cs - ANAYSS N TRANSFORMATONA GRAMMAR BY JOYCE FREDMAN AND THEODORE S. MARTNER This research was suppored in par by he Unied Saes Air Force E!ecronic Sysems Division, under Conrac F96828-C-0035. STANFORD UNVERSTYCOMPUTER SCENCEDEPARTMENT COMPUTATONAbNGUSTCS PROJECT AUGUST 968
-i, _, ;: F AF - 34 CS - ANAYSS N TRANSFORMATONA GRAMMAR r e Joyce Friedman* and Theodore S. Marner by * Presen address: Compuer and Communicaion Sciences Deparmen, Universiy of Michigan, Ann Arbor, Michigan. This research was suppored in par by he Unied Saes Air Force Elecronic Sysems Division, under Conrac F96828-C-0035, a Sanford Universiy.
5 _ :, m ABSTRACT n generaing senences by means of a ransformaional grammar, i is necessary o analyze rees, esing for he presence or absence.. of various srucures. This analysis occurs a wo sages in he generaion process -- during inserion of lexical iems (more precisely, in esing conexual feaures), and during he ransformaion process, when individual ransformaions are being esed for applicabiliy. n his paper we describe a formal sysem for he definiion of ree srucure of senences. The sysem consiss of a formal language for parial or complee definiion of he ree srucure of a senence, --, plus an algorihm for comparison of such a definiion wih a ree. represens a significan generalizaion of Chomsky's noion of "proper analysis", and is flexible enough o be used wihin any ransformaional grammar which we have seen. r -w
ix.,. * 7, ṟ i r-- - TABE OF CONTENTS nroducion... Underlying Conceps... -;... Srucural Descripion... 3 Analyzabiliy... 5 Resricions................,........ 8 Analysis Algorihm...................... 0 Srucural Change...................... 3 Comparison Wih Oher Noaions... 5 Fuure Direcions... 6 i i -
- İ. f nroducion The noion of analysis described here is an ougrowh of a projec which had as is primary goal he biing of a compuer sysem o aid ransformaional grammarians [30..Early in his projec we realized ha cerain aspecs of ransformaional grammar heory had never received he sor of formalizaion necessary for compuer applicaions; his paper is essenially a descripion of our aemp o correc his siuaion in one such area. should be noed ha rigorous formalizaion is no simply an i b -ad hoc - maer in order o be able o use he compuer; quesions of he relaive simpliciy of grammars are realisically answerable only when --. he grammars have been placed in a precise sysem of noaion, and, more imporan, a ransformaional generaive grammar canno be said o have succeeded in defining a language unless i is possible o generae senences by using he grammar wihou any appeal o inuiion. n he firs par of his paper we.,@,efine our noion of a srucural descripion of a senence, and define he condiions under which a senence may be said o be analyzable as such a srucural descripion; discuss our implemenaion of hese conceps, laer we in paricular he algorihm which deermines in wha order he various possible analyses of a senence are produced. Underlying conceps We begin he discussion of srucural descripion by explaining some underlying conceps and giving definiions of cerain key erms. This is in line wih one of he major goals of our projec, namely uniformiy, clariy, and precision of expression. A ransformaional- generaive grammar is a device for generaing \
senences in a language. Noe ha his is a characerizaion raher han a definiion; he only definiion of ransformaional grammar given in his paper will be in erms of is hree componens: phrase srucure, ransformaions, and lexicon... The phrase srucure componen is a phrase srucure grammar. One may commence wih a senence symbol (he leer S) and expand i by means of he grammar ino a base ree which has he node labeled S as is op (roo) node. n his ree, each nonerminal node (node wih branches below i) corresponds o some phrase-srucure rule in he sense ha is label is he lefhand side of he rule and he labels of he nodes immediaely below i are he symbols of he righhand side of he rule in he same lef-o-righ order. The labels of erminal nodes of he ree are erminal symbols of he grammar; he lis of labels of erminal nodes, aken from lef o righ, is he erminal sring of he ree. Nonerminal nodes of he ree are labeled wih nonerminal symbols of he grammar. The nodes immediaely beneah a given node are is daughers, and he given node immediaely dominaes hem; he daughers of is daughers, ec. a node dominaes is daughers, A ree node may have an associaed complex symbol (see below); his complex symbol is no a daugher of he node, bu is raher an adjunc o he label of he node. This ree is : also known as he consiuen srucure of he senence. The ransformaional componen conains ransformaions and a saemen of he order in which hese ransformaions are o be applied. A ransformaion consiss primarily of a srucural descripion and a srucural change; i essenially makes he saemen: "f he ree currenly has his (given) srucure, hen change is srucure in his manner." 2
