f or t he t i me di mensi on . The magni t ude of a const ant quant i t y depends on t he uni t i n whi ch i t i s r equest ed. The bi nar y f unct i on magni t ude maps a const ant quant i t y and a uni t of t he same di mensi on t o a r eal number . For exampl e, t he magni t ude of 12g i n gr ams i s 12 and i t s magni t ude i n ounces i s about 4 . 23 . A uni t of measur e def i nes an absol ut e scal e wi t h a 0 val ue f or quant i t i es of a par t i cul ar di mensi on . The r eal number 0 i s di mensi onl ess and t her ef or e i s di f f er ent f r om ot her quant i t i es whose magni t ude i s 0, such as 0 Newt ons or Of eet . 14 QR- 96 pi ecewi se cont i nuous quant i t i es, quant i t i es, st ep quant i t i esl , and count quant i t i esl . 2.1 .1 . Handl i ng i mpl i ci t dependence on t i me One i mpor t ant aspect of t r ansl at i ng t he semant i cs of quant i t i es i nt o l ogi c i s t he r epr esent at i on of t i me . A t i mequant i t y i s a numer i c, ever ywher e cont i nuous quant i t y whose di mensi on i s t he t i me- di mensi on . Al l t i medependent quant i t i es and r el at i ons i n CML have a t i mequant i t y as an i mpl i ci t ar gument . I n t he t r ansl at i on of CML i nt o l ogi c, t i me i s handl ed i n t hr ee st eps : 1 . Ever y t i me- dependent r el at i on i s augment ed wi t h a f i r st ar gument , whi ch must be a t i me- quant i t y . 2. Ever y t i me- dependent quant i t y, q, i s uni f or ml y t r ansl at ed wi t h t he f ol l owi ng f or m, wher e val ue- at i s a f unct i on of t wo ar gument s, a quant i t y and a t i me, and r et ur ns t he val ue of t he quant i t y at t he t i me : ( l ambda ( ?t l ) ( i f ( = ?t l ?t ) ( val ue- at q ?t i ) ) . 3 . Ever y mat hemat i cal number s ( const ant ext ended t o appl y Ever y mat hemat i cal f unct i on t hat t ypi cal l y appl i es t o quant i t i es) i s pol ymor phi cal l y t o f unct i on quant i t i es as wel l . oper at i on t hat t ypi cal l y appl i es t o number s must be ext ended si mi l ar l y . 3. Language Def i ni t i on A domai n t heor y i n CML i s a f i ni t e set ` } of t he f ol l owi ng t op- l evel f or ms : def Rel at i on f or def i ni ng l ogi cal r el at i ons . def Quant i t yFunct i on f or def i ni ng quant i t i es used i n t he domai n t heor y . def Model Fr agment f or descr i bi ng t he behavi or of model ed ent i t i es under expl i ci t l y speci f i ed condi t i ons . Model f r agment s ar e used t o descr i be phenomena t hat ar i se out of t he i nt er act i ons of a composi t e set of obj ect s ( e . g . , col l i si ons or f l ows) , or t he behavi or of a si ngl e obj ect ( e . g ., a r esi st or , pump, or val ve) . def Ent i t y f or def i ni ng pr oper t i es of per si st ent obj ect s ( e . g . , r esi st or s, cont ai ner s) . def Scenar i o f or def i ni ng i ni t i al val ue pr obl ems consi st i ng of a set of obj ect s, t hei r conf i gur at i on, and i ni t i al val ues f or t he quant i t i es t hat descr i be t hem. I n addi t i on, t he f or ms def Di mensi on, def Uni t , and def Const ant Quant i t y ar e pr ovi ded f or def i ni ng new or St ep quant i t i es ar e pi ecewi se cont i nuous quant i t i es t hat ar e const ant over ever y cont i nuous i nt er val . 2 Count quant i t i es ar e st ep quant i t i es t hat have nonnegat i ve i nt eger val ues and ar e di mensi onl ess . 3 Not e t hat such a mat hemat i cal r el at i on i s f al se when any of i t s ar gument s i s undef i ned . a Thus, i mpl ement at i ons must al l ow f or use bef or e def i ni t i on . der i ved di mensi ons, new or der i ved uni t s, and uni ver sal const ant s, r espect i vel y . The gener al synt ax of a f or m i s t he f or m i dent i f i er ( e . g ., def Quant i t yFunct i on) , f ol l owed by i t s name, f ol l owed by a ser i es of keywor d/ val ue pai r s . Some keywor ds ar e opt i onal , as i ndi cat ed by t he sur r oundi ng br acket s i n t he gr ammar ( i . e . , [ : di mensi on] ) . Wher ever a keywor d/ val ue pai r appear s, an ar bi t r ar y number of ot her , i mpl ement at i on speci f i c, keywor ds ar e al l owed . I f t he domai n t heor i es empl oyi ng such keywor ds ar e t o be por t abl e, however , t he f ol l owi ng r est r i ct i on must be sat i