The lexical componen conains a lis of vocabulary words, each of which has an associaed complex symbol. A complex symbol is a. collecion of feaure specificaions which describe boh he inheren characerisics of he word (e.ga., Noun or Verb, +HUMAN or -HUMAN (or neiher), ec.) (inheren feaures), and he sor of senence environmen ino which i can be insered (conexual feaures). exical inserion aaches vocabulary words o he erminal nodes of. a ree in posiions where all of heir feaure specificaions are me. insers heir complex symbols ino he ree a he same ime. Since boh he conexual feaure and he srucural descripion of a ransformaion ask he quesion "Does he ree we are working wih have his srucure?", hey can be reaed in he same manner for mos purposes. We will say in boh cases ha he senence ree is analyzable as he srucural descripion if he answer o he above quesion is affirmaiv. The process of answering he quesion is analysis; a maching of nodes in he senence ree wih heir counerpars in he srucural descripion will be an analysis of he senence ree as he srucural descripion. Srucural descripion We have defined he formas for wriing ransformaional grammars. in our sysem in a modificaion of he Backus-Naur form (BNF) used o de- fine compuer programming languages [5]. n BNF, he definiion of a srucural descripion and a conexual feaure descripion are: srucural descripion ::= srucural analysis op[,where resricion]. conexual feaure descripion ::= ( srucure op[,whfxe resricion] > srucural analysis ::= lis[ erm ] : erm: = op[ ineger ] srucure or op[ ineger ] choice or skip * 3
srucure ::= elemen op [ complex symbol ] op[ op[ 7 ] op [ / ] (srucural analysis) ] elemen ::= node or * or choice ::= skip ::= $ ( clis[ srucural analysis > This definiion can be hough of as a procedure for checking wheher a sring of characers is one of he underlined iems. The :- :- may be read "is a". The operaor op[ ] means ha whaever is beween he brackes may or may no be presen. The noaion A or B is obvious. The operaor lis[ ] means ha one or more of whaever is beween he -=. brackes should be presen; for example, lis[a or B ] could be A or B or A A or A B or A B B A A ec. The operaor clis [ resembles lis[ ], bu separae occurrences of whaever is beween he brackes are separaed by commas; for example, clis[ A or B ] could be A or B or A,A or A,B or A,A,B,A,B ec. All oher symbols which are no underlined mean hemselves. There are four iems lef undefined by he above; hese are resricion, which will be discussed. laer, complex symbol, which is defined in [4], ineger, which is any posiive ineger, and node, which may be any sring of leers and digis saring wih a leer or may be a boundary symbol ( # ). For example, $ l(en,ng) 2(HAVE,BE) $. is a srucural descripion which is he srucural analysis $ l(en,ng) 2(HAVE,BE) $ followed by a his srucural analysis is a lis of he erms $ ) l(en,ng) J 2(~V-W@ > $ ; he firs and las of hese erms are skips, each of which is he symbol& while he second and hird are he choices (ENJNG) "clis" is pronounced see-lis, and is a noun of he same ype as "herd". 4
and (HAVE,BE) p receded by he inegers and 2; each choice consiss of a ( followed by a clis of srucural analyses EN,NG and HAVE,BE followed by a ) j each srucural analysis here is a lis of exacly one erm, which is a srucure wihou any preceding ineger; each of hese srucures is an elemen wihou any of he opional iems, and each elemen is a node. The above descripion has no in any way explained he meaning of hese iems; i has simply defined how o wrie hem., The meaning of srucural descripion and conexual feaure descripion can be bes explained in erms of analyzabiliy and analysis, since heir purpose is precisely-o es rees for analyzabiliy and o provide analyses of rees. Alhough a srucural descripion conains a srucural analysis e and a conexual feaure descripion conains a srucure, he recursiveness of heir definiions makes hem very similar. The difference sems from he fac ha when ransformaions are being applied he posiion of he op node of he curren ree is known, while during lexical inserion only he erminal node a which inserion is being aemped is known. For his reason, he conexual feaure mus specify he label of a node somewhere above he inserion node which can serve as ree op. n he following discussion, whenever a srucural descripion is referred o, we will mean eiher a srucural descripion or a conexual feaure descripion. Analyzabiliy We will define analyzabiliy in wo phases; firs we will consider a srucural analysis or srucure wihou any associaed resricion, and hen we will consider how he presence of a resricion modifies he 5
definiion. f a srucural descripion is simply a lis of elemens, analyzabiliy is similar o Chomsky's noion of "proper analysis" [l]. A ree is analyzable as a srucural descripion of his form if a one-o-one mach of cerain ree nodes wih all of he srucural descripion elemens can be found such ha:. Each erminal node in he ree is, or is dominaed by, exacly one node in he mach. 2. ef-o-righ order of elemens corresponds o lef-o-righ order of maching ree nodes. 3a. For each elemen which is a node, he label of he maching ree node is he same as he node. 3b. For each elemen which is a, he maching ree node is he node a which lexicon inserion is currenly being aemped. (Noe ha a * will hus mach any one ree node, regardless of is a label.) A complex symbol following an elemen requires ha a corresponding complex symbol be aached o he maching ree node. "Corresponding" has a differen meaning for lexicon inserion han for ransformaions; in he case of lexicon inserion he es is compaibiliy (roughly, no conflicing feaure specificaions; see [4] for a precise,definiion), while for ransformaions he es is inclusion (ha is, he complex symbol in he ree conains every feaure specificaion of he one in he srucural descripion). A skip (he $ symbol) maches no a single node, bu any sring of adjacen erminal nodes. may mach a sring of zero nodes, in which case i is said o be null. The "rangk'af a skip is defined in 6
i f! erms of he elemens on eiher side; i is he se of ree nodes which dominae (or equal) he nodes maching he skip and do no dominae he nodes mached by hese elemens. n oher words, he range of a skip is precisely hose ree nodes which would have o be deleed if he skip were no presen in order o have he analysis of he ree as he srucural descripion be he same as before. The maching of a choice is somewha more complex. The procedure depends on wheher he clis wihin he choice has only one srucural analysis, or more i is regarded as i is analyszable han one. f here is only one srucural analysis, opional; ha is, he ree is analyzable eiher if as a similar srucural descripion wihou he parenheses of he choice, or if i is analyzable as a similar srucural descripion wihou any of he choice being presen. f here is more han one srucural analysis in he clis, a ree is analyzable if i is analyzable as a similar srucural descripion wih some one of he srucural analyses in place of he choice. (Noe ha he only requiremen here is ha a leas one srucural analysis will work; if several differen ones could be analyzably subsiued; i merely means ha he ree is analyzable as his srucural descripion in several ways.) A srucural analysis wihin angle brackes following an elemen represens a "subanalysis". The analysis of he whole ree as he srucural descripion is unchanged, bu in order ha he ree be analyzable, here is a furher requiremen on analyzabiliy of he subree headed by he node mached o he head elemen of he anglebrackeed srucural analysis. The exac requiremen depends on he presence of he opional modifiers and /. f only a / is 7
presen, his sub-ree mus be analyzable in he usual sense, wih he minor excepion ha he op node of he subree is no allowed o mach any elemen in he srucural analysis. f neiher modifier is presen, he subree mus be analyzable in he above sense, wih he furher resricion ha any elemen in he srucural analysis mus mach a ree node which is immediaely dominaed by he op node of he subree. n he case of conexual feaures, his corresponds o Chomsky's noion of sric local subcaegorizaion [2]. f a modifier is presen, i means ha he sub-ree mus no be analyzable in he sense defined above. negers do no direcly ener ino he analysis process. They are used o permi reference o ree nodes in a resricion or a srucural change. An ineger preceding a srucure refers o he ree node which maches he elemen heading ha srucure. An ineger preceding a choice is handled exacly as if i had been wrien a he beginning of every srucural analysis in he clis of he choice. Noe ha complex symbols are no numbered direcly; he ineger aaches o he ree node and will refer o he complex symbol associaed wih ha node in any conex which requires a complex symbol. Resricions f a srucural descripion or conexual feaure descripion has an associaed resricion, analysis proceeds exacly as above, excep ha he analysis of he ree mus also mee he resricion in order for he ree o be analyzable. The BNF forma for resricion is:
resricion ::= booleancombinaion[ condiion ] condiion ::= unary condiion or binary condiion unary condiion ::= unary relaion ineger binary condiion ::= ineger binary ree relaion node designaor or ineger binary complex relaion complex symbol designaor node designaor ::= ineger or node complex symbol designaor ::= complex symbol or ineger where booleancombinaion[ condiion ] means any Boolean combinaion of condiions which can be expressed using he connecives, &, \ (no, and, or) and parenheses. The condiions now in he sysem are: (unary condiions) he mach mus be o a erminal/ree node; or null (in he case of an opion); also a special condiion useful where more han one analysis is o be found, e.g. ha he mach in he curren analysis be o a differen ree node han in any of he previous successful analyses. (binary ree condiions) corresponding complex symbol); equaliy of rees (including ideniy of dominance wihou searching below a senence. symbol; unresriced dominance; dominaion by a specified node. (binary complex condiions) inclusion of complex symbols; nondisincness of complex symbols; and compaibiliy of complex symbols (see [4). The resricion on a srucural descripion is esed whenever a new mach is found for a srucure wih a corresponding ineger. f he resricion fails, he srucure does no mach. n a condiional srucural change, a resricion may be used o selec one of wo possible srucural changes (see below). s 9
j is Analysis Algorihm n his secion we discuss he algorihm used o find a paricular analysis of a ree as a srucural descripion. o do wih he quesion of analyzabiliy; This algorihm has nohing i merely decides he order in which several possible analyses are aken if a senence ree can be analyzed in more han one way as a paricular srucural descripion. This is paricularly imporan if he ransformaion specifies ha only one analysis is o be found. Analysis commences wih a ree marker poining o he op node of he ree and a srucural descripion marker poining o he firs iem in he --. srucural descripion. The procedure depends on he naure of his iem. negers and skips are skipped bu remembered. For an elemen (i.e., he beginning of a srucure), a mach is aemped. A * will mach any ree node, a node will mach a node wih he same label, and a will mach he curren lexical inserion node. f here is no a mach, he ree marker is moved o poin o he lefmos daugher of he curren node, and maching is aemped again. f no mach is found of a erminal node and no skip preceded he curren elemen, he backup procedure is enered (see below). f a skip preceded, he ree marker is moved o he op of he ree branch jus righ of he curren branch,. and maching is aemped again; in his case, he backup procedure is enered only if no mach can be found for he righmos erminal node of he ree. f a mach is found and a complex symbol follows he elemen, i will be compared o he complex symbol aached o he maching ree node for compaibiliy (in a conexual feaure descripion) or inclusion 0
i &.. (in a srucural descripion). condiions involving his ineger are checked. condiion, mached. f an ineger precedes he elemen, any n he case of a binary no checking is performed unil boh inegers have been Failure of any of hese ess causes analysis o proceed as if he node had no mached he elemen. f he srucural descripion marker is poining o a choice insead of an elemen, he procedure o be followed depends on wheher he clis of he choice conains only one srucural analysis (an opion), or more han one (a rue choice). For an opion, he ( of he choice is ignored; opions affec only he backup procedure. For a rue choice, a more complicaed procedure is necessary. Firs, a lis is made of all elemens which could possibly be firs in he choice, in lef-origh order. For example, if he choice were (A, (B)(W), k E, % (W)) 9 his lis would be A - B - C - D - E - F - G e The elemen-maching procedure is hen followed as above, bu a each ree node all of he possible elemens are esed for maches and for saisfacory complex Nsymbols a and u inegers. r a l l y, only hose elemens which are preceded by skips are esed afer a erminal-node failure. When a saisfacory mach has been found beween a ree node and some elemen, analysis proceeds along he associaed srucural analysis of he choice, a. he end of which i coninues f a srucural analysis following he choice. wihin angle brackes follows an elemen ha has been saisfacorily mached, a record is made of relevan informaion abou he curren saus of hings, and analysis commences again, using he angle-brackeed srucural analysis and he subree headed by he node mached o he elemen. f no / preceded, he ree