sf i ed . I f t he keywor ds af f ect t he behavi or al i nf er ences ent ai l ed by t he domai n t heor y, t hen t hey shoul d onl y st r engt hen or annot at e t he behavi or al i nf er ences . Thi s al l ows ot her i mpl ement at i ons t o i gnor e t he addi t i onal keywor ds and st i l l dr aw cor r ect , i f weaker concl usi ons . Domai n t heor i es t hat empl oy an ext ensi on t hat sat i sf i es t hi s cr i t er i on wi l l be shar abl e acr oss i mpl ement at i ons . The r at i onal e i s t hat var i ous gr oups wi l l want t o add f i el ds t hat f aci l i t at e expl anat i on t ool s or suppor t sof t war e engi neer i ng of l ar ge knowl edge bases ( e . g . , shor t names, aut hor s, poi nt er s t o ext ended document at i on, et c . ) . A secondar y pur pose i s t o al l ow f or l ocal ext ensi ons t o t he l anguage as t he need ar i ses, wi t hout havi ng t o change t he The i mpact such common l anguage speci f i cat i on . ext ensi ons may have on shar abi l i t y and t he semant i cs of a gi ven domai n t heor y i s not addr essed her e . I n some cases, par t i cul ar l y qual i t at i ve si mul at i on, t he added i nf or mat i on may si mpl y pr ovi de monot oni c r educt i ons i n ambi gui t y . I n ot her cases, par t i cul ar l y i n t he pr esence of a cl osed wor l d assumpt i on, t he nat ur e of t he pr edi ct ed behavi or may be f undament al l y af f ect ed . Tabl e 1 shows t he synt ax f or t he t op- l evel f or ms wi t h some exampl es . The def i ni t i ons f or t he i nt er medi at e f or ms used i n t hi s t abl e ar e gi ven i n Tabl e 2 . The f ol l owi ng sect i ons di scuss each f or m i n det ai l . 3 . 2. Quant i t y Funct i ons The def Quant i t yFunct i on f or m def i nes a f unct i on t hat maps a t upl e of obj ect s t o a quant i t y . The quant i t y i s i t sel f a f unct i on of t i me . I n addi t i on t o bei ng gl obal l y def i ned vi a def Quant i t yFunct i on, quant i t y f unct i ons may al so be def i ned wi t hi n model f r agment and ent i t y def i ni t i ons i n t he quant i t i es cl ause. The name i s a f unct i on const ant nami ng an n- ar y f unct i on t hat r et ur ns a t i me- dependent quant i t y . The xt . . . x ar e l ogi cal var i abl es . => The asent ence i s a l ogi cal sent ence t hat may ment i on t he var i abl es x i. I t may be used t o pl ace r est r i ct i ons on t he quant i t y' s val ues, or asser t t hi ngs, such as t ype i nf or mat i on, about t he xi . Di mensi on The di mens i on ex pr es s i on ( see def Di mensi on f or t he compl et e synt ax) speci f i es t he di mensi on of t he quant i t i es r et ur ned by t he quant i t y f unct i on . Non- numer i c I f non- numer i c i s t r ue, t hen t he quant i t i es r et ur ned by t he f unct i on ar e non- numer i c, ot her wi se t hey ar e numer i c . Pi ecewi se- cont i nuous I f pi ecewi se- cont i nuous i s t r ue, t hen t he quant i t i es r et ur ned by t he f unct i on ar e pi ecewi se- cont i nuous . St ep- quant i t y I f st ep- quant i t y i s t r ue, t hen t he quant i t i es r et ur ned by t he f unct i on ar e st ep- quant i t i es . Count - quant i t y I f count - quant i t y i s t r ue, t hen t he quant i t i es r et ur ned by t he f unct i on ar e di mensi onl ess count - quant i t i es . 3. 3. Model Fr agment s and Ent i t i es Thi s sect i on def i nes t he synt ax and semant i cs f or t he key CML f or ms def Model Fr agment and i t s r est r i ct ed ver si on def Ent i t y . The def Model Fr agment f or m def i nes a cl ass of 3 . 1 Rel at i ons and Funct i ons phenomena, whi ch ar e descr i bed by a set of obj ect s I n t he def Rel at i on f or m, t he symbol Name i s a gl obal i nvol ved, st at i c at t r i but es and t i me- dependent quant i t i es . I t r el at i on const ant nami ng a r el at i on of ar i t y n ; t he xi ar e al so def i nes consequences t hat hol d onl y when an i nst ance l ogi cal var i abl es, one f or each ar gument of Name. Al l uses of t he cl ass i s act i ve . The def Model Fr agment f or m may of Name i n t he domai n t heor y shoul d be consi st ent wi t h t he def i ne condi t i ons suf f i ci ent t o i mpl y t he exi st ence of an i nst ance, i n addi t i on t o t he necessar y consequences t her eof . speci f i ed