marker is only allowed o poin o immediae daughers of he op node during his analysis, insead of looking all he way down o erminal nodes. f a preceded and he subree is no analyzable, or if no preceded and he subree is analyzable, analysis coninues following he angle-brackeed srucural analysis; oherwise, analysis proceeds as if he head elemen had no mached is ree node. When a srucure has been successfully mached, he ree marker is moved o poin o he op node of he ree branch immediaely o he righ of he ree node maching he head elemen, and analysis proceeds. The ree is analyzable as he srucural descripion if he righmos elemen no wihin angle brackes successfully maches a ree node on he righmos branch of he ree, or if he righmos such elemen has been successfully mached in any way and a skip follows i. The backup procedure is enered when no ree node can be found which successfully maches he curren elemen or choice. moves he srucural descripion marker backward o he lef unil i encouners a previously-mached elemen (in which case i preends ha his elemen did no mach is ree node and sars forward again), or he ( of a one-srucural analysis choice (in which case i hops o he ) of he choice and sars forward), or he lefhand end of he srucural descripion (in which case he ree is no analyzable as he srucural descripion). For cerain ransformaions, all possible analyses of he ree are required insead of jus one. n his case, afer each analysis is found, he backup procedure is enered o find he nex one, unil i 2
finally claims unanalyzabiliy. Srucural Change Because of he close relaionship beween he srucural descripion.. and srucural change of a ransformaion, any comparison of our sysem wih ohers requires ha he whole concep of ransformaion be considered a once. For ha reason, we now give a descripion of he srucural change process. srucural change is: srucural change change insrucion condiional change The BNF descripion of he form of a..=.. clis[ change insrucion ] : : = change or condiional change..=.. F ( resricion > THEN ( srucural change ) op[ ESE ( srucural change > f e change : : = unary operaor ineger or ree designaor binary ree operaor ineger or complex symbol designaorybinar or ineger complex symbol designaor ernary complex operaor ineger n e g e r ree designaor ::= ( ree ) or ineger or *node complex symbol designaor : :-- complex symbol or ineger The operaors are given by a lis in he BNF form and are discussed below. f he curren senence ree is analyzable as a srucural descripion and he ransformaion is o be performed, each change insrucion in he clis is performed in he order of occurrence in he clis. Tree nodes have been mached o inegers by he analysis 3
, ; :. ; e process; is ineger (s). a change modifies he ree srucure a he nodes mached o The change operaors currenly in he sysem are:.. (unary operaors) erasure of he node, all nodes dominaed by i, and all non-branching nodes dominaing i, (binary ree operaors) adjuncion, lef and righ siser, daugher, and aun and subsiuion, wih or wihou erasure of he original occurrence of he copied node, and opionally wih special reamen of he non-branching nodes which dominae (as in [p]). (binary complex operaors) erasure of, merging of, or erasure of --. all bu, specified feaure specificaions in he complex symbol associaed wih he node, (ernary complex operaors) one node's complex symbol o anoher's merging of specified feaures from A condiional change causes he srucural change following THEN o be performed if he resricion is me; oherwise he srucural change following ESE is performed, if here is one. The change operaors discussed above may be broken down ino four ypes: erasure, copying, moving and complex symbol manipulaion. Permuaions are no given direcly, a a ime. PASSVE > since only one move can be made The only ransformaion of his ype ha we have seen is for which we require hree changes (copy, move, erase) o inerchange he subjec and objec. The srucural change operaors include all of hose of he MTBE grammar [ll] as well as hose of he BM core grammar [P. The addiion of "Chomsky-adjuncion" is planned. 4