const r ai nt s . The def Ent i t y f or m i s a r est r i ct ed ver si on of => The asent ence i s a l ogi cal sent ence t hat may ment i on def Model Fr agment t hat i s used f or def i ni ng pr oper t i es of t he var i abl es xi . I f pr esent , t he sent ence ( => ( Name a per si st ent obj ect t hat ar e al ways t r ue . The def Ent i t y xi . . . xn) asent ence ) i s t r ue . f or m def i nes onl y necessar y consequences of an obj ect <_> The asent ence i s a l ogi cal sent ence t hat may bei ng an i nst ance of t he cl ass, not condi t i ons suf f i ci ent t o ment i on t he var i abl es xi . I f pr esent , t he sent ence i mpl y t he exi st ence of an i nst ance . ( <=> ( Name . X( . . . xn) asent ence ) i s t r ue . The def Ent i t y and def Model Fr agment f or ms have been Funct i on I f f unct i on i s t r ue, t hen t he r el at i on Name i s a desi gned t o suppor t an obj ect - or i ent ed st yl e of def i ni ng f unct i on . That i s, t he f i r st n- 1 ar gument s t o Name domai n t heor i es . Each f or m def i nes a cl ass of obj ect s uni quel y det er mi nes t he nt h and ( Name xt . . . x zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA _1) speci f i ed by set s of st at i c at t r i but es and t i me dependent may be used as a t er m denot i ng xn. quant i t i es . These at t r i but es and quant i t i es ar e ef f ect i vel y t i me- dependent I f t i me- dependent i s t r ue, t hen Name sl ot s def i ned on i nst ances of t he cl ass . Fur t her mor e, t hese i s a t i me- dependent r el at i on and appear ances of Name cl asses may be ar r anged i n a hi er ar chy vi a t he subcl ass- of i n a CML f or m must be handl ed speci al l y . cl ause . Bobr ow 15 Synt ax Ex ampl es ( def Rel at i on Name ( XI . . . xn) [ : document at i on st r i ng ] ( def Rel at i on cont ent s ( ?x ?y) : => ( and ( cont ai ner ?x) ( cont ai ned- st uf f ?y) ) : <=> ( cont ai ned- i n ?y ?x) ) ( def Rel at i on f ahr enhei t ( ?t ?f ) : <=> ( == ?f ( : => asent ence ] ( : <_> asent ence ] [ : f unct i on bool ean ] ( - ( magni t ude ?t r anki ne) 459 . 7) ) : f unct i on t r ue) ( def Rel at i on above ( ?x ?y) : t i me- dependent t r ue ( def Quant i t yFunct i on mass ( ?x) : => ( physi cal - obj ect ?x) : di mensi on mass- di mensi on) ( def Quant i t yFunct i on densi t y ( ?x) : => ( physi cal - obj ect ?x) : di mensi on ( / mass- di mensi on ( expt l engt h- di mensi on 3) ) ) [ di me- dependent bool ean ] ) ( def Quant i t yFunct i on Name ( xI . . . xn) [ : document at i on st r i ng ] [ : => asent ence ] [ : di mensi on di mensi on expr essi on ] ( : pi ecewi se- cont i nuous bool ean ] [ : st ep- quant i t y bool ean ] [ : count - quant i t y l ean ] [ : non- numer i c bool ean ] 1 ( def Model Fr agment Name [ : document at i on st r i ng ] [ : subcl ass- of l sl . . . s] [ : par(tpi ci pant sanq ( ar t i c ant [ : t ype W e. ] ) . . . ) ] e p [ : condi t i ons condi t i ons ] [ : quant i t i es ( ( quant i t y I keywor ds 1) . . . q) ] [ : at t r i but es ( ( at t r i ut [ ape ttr el ] ) . . . [ : consequences consequences ] ) a] ( def Ent i t y Name [ : document at i on st r i ng ] [ : subcl ass- of cl ass ) . . . s] [ : quant i t i es ( ( uant i l keywor ds 1) . . . q) ] [ : at t r i but es ( ( at t r i but e) [ : t ype at t r el ] ) . . . a) ] [ : consequences consequences ] ) ( def Model Fr agment Cont ai ned- St uf f : subcl ass- of ( physi cal - obj ect ) : par t i ci pant s ( ( sub : t ype subst ance) ( ct nr : t ype f l ui d- cont ai ner ) ) : condi t i ons ( ( > ( amount - of - i n sub ct nr ) ( * 0 gr ams) ) ) : quant i t i es ( ( pr essur e : di mensi on pr essur e- di mensi on) ( mass : di mensi on mass- di mensi on) ) : consequences ( ( == mass amount - of - i n sub ct nr ) ( def Ent i t y Can : subcl ass- of ( physi cal - obj ect Cont ai ner ) : quant i t i es ( ( hei ght : di mensi on l engt h- di mensi on) ( di amet er : di mensi on l engt h- di mensi on) ( vol ume : di mensi on vol ume- di mensi on) ) : consequences ( ( == ( vol ume : sel f ) ( * PI ( expt ( / di amet er 2) 2) hei ght ) ) ) ) Tabl e 1 : Synt ax and exampl es of t op- l evel f or ms Synt ax Ex am l es ( def i mensi on Name : document at i on " i n [ : = di mensi on expr essi on ] ~ ( def Di mensi on ener gy- di mensi on ( * mass- di mensi on l engt h- di mensi on ( expt t i me- di mensi on - 2) ) ) ( def Uni C i nch ( def Uni t Name : _ ( * 2 . 54 ( * met er 0 . 01) ) ) [ : document at i on st r i ng ] [ : = quant i t y exnr essi on ] [ : di mensi on di mensi on expr essi on ] ) ( def Const ant Quant i t y Pi ( def Const ant Quant i t y Name : = ( acos - 1) ) [ : document at i on t r i n ] ( def Const ant Quant i t y Bol t zman- Const ant [ : =, ?ent i t y ex . zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA " ' on ] : = ( * 1 . 380658 ( / Joul e Kel vi n) ) ) [ : di mensi on di mensi on expr essi on ] ) ( def Scenar i o wat er - heat i ng- exampl e : document at i on " A can cont ai ni ng wat er i s pl aced di r ect l y above a gas- heat er , whi ch i s i ni t i al l y l i t . " : I ndi vi dual s ( ( C : t ype Can) ( H : t ype Gas- heat er ) ( W: t ype Cont ai ned- wat er ) ) : i ni t i al l y ( ( > ( amount - of - i n WC) ( * 0 gr ams) ) ) : t hr oughout ( ( _ ( hei ght A) ( * 0 . 2 met er ) ) ( _ ( di amet er A) ( * 0. 15 met er ) ) ( f l ame- l i t - p H t r ue) ( di r ect l y- above C H ( def Scenar i o Name [ : document at i on st r i ng ] [ : i ndi vi dual s ( ( i ndi vi dual [ : t ype t yke] ) * ) ] [ : i ni t i al l y asent ences ] [ : t hr oughout asent ences ] Tabl e 1 : cont . Addi t i onal Synt ax di mensi on expr essi on di mensi on I ( * di mensi on expr essi on +) I ( expt di mensi on expr essi on number ) I ( l di mensi on expr essi on di mensi on expr essi on) quant i t y expr essi on uni t I quant i t y I ( mat hon quant i t y expr essi on +) asent ence : : = ( and l i t er al * ) l i t er al : : = ( r el const t er m* ) I - ( ' not ( r el const t er m * ) ) Tabl e 2 : Some Addi t i onal Synt ax Name The name of t he model f r agment or ent i t y, name , i s a r el at i on const ant nami ng t he cl ass of i nst ances . Subcl ass- of The subcl ass- of cl ause al l ows a hi er ar chy t o be def i ned . Each cl ass i s t he name of a model f r agment or ent i t y def i ni t i on . An i nst ance of name i s al so an i nst ance of each super cl ass . As a consequence, al l of t he par t i ci pant , quant i t y, and at t r i but e f unct i ons def i ned f or each st eer ar e al so def i ned f or name . Par t i ci pant s The par t i ci pant s cl ause i dent i f i es t he obj ect s t hat par t i ci pat e i n t he model f r agment i nst ance . Each par t i ci pant i s a f unct i on const ant t hat names a unar y f unct i on whi ch may be appl i ed t o an i nst ance t o access t he cor r espondi ng par t i ci pant ; each I f i s a r el at i on const ant t hat names a cl ass ( unar y r el at i on) of whi ch t he par t i ci pant i s an i nst ance. Condi t i ons The condi t i ons cl ause speci f i es t he condi t i ons under whi ch an i nst ance of a model f r agment i s act i ve . I f t he condi t i ons hol d over t he speci f i ed par t i ci pant s, t hen an i nst ance of t he model f r agment exi st s wi t h t he speci f i ed quant i t i es and at t r i but es . Condi t i ons i s an i mpl i ci t conj unct i on of l i t er al s . The bi nar y r el at i ons same and di f f er ent may be used i n t he condi t i ons t o st at e t hat t wo par t i ci pant s ar e t he same or di f f er ent f r om each ot her . At t r i but es The at t r i but es cl ause may be used t o def i ne st at i c at t r i but es of an i nst ance . Each at t r i but e i s a symbol nami ng a f unct i on t hat i s t ot al l y def i ned f or i nst ances of name . The at t r i but es ar e pol ymor phi c, t hat i s, an at t r i but e of t he same name may be def i ned f or anot her unr el at ed f or m wi t h a di f f er ent t ype . Bobr ow 17 Quant i t i es The quant i t i es cl ause may be used t o l ocal l y def i ne quant i t i es t hat descr i be an i nst ance . The keywor ds ar e t he keywor d opt i ons def i ned f or def Quant i t yFunct i on, except t hat => i s not al l owed . Such i mpl i cat i ons may be pl aced i n t he consequences cl ause . The quant i t i es ar e pol ymor phi c, t hat i s, a quant i t y of t he same name may be def i ned f or anot her unr el at ed model f r agment , but have di f f er ent pr oper t i es . Nonet hel ess, quant i t y f unct i ons def i ned i n a quant i t i es cl ause must be consi st ent wi t h any