f i.- f c! Comparisons wih oher noaions n a ransformaion, our srucural analysis plays essenially he same role as he "srucural descripion" and "srucural analysis" which were firs used by Chomsky. As an example, here is a ransformaion from Rosenbaum and ochak [p]: 60. WHPD2 WH pronoun Deleion 2 OB X WH + NDEF + (ever) ' 2 3 4 --- --- > 2 fl 4 n our sysem his would be wrien TRANS--'60 WHPR2 "WH PRONOUN DEETON 2" OB AACC. SD $ WH NDEF (EVER) N +PRO +SG) $. SC ERASE. The firs line gives he ransformaion idenificaion and he condiions of applicabiliy. n his case he ransformaion number and name are followed by a commen and by parameers specifying ha he ransformaion is obligaory (OB), is in group, and ha i is o be applied by firs finding all possible analyses and hen performing he changes for each of hem (AACC). A full discussion of he possible parameers is given in [6]. The second line is our srucural descripion. As can be seen, he deails of he represenaion are differen, he major feaures are he same. We chose he $ symbol raher han X, Y, Z o represen variables because hese leers are possible labels for nodes. This decision reinforces he idea ha a variable need no be a consiuen. The sandard use of parenheses for opions is carried over ino our noaion; * in addiion, we reflec he use of curly brackes for a choice 5
i f by allowing a clis of srucural analyses wihin parenheses. noaion for complex symbols resembles sandard noaion excep for he use of verical bars in place of square brackes; discussion of complex symbols in he sysem. is in our use of numbers, Our see [4] for a complee The mos significan change since we allow only consiuens o be numbered, and do no require numbering of iems which are no referred o in eiher he srucural change or he resricion. This is a resul of our reamen of ransformaions as changes of posiion of single consiuens raher han rearrangemens of he whole ree. aken in he MTRE grammars [ll]; -=. symbol operaions. n his we follow he approach we have exended he approach o complex Gross [7] and onde and Schoene [8] have also developed noaions for ransformaions, in boh cases for use wih grammar esers. Boh noaions differ from ours in form and have less power in he srucural descripion. For example, Gross does no include complex symbols; neiher allows any equivalen of ; immediae dominance be expressed as a resricion. onde and Schoene require ha However, boh sysems conain more powerful noaions han ours for srucural change. Fuure direcions The analysis algorihm was designed o correspond o he linguisic heory based on Aspecs [2]. changes in he heory; Since ha ime here have been radical he change of paricular imporance for analysis is he srong noion of general consrains on ransformaions, following from he work of Ross [lo]. Thus, if he sysem is o be exended and kep curren wih he heory, he firs changes will need o be in devisi if noaions and algorihms for he implemenaion of,\ 6
r j ii general condiions on he applicabiliy of ransformaions. ----- 7
-- --- -- - - i- REFERENCES [ l] Chomsky, N. and Miller, G. A. nroducion o he formal analysis of naural languages. in ue, R. D., Bush, R. R., > and Galaner, E. (Ed&), Handbook of Mahemaical Psychology, Volume Wiley (963). [ 23 Chomsky, N. Aspecs of he Theory of Synax. M--T. Press, Cambridge, Massachuses (965). [ 33 Friedman, J. A compuer sysem for ransformaional grammar. ~~-84, M-2, Compuer Science Deparmen, Sanford Universiy (January, 968). [ 4 Friedman, J., and Bred, T. H. exical inserion in ransformaional grammar. CS-03, AF-25, Compuer Science Deparmen, Sanford Universiy (June, 968). [ 5 Friedman, J., and Doran, R. W. A formal synax for ransformaional grammar. CS-95, ~~-24, Compuer Science Deparmen, Sanford Universiy (March, 968). [ 6 Friedman, J., and Pollack, B. W. A conrol language for ransformaional grammar. Compuer Science Deparmen, Sanford Universiy (Sepember, 968). [7 Gross. N. A compuer program for esing grammars on-line. mimeographed (968). [ 8 onde, D. ;., and Schoene, W. J. TGT: ransformaional grammar eser. Sysems Developmen Corporaion (967). [ 9 Rosenbaum, R., and ochak, K. The BM core grammar of English. n ieberman, D. (Ed.) Specificaion and uilizaion of a ransformaional grammar. ~~~~~-66-270 (966). [lo] Ross, J. R. (967). Consrains on variables in synax. M--T. Thesis [ll] Zwicky, A. M., Friedman, J., Hall, B. C., and Walker, D. E. The MTRE synacic analysis procedure for ransformaional grammars. Fall Join Compuer Conference 27 (965)., 37-326. 8