of t he const r ai nt s i mposed by a def Quant i t yFunct i on def i ni t i on of t he same name . For exampl e, ent i t y def i ni t i ons Li qui d and Sand can bot h def i ne a quant i t y cal l ed Amount - of wi t h di mensi ons vol umedi mensi on and mass- di mensi on, r espect i vel y . However , i f t her e i s a separ at e gl obal def i ni t i on of Amount - of usi ng t he def Quant i t yFunct i on f or m, whi ch speci f i es t he di mensi on t o be vol umedi mensi on, t he quant i t y def i ni t i on of Amount - of i n Sand i s di sal l owed si nce i t i s i nconsi st ent wi t h t he gl obal def i ni t i on Consequences The consequences cl ause hol ds whenever an i nst ance i s act i ve . The consequences i s an i mpl i ci t conj unct i on of l i t er al s . The pr i mar y r ol e of t he consequences i s t o est abl i sh equat i ons t hat hel p t o def i ne t he behavi or of t he par t i ci pant s . I n addi t i on t o equat i ons, ot her l ogi cal r el at i ons may al so be asser t ed . 3 . 3 . 1 Synt act i c Sugar I n or der t o al l ow f or mor e conci se and r eadabl e def i ni t i ons, t he def Ent i t y and def Model Fr agment f or ms pr ovi de some synt act i c sugar . Sel f The symbol sel f may be used t o r ef er t o t he cur r ent i nst ance . Not e t hat i t may not be used i n t he condi t i ons cl ause of a model - f r agment def i ni t i on wi t h no super cl asses, as t hi s woul d pl ace i t out si de of t he scope wi t hi n whi ch t he i nst ance exi st s . Nam The user pr ovi ded symbol f or t he name of a model f r agment or ent i t y may be used i nst ead of sel f and i s compl et el y equi val ent . uant ' The symbol f or any nt i may be used t o r ef er t o t he appr opr i at e quant i t y wi t hi n t he consequences cl ause . Thi s i s compl et el y equi val ent t o t he mor e ver bose f or m ( uant i sel f ) , whi ch may al so be used . At t r i but e The symbol f or any at t r i but e may be used t o r ef er t o t he appr opr i at e at t r i but e wi t hi n t he consequences cl ause . Thi s i s compl et el y equi val ent t o t he mor e ver bose f or m ( at t r i but e sel f ) , whi ch may al so be used . Par t i ci pant I n a model f r agment def i ni t i on, t he user pr ovi ded symbol f or each par t i ci pant may be used t o r ef er t o t hat par t i ci pant . Out si de of t he condi t i ons , t he mor e ver bose f or m ( par t i ci pant sel f ) may al so be used . 18 QR- 96 3. 4. Semant i cs The f ul l semant i cs of t he CML f or ms ar e def i ned i n e pr ovi de an [ Fal kenhai ner , Far quhar et al . 1994] . W i nf or mal account of t hem her e, st ar t i ng wi t h t he si mpl er def Ent i t y f or m. The def Ent i t y f or m def i nes a cl ass of obj ect s . I f any obj ect i s a member of t he cl ass, t hen t he quant i t i es and at t r i but es def i ned i n t he f or m appl y t o i t , and t he consequences ar e t r ue f or t hem. Ent i t i es may be st r uct ur ed i nt o a hi er ar chy usi ng t he subcl ass- of cl ause ; al l quant i t i es, at t r i but es, and consequences t hat appl y t o a super cl ass al so appl y t o t he subcl ass . That i s, al l i nher i t ance i s monot oni c - t her e i s no way t o over - r i de def aul t val ues t hat ar e i nher i t ed . A def Model Fr agment f or m wi t hout any super cl asses i s al so si mpl e t o under st and . I f t he par t i ci pant s exi st and sat i sf y t he t i me- i ndependent condi t i ons, t hen an i nst ance of t he model f r agment exi st s . At any moment t hat t he t i medependent condi t i ons hol d, t he model i nst ance i s act i ve and t he consequences hol d . I f t he t i me- dependent condi t i ons do not hol d, t he consequences ar e not i mpl i ed . A def Model Fr agment f or m wi t hout super cl asses def i nes suf f i ci ent condi t i ons f or an i nst ance t o exi st . A def Model Fr agment f or m wi t h super cl asses i s somewhat mor e compl ex . I f t her e i s some obj ect t hat i s an i nst ance of al l of t he def i ni t i on' s super cl asses and t he def i ni t i on' s par t i ci pant s exi st and i t s t i me- i ndependent condi t i ons hol d, t hen t hat obj ect i s al so an i nst ance of t he def i ni t i on . Act i vi t y and consequences ar e handl ed j ust as A f or model f r agment s wi t hout super cl asses . def Model Fr agment f or m wi t h super cl asses def i nes necessar y condi t i ons f or an obj ect t o be an i nst ance . The pr evi ous par agr aphs descr i be CML as i t has been def i ned and i s consi st ent wi t h i t s pr edecessor l anguages . Thi s scheme i s ext r emel y usef ul f or pr ovi di ng addi t i onal i nf or mat i on about concr et e physi cal phenomena i n a l i br ar y . For i nst ance, a l i br ar y mi ght i ncl ude one def i ni t i on f or f l ui d- f l ow t hat hel d whenever t her e wer e t wo cont ai ner s connect ed by a por t . Subcl asses of f l ui d- f l ow mi ght i ncl ude l ami nar f l ow, t ur bul ent f l ow, and so on . Thi s scheme, however , has an i mpor t ant shor t comi ng t hat i t does not al l ow abst r act model f r agment s t o be def i ned . To under st and t hi s di f f i cul t y, consi der an exampl e of a l i br ar y of chemi cal r eact i ons . Such a l i br ar y mi ght i ncl ude model f r agment s f or bi nar y chemi cal r eact i ons, such as oxi dat i on, bet ween subst ances . Ther e ar e a f ew t hi ngs t hat can be sai d about al l bi nar y chemi cal r eact i ons such as " t her e ar e t wo di st i nct r eact ant s" . Thus, Bi nar yr eact i on, t he cl ass of al l bi nar y r eact i ons, may have t wo par t i ci pant s, React ant - 1 and React ant - 2 and a condi t i on t hat t hey ar e di st i nct . I t i s not nat ur al , however , t o speci f y f ur t her e condi t i ons under whi ch a gener i c bi nar y r eact i on occur s . Thi s i s much easi er t o say about a speci f i c chemi cal r eact i on . Oxi dat i on, a subcl ass of Bi nar yr eact i on, may have t he condi t i on t hat React ant - 1 i s an oxi dant , and React ant - 1 and React ant - 2 ar e i n cont act . Gi ven a si t uat i on i nvol vi ng t hr ee chemi cal subst ances, A, B, and C, such t hat onl y A i s an oxi dant , and A and B ar e i n cont act wi t h each ot her , one woul d expect exi st ance of onl y one bi nar y chemi cal r eact i on, whi ch i s al so an oxi dat i on r eact i on, t o be i nf er r ed . However , f r om t he semant i cs of t he model f r agment s descr i bed above, t her e woul d be si x i nst ances of abst r act bi nar y r eact i ons, one f or each possi bl e combi nar i on of A, B, and C. Al t hough t he cur r ent i nt er pr et at i on i s coher ent and l ogi cal l y consi st ent , i t poses a pr act i cal pr obl em t hat i t enabl es a l ar ge number of uni nt er est i ng model f r agment i nst ances t o be i nf er r ed . We ar e cur r ent l y consi der i ng an al t er nat e scheme t hat suppor t s abst r act model f r agment s wi t h or wi t hout super cl asses . 3. 5 . Di mensi ons, Uni t s, and Const ant s The vocabul ar y used t o descr i be quant i t i es var i es f r om one domai n t o anot her . For t hi s r eason, i t i s essent i al t o be abl e t o def i ne new di mensi ons and uni t s . Of t en, t hese wi l l be der i ved f r om t he base set of SI di mensi ons and uni t s ( e . g . , an el ect r o- magnet i c domai n t heor y mi ght def i ne a di mensi on f or magnet i c- f l ux and i t s SI der i ved uni t , t he Weber ) . I f t he new di mensi on i s r educi bl e t o ot her di mensi ons, t he di mensi on expr essi on must be pr ovi ded . The t op- l evel f or ms def Di mensi on and def Uni t pr ovi de t hi s f aci l i t y . The f or m def Const ant Quant i t y i s al so pr ovi ded f or def i ni ng gl obal named const ant s . Ever y CML i mpl ement at i on shoul d have a bui l t - i n l i br ar y of def i ni t i ons f or t he basi c SI di mensi ons and uni t s : t i me- di mensi on, l engt h- di mensi on, t emper at ur e di mensi on, mass- di mensi on, l umi nosi t y- di mensi on, char ge- di mensi on, amount - di mensi on ( usual l y measur ed i n mol es) , and di mensi onl ess . The l i br ar y shoul d al so i ncl ude t he def i ni t i ons f or t he common SI uni t s i ncl udi ng t he base uni t s, met er , ki l ogr am, second, amper e, Kel vi n, mol e, as wel l as t he der i ved uni t s Her t z, Newt on, Pascal , Joul e, Wat t , Coul omb, vol t , Far ad, ohm, Si emens, Weber , Tesl a, and Henr y . Except f or di mensi onl ess, di mensi ons ar e, by convent i on, named by af f i xi ng - di mensi on t o t he st andar d Engl i sh wor d . Thi s makes i t st r ai ght f or war d t o di st i ngui sh bet ween di mensi ons and si mi l ar l y named quant i t y f unct i ons . I f a def Uni t l acks t he = ar gument , t hen i t def i nes a f undament al uni t . A f undament al uni t def i ni t i on must have ei t her a di mensi on ( as i n t he met er exampl e) or a uant i eMr essi on , i n whi ch case t he di mensi on i s i nf er r ed f r om t hat of t he guant i t y expr essi on . I f t he expr essi on i s compl ex, i t may be mor e i nf or mat i ve t o pr ovi de t he di mensi on expl i ci t l y . The def Const ant Quant i t y f or m i s i dent i cal t o def Uni t , except t hat = must be pr ovi ded . 3. 6 . I ndi vi dual s The i ndi vi dual s cl ause speci f i es a set of named obj ect s t hat ar e assumed t o exi st i ni t i al l y . The domai n t heor y may i mpl y t he exi st ence of ot her i ndi vi dual s . The i ndi vi dual i s an obj ect const ant denot i ng an obj ect , not a r el at i on or f unct i on . I ni t i al l y The i ni t i al l y cl ause speci f i es condi t i ons t hat i ni t i al l y hol d i n t he scenar i o . I t i s an i mpl i ci t conj unct i on of l i t er al s . I t may speci f y r el at i ons bet ween quant i t i es, t i me- dependent r el at i ons, and per haps an assi gnment f or t he quant i t y t i me . Thr oughout The t hr oughout cl ause speci f i es condi t i ons t hat hol d t hr oughout t he scenar i o . I t i s a l i st of l i t er al s under an i mpl i ci t conj unct i on . Scenar i os The def Scenar i o f or m i s used f or set t i ng up pr obl ems i n whi ch t he behavi or of a syst em i s t o be pr edi ct ed f r om a set of i ni t i al condi t i ons . 4. Equat i ons CML pr ovi des a base set of mat hemat i cal f unct i ons and oper at or s t hat can be used i n t he consequences and condi t i ons of model f r agment and ent i t y def i ni t i ons as wel l as i ni t i al l y and t hr oughout cl auses of scenar i o def i ni t i ons . The mat hemat i cal f unct i ons and r el at i ons can be appl i ed t o t i me dependent var i abl es as wel l as t i me i ndependent ones . The r el at i ons on quant i t i es i ncl uded : <, <=, >=, >, ==, posi t i ve, negat i ve, zer o, i nt eger , odd, even . CML i ncl udes mat hemat i cal f unct i ons as def i ned i n t he Common Li sp st andar d ( +, - , * , / , abs, acos, acosh, asi n, asi nh, at an, at anh, cos, cosh, exp, expt , l og, max, mi n, mod, si gnum, si n, si nh, sqr t , t an, t anh) ; t he t i me der i vat i ve d/ dt ; t he qual i t at i ve r el at i ons M+, M- M+O, M- 0, Q= ; and t he composabl e equat i ons C+, C- , Qpr op+, Qpr op+O, Qpr op- 0, I +, I . The f ul l semant i cs of t hese f unct i ons and r el at i ons ar e def i ned i n [ Fal kenhai ner , Far quhar et al . 1994] . Tabl e 3 summar i zes t he der i vat i ve, qual i t at i ve const r ai nt s, and composabl e equat i ons . 5. Concl usi on I n t hi s paper , we have pr esent ed CML, t he knowl edge r epr esent at i on l anguage f or t he composi t i onal model i ng par adi gm. The mai n advant age of composi t i onal model i ng i s i t s modul ar i t y . Wr i t i ng model f r agment s, each descr i bi ng a si ngl e phenomenon, i s a much easi er t ask t han composi ng a compl et e model f or ever y possi bl e syst em and quer y . Even so, const r uct i ng such a domai n t heor y i s a subst ant i al under t aki ng . Thus, t he maj or goal of CML i s t o suppor t t he i nt er change and r euse of such t heor i es . To enabl e shar i ng of knowl edge st at ed i n CML, t he semant i cs of CML i s f ul l y def i ned i n KI F. The l anguage pr esent ed her e i s t he base l anguage of CML, whi ch al l t he i mpl ement at i ons of model i ng syst ems usi ng CML ar e expect ed t o suppor t . Var i ous ext ensi ons t o t he base l anguage wi l l undoubt edl y be needed t o accommodat e domai n- speci f i c r epr esent at i onal needs . Some of such ext ensi ons t hat we ar e consi der i ng ar e t he f ol l owi ng : Bobr ow 19 For ms Exampl es Meani ng ( d/ dt x) d/ dt x ( M+ y x) M- x ( M+0 y x) M- 0 x ( Q= x y) ( > ( d/ dt ( l ocat i on m) 0) d/ dt os m vel m ( M+ ( l evel w) ( pr essur e w) ) M- vol w ( space c ( M+0 ( l evel w) ( pr essur e w ( C+ y x) ( C- y x) ( C+ ( net c) ( i n 1 c) ) ( C- ( net c) ( out c) ) ( Qpr op+ y x) ( Qpr op- y x) ( Qpr op+ ( si ze ( dr ai n c) ) ( out c) ) ( Qpr op+0 y x) ( Qpr op- 0 y x) ( Qpr op+0 ( cur r ent w) ( conduct ance w) ) ( C* y x) x C/ ( cor r espondence y v x1 v I . . . x n v n ) ( C* ( magni f i cat i on scope) ( magni f i cat i on l ens ( cor r espondence ( l evel c) t op ( vol ume c) f ul l ) The t i me der i vat i ve of x . The t i me der i vat i ve of x i s The quant i t y y i s a i n( de) cr easi ng monot oni c f unct i on of x . Y i s a monot oni c i n( de) cr easi ng f unct i on of x, but asses t hr ough t he or i gi n . X and y and t hei r der i vat i ves have t he same si gn . A somewhat weaker st at ement t han M+O. Composabl e addi t i on and subt r act i on . X i n( de) cr ement s y . Not e t hat t hese can be mi xed wi t h ro s. Composabl e qual i t at i ve pr opor t i onal i t i es . Not e t hat t hese can be mi xed wi t h C+, C- . Qpr op+ i s equi val ent t o a C+ chai ned t o an M+ . Si mi l ar t o Qpr op, but i f al l of t he composed equat i ons on y ar e C+, C, Qpr op+0, Qpr op- 0, t hen =0 when t he x' s ar e 0. Si mi l ar t o C+, C- , but x mul t i pl i es ( di vi des) i nt o y . I f t her e i s a f unct i on f such t hat y=f ( x I . . . x n) t hen when xi =vi y=v . The xi ar e quant i t y f unct i ons, and t he vi ar e val ues. Tabl e 3 : Qual i t at i ve Rel at i ons and Composi t i onal Equat i ons Ext ensi on t o t he r epr esent at i on of quant i t i es t o i ncl ude vect or s and mat r i ces . Ext ensi on t o t he not i on of mat hemat i cal f unct i ons t o i ncl ude mat hemat i cal r el at i ons r epr esent ed by ar bi t r ar y ext er nal dat a st r uct ur es such as dat abases and f or ei gn pr ocedur es . Expansi on of t he mat hemat i cal vocabul ar y t o i ncl ude par t i al di f f er ent i al equat i ons . Gener al i zat i on of t he model f r agment r epr esent at i on t o r epr esent non- numer i c and di scont i nuous changes . Repr esent at i on of pr ocedur al speci f i cat i ons such as pr escr i bed oper at or pr ocedur es . The det ai l ed speci f i cat i on of t he synt ax and semant i cs of t he l anguage al ong wi t h di scussi ons of desi gn r at i onal e and i mpl ement at i on consi der at i ons can be f ound i n [ Fal kenhai ner , Far quhar et al . 1994] . To f aci l i t at e const r uct i on of domai n t heor i es i n CML, we have i mpl ement ed a web- based CML edi t or f or br owsi ng, cr eat i ng and edi t i ng CML domai n t heor i es . The edi t or , whi ch i s publ i cl y accessi bl e on t he W W W , pr ovi des a f ul l , di st r i but ed col l abor at i ve edi t i ng envi r onment . W e ar e al so i n t he pr ocess of i mpl ement i ng a model f or mul at i on and si mul at i on syst em, whi ch wi l l make use of t he CML l i br ar y . The syst em wi l l be al so publ i cl y accessi bl e as a ser vi ce on t he W W W . W e hope t hat t he avai l abi l i t y of t hese ser vi ces wi l l f aci l i t at e devel opment of a si gni f i cant publ i c l i br ar y of domai n t heor i es by t hi s r esear ch communi t y and t hat i t wi l l spur f ur t her r esear ch and devel opment i n t he f i el d . 20 QR- 96 Acknowl edgement The aut hor s t hank Vi j ay Sar aswat f or usef ul comment s on t he l anguage speci f i cat i ons . The r esear ch by t he aut hor s ar e suppor t ed i n par t by t he f ol l owi ng agenci es : For bus by t he Of f i ce of Naval Resear ch, Far quhar , Fi kes, Gr uber , and I wasaki by ARPA and NASA/ ARC under cont r act NAG2581 ( ARPA or der 8607) , and Kui per s by NSF gr ant s I RI 9216584 and I RI - 9504138 and by NASA gr ant s NCC 2760 and NAG2- 994 . Ref er ences Cr awf or d, J . , Far quhar , A. , and Kui per s, B. ( 1990) . PC: A Compi l er f r om Physi cal Model s i nt o Qual i t at i ve Di f f er ent i al Equat i ons . The Ei ght h Nat i onal Conf er ence on Ar t i f i ci al I nt el l i gence, Fal kenhai ner , B . , For bus, K . ( 1991) . " Composi t i onal model i ng : f i ndi ng t he r i ght model f or t he j ob . " Ar t i f i ci al I nt el l i gence 51( 1- 3) : Fal kenhai ner , B. , Far quhar , A. , Bobr ow, D. , Fi kes, R. , For bus, K. , et al . ( 1994) . CML : A Composi t i onal Techni cal r epor t KSL- 94- 16, Model i ng Language . 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